Theory Wiki - User contributions [en]

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T22:16:44Z

Timothy Nokes: /* Study 2 (Laboratory) */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008; Analysis on-going
|}
 
====Study 2 (Laboratory)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || June, 2008
|-
| '''Study End Date''' || August, 2008
|-
| '''LearnLab Site''' || University of Pittsburgh
|-
| '''Number of Students''' || anticipated 60
|-
| '''Total Participant Hours''' || anticipated 240
|-
| '''Data Shop''' || Expected Fall, 2008
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through [[self-explanation]] of how [[worked examples]] are related to the principles. The second path is learning a schema through [[analogical comparison]] of two examples and then relating that schema to the principle. These hypotheses are tested in both a [[in vivo experiment]] in the [[Physics]] LearnLab as well as laboratory studies.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables [[robust learning]] including [[long-term retention]], [[transfer]], and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
All three groups receive principle booklets providing textual descriptions of physics principles (rules) for rotational kinematics (e.g., angular velocity, angular displacement, etc.), pairs of [[worked examples]], as well as isomorphic problem solving tasks. The primary manipulation is the activity engaged in during learning.
*Control - Reading
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step. Next, they solve two isomorphic problems^.
*Self-Explain
**Participants first read through the principle booklets. Next they are given the first of the [[worked examples]] and are instructed to self-explain each solution step. After self-explaining they read through explanations for each step (same as control). After completing the first example they perform the same task for the second example. Next they solve one isomorphic problem^.
*Analogy
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step (same as control). Then they are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, they solve one isomorphic problem^.

^The control group solves two problem isomorphs whereas the self-explanation and analogy groups only solve one to control for time on task.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Self-explanation group: Content of explanations
*Analogy group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving
***Solving a problem requiring the application of the same principles, concepts, and equations but asks the student to find a different sought value (almost identical to learning problem)
***Solving a problem requiring the application of the same principles, concepts, and equations but includes additional IRRELEVANT information in the problem statement. To solve this problem correctly a student must have deeper understanding of the meaning of the variables. One cannot rely on superficial surface strategies.
*[[Transfer]]
**Multiple choice
***A novel test that assesses qualitative understanding of the concepts. Students are asked to reason about concepts and principles.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Homework and Final exam performance

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance

===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**[[Self-explanation]] can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**[[Analogical comparison]] can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Problem solving: different sought: Analogy = Self-explanation = Control; accuracy
**Problem solving: irrelevant info: Analogy = Self-explanation > Control; accuracy
**Multiple choice: Analogy = Self-explanation > Control; more likely to get understand the concepts facilitating qualitative reasoning.

*Andes performance: Analogy = Self-explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T22:16:09Z

Timothy Nokes: /* Study 1 (In Vivo) */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008; Analysis on-going
|}
 
====Study 2 (Laboratory)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || June, 2008
|-
| '''Study End Date''' || August, 2008
|-
| '''LearnLab Site''' || University of Pittsburgh
|-
| '''Number of Students''' || anticipated: 60
|-
| '''Total Participant Hours''' || anticipated 240
|-
| '''Data Shop''' || Expected Fall, 2008
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through [[self-explanation]] of how [[worked examples]] are related to the principles. The second path is learning a schema through [[analogical comparison]] of two examples and then relating that schema to the principle. These hypotheses are tested in both a [[in vivo experiment]] in the [[Physics]] LearnLab as well as laboratory studies.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables [[robust learning]] including [[long-term retention]], [[transfer]], and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
All three groups receive principle booklets providing textual descriptions of physics principles (rules) for rotational kinematics (e.g., angular velocity, angular displacement, etc.), pairs of [[worked examples]], as well as isomorphic problem solving tasks. The primary manipulation is the activity engaged in during learning.
*Control - Reading
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step. Next, they solve two isomorphic problems^.
*Self-Explain
**Participants first read through the principle booklets. Next they are given the first of the [[worked examples]] and are instructed to self-explain each solution step. After self-explaining they read through explanations for each step (same as control). After completing the first example they perform the same task for the second example. Next they solve one isomorphic problem^.
*Analogy
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step (same as control). Then they are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, they solve one isomorphic problem^.

^The control group solves two problem isomorphs whereas the self-explanation and analogy groups only solve one to control for time on task.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Self-explanation group: Content of explanations
*Analogy group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving
***Solving a problem requiring the application of the same principles, concepts, and equations but asks the student to find a different sought value (almost identical to learning problem)
***Solving a problem requiring the application of the same principles, concepts, and equations but includes additional IRRELEVANT information in the problem statement. To solve this problem correctly a student must have deeper understanding of the meaning of the variables. One cannot rely on superficial surface strategies.
*[[Transfer]]
**Multiple choice
***A novel test that assesses qualitative understanding of the concepts. Students are asked to reason about concepts and principles.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Homework and Final exam performance

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance

===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**[[Self-explanation]] can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**[[Analogical comparison]] can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Problem solving: different sought: Analogy = Self-explanation = Control; accuracy
**Problem solving: irrelevant info: Analogy = Self-explanation > Control; accuracy
**Multiple choice: Analogy = Self-explanation > Control; more likely to get understand the concepts facilitating qualitative reasoning.

*Andes performance: Analogy = Self-explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T22:13:18Z

Timothy Nokes: /* Expected Findings */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008; Analysis on-going
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through [[self-explanation]] of how [[worked examples]] are related to the principles. The second path is learning a schema through [[analogical comparison]] of two examples and then relating that schema to the principle. These hypotheses are tested in both a [[in vivo experiment]] in the [[Physics]] LearnLab as well as laboratory studies.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables [[robust learning]] including [[long-term retention]], [[transfer]], and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
All three groups receive principle booklets providing textual descriptions of physics principles (rules) for rotational kinematics (e.g., angular velocity, angular displacement, etc.), pairs of [[worked examples]], as well as isomorphic problem solving tasks. The primary manipulation is the activity engaged in during learning.
*Control - Reading
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step. Next, they solve two isomorphic problems^.
*Self-Explain
**Participants first read through the principle booklets. Next they are given the first of the [[worked examples]] and are instructed to self-explain each solution step. After self-explaining they read through explanations for each step (same as control). After completing the first example they perform the same task for the second example. Next they solve one isomorphic problem^.
*Analogy
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step (same as control). Then they are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, they solve one isomorphic problem^.

^The control group solves two problem isomorphs whereas the self-explanation and analogy groups only solve one to control for time on task.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Self-explanation group: Content of explanations
*Analogy group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving
***Solving a problem requiring the application of the same principles, concepts, and equations but asks the student to find a different sought value (almost identical to learning problem)
***Solving a problem requiring the application of the same principles, concepts, and equations but includes additional IRRELEVANT information in the problem statement. To solve this problem correctly a student must have deeper understanding of the meaning of the variables. One cannot rely on superficial surface strategies.
*[[Transfer]]
**Multiple choice
***A novel test that assesses qualitative understanding of the concepts. Students are asked to reason about concepts and principles.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Homework and Final exam performance

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance

===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**[[Self-explanation]] can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**[[Analogical comparison]] can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Problem solving: different sought: Analogy = Self-explanation = Control; accuracy
**Problem solving: irrelevant info: Analogy = Self-explanation > Control; accuracy
**Multiple choice: Analogy = Self-explanation > Control; more likely to get understand the concepts facilitating qualitative reasoning.

*Andes performance: Analogy = Self-explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T22:09:30Z

Timothy Nokes: /* Dependent Variables */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008; Analysis on-going
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through [[self-explanation]] of how [[worked examples]] are related to the principles. The second path is learning a schema through [[analogical comparison]] of two examples and then relating that schema to the principle. These hypotheses are tested in both a [[in vivo experiment]] in the [[Physics]] LearnLab as well as laboratory studies.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables [[robust learning]] including [[long-term retention]], [[transfer]], and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
All three groups receive principle booklets providing textual descriptions of physics principles (rules) for rotational kinematics (e.g., angular velocity, angular displacement, etc.), pairs of [[worked examples]], as well as isomorphic problem solving tasks. The primary manipulation is the activity engaged in during learning.
*Control - Reading
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step. Next, they solve two isomorphic problems^.
*Self-Explain
**Participants first read through the principle booklets. Next they are given the first of the [[worked examples]] and are instructed to self-explain each solution step. After self-explaining they read through explanations for each step (same as control). After completing the first example they perform the same task for the second example. Next they solve one isomorphic problem^.
*Analogy
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step (same as control). Then they are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, they solve one isomorphic problem^.

^The control group solves two problem isomorphs whereas the self-explanation and analogy groups only solve one to control for time on task.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Self-explanation group: Content of explanations
*Analogy group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving
***Solving a problem requiring the application of the same principles, concepts, and equations but asks the student to find a different sought value (almost identical to learning problem)
***Solving a problem requiring the application of the same principles, concepts, and equations but includes additional IRRELEVANT information in the problem statement. To solve this problem correctly a student must have deeper understanding of the meaning of the variables. One cannot rely on superficial surface strategies.
*[[Transfer]]
**Multiple choice
***A novel test that assesses qualitative understanding of the concepts. Students are asked to reason about concepts and principles.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Homework and Final exam performance

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance

===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**[[Self-explanation]] can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**[[Analogical comparison]] can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T22:08:25Z

Timothy Nokes: /* Hypotheses */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008; Analysis on-going
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through [[self-explanation]] of how [[worked examples]] are related to the principles. The second path is learning a schema through [[analogical comparison]] of two examples and then relating that schema to the principle. These hypotheses are tested in both a [[in vivo experiment]] in the [[Physics]] LearnLab as well as laboratory studies.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables [[robust learning]] including [[long-term retention]], [[transfer]], and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
All three groups receive principle booklets providing textual descriptions of physics principles (rules) for rotational kinematics (e.g., angular velocity, angular displacement, etc.), pairs of [[worked examples]], as well as isomorphic problem solving tasks. The primary manipulation is the activity engaged in during learning.
*Control - Reading
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step. Next, they solve two isomorphic problems^.
*Self-Explain
**Participants first read through the principle booklets. Next they are given the first of the [[worked examples]] and are instructed to self-explain each solution step. After self-explaining they read through explanations for each step (same as control). After completing the first example they perform the same task for the second example. Next they solve one isomorphic problem^.
*Analogy
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step (same as control). Then they are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, they solve one isomorphic problem^.

^The control group solves two problem isomorphs whereas the self-explanation and analogy groups only solve one to control for time on task.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Self-explanation group: Content of explanations
*Analogy group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving
***Solving a problem requiring the application of the same principles, concepts, and equations but asks the student to find a different sought value (almost identical to learning problem)
***Solving a problem requiring the application of the same principles, concepts, and equations but includes additional IRRELEVANT information in the problem statement. To solve this problem correctly a student must have deeper understanding of the meaning of the variables. One cannot rely on superficial surface strategies.
*[[Transfer]]
**Multiple choice
***A novel test that assesses qualitative understanding of the concepts. Students are asked to reason about concepts and principles.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance

===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**[[Self-explanation]] can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**[[Analogical comparison]] can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T22:08:16Z

Timothy Nokes: /* Hypotheses */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008; Analysis on-going
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through [[self-explanation]] of how [[worked examples]] are related to the principles. The second path is learning a schema through [[analogical comparison]] of two examples and then relating that schema to the principle. These hypotheses are tested in both a [[in vivo experiment]] in the [[Physics]] LearnLab as well as laboratory studies.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables [[robust learning]] including [[long-term retention]], [[transfer]], and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
All three groups receive principle booklets providing textual descriptions of physics principles (rules) for rotational kinematics (e.g., angular velocity, angular displacement, etc.), pairs of [[worked examples]], as well as isomorphic problem solving tasks. The primary manipulation is the activity engaged in during learning.
*Control - Reading
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step. Next, they solve two isomorphic problems^.
*Self-Explain
**Participants first read through the principle booklets. Next they are given the first of the [[worked examples]] and are instructed to self-explain each solution step. After self-explaining they read through explanations for each step (same as control). After completing the first example they perform the same task for the second example. Next they solve one isomorphic problem^.
*Analogy
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step (same as control). Then they are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, they solve one isomorphic problem^.

^The control group solves two problem isomorphs whereas the self-explanation and analogy groups only solve one to control for time on task.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Self-explanation group: Content of explanations
*Analogy group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving
***Solving a problem requiring the application of the same principles, concepts, and equations but asks the student to find a different sought value (almost identical to learning problem)
***Solving a problem requiring the application of the same principles, concepts, and equations but includes additional IRRELEVANT information in the problem statement. To solve this problem correctly a student must have deeper understanding of the meaning of the variables. One cannot rely on superficial surface strategies.
*[[Transfer]]
**Multiple choice
***A novel test that assesses qualitative understanding of the concepts. Students are asked to reason about concepts and principles.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance

===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**[[Self-explaination]] can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**[[Analogical comparison]] can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T22:08:00Z

Timothy Nokes: /* Hypotheses */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008; Analysis on-going
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through [[self-explanation]] of how [[worked examples]] are related to the principles. The second path is learning a schema through [[analogical comparison]] of two examples and then relating that schema to the principle. These hypotheses are tested in both a [[in vivo experiment]] in the [[Physics]] LearnLab as well as laboratory studies.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables [[robust learning]] including [[long-term retention]], [[transfer]], and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
All three groups receive principle booklets providing textual descriptions of physics principles (rules) for rotational kinematics (e.g., angular velocity, angular displacement, etc.), pairs of [[worked examples]], as well as isomorphic problem solving tasks. The primary manipulation is the activity engaged in during learning.
*Control - Reading
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step. Next, they solve two isomorphic problems^.
*Self-Explain
**Participants first read through the principle booklets. Next they are given the first of the [[worked examples]] and are instructed to self-explain each solution step. After self-explaining they read through explanations for each step (same as control). After completing the first example they perform the same task for the second example. Next they solve one isomorphic problem^.
*Analogy
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step (same as control). Then they are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, they solve one isomorphic problem^.

^The control group solves two problem isomorphs whereas the self-explanation and analogy groups only solve one to control for time on task.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Self-explanation group: Content of explanations
*Analogy group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving
***Solving a problem requiring the application of the same principles, concepts, and equations but asks the student to find a different sought value (almost identical to learning problem)
***Solving a problem requiring the application of the same principles, concepts, and equations but includes additional IRRELEVANT information in the problem statement. To solve this problem correctly a student must have deeper understanding of the meaning of the variables. One cannot rely on superficial surface strategies.
*[[Transfer]]
**Multiple choice
***A novel test that assesses qualitative understanding of the concepts. Students are asked to reason about concepts and principles.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance

===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**[[Self-explaining]] can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**[[Analogical comparison]] can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T22:06:18Z

Timothy Nokes: /* Dependent Variables */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008; Analysis on-going
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through [[self-explanation]] of how [[worked examples]] are related to the principles. The second path is learning a schema through [[analogical comparison]] of two examples and then relating that schema to the principle. These hypotheses are tested in both a [[in vivo experiment]] in the [[Physics]] LearnLab as well as laboratory studies.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables [[robust learning]] including [[long-term retention]], [[transfer]], and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
All three groups receive principle booklets providing textual descriptions of physics principles (rules) for rotational kinematics (e.g., angular velocity, angular displacement, etc.), pairs of [[worked examples]], as well as isomorphic problem solving tasks. The primary manipulation is the activity engaged in during learning.
*Control - Reading
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step. Next, they solve two isomorphic problems^.
*Self-Explain
**Participants first read through the principle booklets. Next they are given the first of the [[worked examples]] and are instructed to self-explain each solution step. After self-explaining they read through explanations for each step (same as control). After completing the first example they perform the same task for the second example. Next they solve one isomorphic problem^.
*Analogy
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step (same as control). Then they are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, they solve one isomorphic problem^.

^The control group solves two problem isomorphs whereas the self-explanation and analogy groups only solve one to control for time on task.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Self-explanation group: Content of explanations
*Analogy group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving
***Solving a problem requiring the application of the same principles, concepts, and equations but asks the student to find a different sought value (almost identical to learning problem)
***Solving a problem requiring the application of the same principles, concepts, and equations but includes additional IRRELEVANT information in the problem statement. To solve this problem correctly a student must have deeper understanding of the meaning of the variables. One cannot rely on superficial surface strategies.
*[[Transfer]]
**Multiple choice
***A novel test that assesses qualitative understanding of the concepts. Students are asked to reason about concepts and principles.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance

===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T21:59:50Z

Timothy Nokes: /* Independent Variables */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008; Analysis on-going
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through [[self-explanation]] of how [[worked examples]] are related to the principles. The second path is learning a schema through [[analogical comparison]] of two examples and then relating that schema to the principle. These hypotheses are tested in both a [[in vivo experiment]] in the [[Physics]] LearnLab as well as laboratory studies.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables [[robust learning]] including [[long-term retention]], [[transfer]], and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
All three groups receive principle booklets providing textual descriptions of physics principles (rules) for rotational kinematics (e.g., angular velocity, angular displacement, etc.), pairs of [[worked examples]], as well as isomorphic problem solving tasks. The primary manipulation is the activity engaged in during learning.
*Control - Reading
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step. Next, they solve two isomorphic problems^.
*Self-Explain
**Participants first read through the principle booklets. Next they are given the first of the [[worked examples]] and are instructed to self-explain each solution step. After self-explaining they read through explanations for each step (same as control). After completing the first example they perform the same task for the second example. Next they solve one isomorphic problem^.
*Analogy
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step (same as control). Then they are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, they solve one isomorphic problem^.

^The control group solves two problem isomorphs whereas the self-explanation and analogy groups only solve one to control for time on task.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance
===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T21:59:17Z

Timothy Nokes: /* Independent Variables */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008; Analysis on-going
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through [[self-explanation]] of how [[worked examples]] are related to the principles. The second path is learning a schema through [[analogical comparison]] of two examples and then relating that schema to the principle. These hypotheses are tested in both a [[in vivo experiment]] in the [[Physics]] LearnLab as well as laboratory studies.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables [[robust learning]] including [[long-term retention]], [[transfer]], and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
All three groups receive principle booklets providing textual descriptions of physics principles (rules) for rotational kinematics (e.g., angular velocity, angular displacement, etc.), pairs of [[worked examples]], as well as isomorphic problem solving tasks. The primary manipulation is the activity engaged in during learning.
*Control - Reading
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step. Next, they solve two isomorphic problems^.
*Self-Explain
**Participants first read through the principle booklets. Next they are given the first [[worked example[s]] and are instructed to self-explain each solution step. After self-explaining they read through explanations for each step (same as control). After completing the first example they perform the same task for the second example. Next they solve one isomorphic problem^.
*Analogy
**Participants first read through the principle booklets. Next they read through the two [[worked examples]] one at a time. Each example includes an explicit explanation/justification for each step (same as control). Then they are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, they solve one isomorphic problem^.

^The control group solves two problem isomorphs whereas the self-explanation and analogy groups only solve one to control for time on task.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance
===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T21:57:56Z

Timothy Nokes: /* Independent Variables */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008; Analysis on-going
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through [[self-explanation]] of how [[worked examples]] are related to the principles. The second path is learning a schema through [[analogical comparison]] of two examples and then relating that schema to the principle. These hypotheses are tested in both a [[in vivo experiment]] in the [[Physics]] LearnLab as well as laboratory studies.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables [[robust learning]] including [[long-term retention]], [[transfer]], and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
All three groups receive principle booklets providing textual descriptions of physics principles (rules) for rotational kinematics (e.g., angular velocity, angular displacement, etc.), pairs of [[worked examples]], as well as isomorphic problem solving tasks. The primary manipulation is the activity engaged in during learning.
*Control - Reading
**Participants first read through the principle booklets. Next they read through the two [[worked example]]s one at a time. Each example includes an explicit explanation/justification for each step. Next, they solve two isomorphic problems^.
*Self-Explain
**Participants first read through the principle booklets. Next they are given the first [[worked example]] and are instructed to self-explain each solution step. After self-explaining they read through explanations for each step (same as control). After completing the first example they perform the same task for the second example. Next they solve one isomorphic problem^.
*Analogy
**Participants first read through the principle booklets. Next they read through the two [[worked example]]s one at a time. Each example includes an explicit explanation/justification for each step (same as control). Then they are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, they solve one isomorphic problem^.

^The control group solves two problem isomorphs whereas the self-explanation and analogy groups only solve one to control for time on task.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance
===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T21:35:45Z

Timothy Nokes: /* Research Question */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008; Analysis on-going
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through [[self-explanation]] of how [[worked examples]] are related to the principles. The second path is learning a schema through [[analogical comparison]] of two examples and then relating that schema to the principle. These hypotheses are tested in both a [[in vivo experiment]] in the [[Physics]] LearnLab as well as laboratory studies.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables [[robust learning]] including [[long-term retention]], [[transfer]], and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two [[worked examples]]. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two [[worked examples]] and are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance
===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T21:35:23Z

Timothy Nokes: /* Research Question */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008; Analysis on-going
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through [[self-explanation]] of how [[worked examples]] are related to the principles. The second path is learning a schema through [[analogical comparison]] of two examples and then relating that schema to the principle. These hypotheses are tested in both a [[in vivo experiment]] in the [[Physics]] LearnLab as well as laboratory studies.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables robust learning including [[long-term retention]], [[transfer]], and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two [[worked examples]]. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two [[worked examples]] and are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance
===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T21:32:01Z

Timothy Nokes: /* Abstract */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008; Analysis on-going
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through [[self-explanation]] of how [[worked examples]] are related to the principles. The second path is learning a schema through [[analogical comparison]] of two examples and then relating that schema to the principle. These hypotheses are tested in both a [[in vivo experiment]] in the [[Physics]] LearnLab as well as laboratory studies.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables the reliable retrieval and use of those concepts to solve novel problems and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two [[worked examples]]. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two [[worked examples]] and are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance
===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Coordinative Learning

2008-05-27T21:30:03Z

Timothy Nokes: /* Glossary */

= The PSLC Coordinative Learning cluster =

== Abstract ==
The studies in the Coordinative Learning cluster tend to focus on varying ''a)'' the types of information available to learning or ''b)'' the instructional methods that they employ. In particular, the studies focus on the impact of having learners coordinate two or more types. Given that the student has multiple [[sources]]/methods available, two factors that might impact learning are:

*What is the relationship between the content in the two sources or the content generated by the two methods? Our hypothesis is that the two sources or methods facilitate [[robust learning]] when a [[knowledge component]] is difficult to understand or absent in one and is present or easier to understand in the other.
*When and how does the student coordinate between the two sources or methods? Our hypothesis is that students should be encouraged to compare the two, perhaps by putting them close together in space or time.

At the micro-level, the overall hypothesis is that robust learning occurs when the [[learning event space]] has target paths whose [[sense making]] difficulties complement each other (as expressed in the first bullet above) and the students make path choices that take advantage of these [[complementary]] paths (as in the second bullet, above). This hypothesis is just a specialization of the [[Root_node|general PSLC hypothesis]] to this cluster.

The matrix below shows how studies in this cluster (pages for these studies can be found Descendants section below) either test or make use of various [[instructional method|instructional methods]] or treatments. When a study tests an instructional method a "v" is one shown in the appropriate cell to indicate that that method is '''varied''' in the study, that is, the [[robust learning]] gains of an experimental condition that receives this method are contrasted with those of an otherwise equivalent control condition that does not receive this method. In this case (when a "v" is present), the study tests the [[InstructionalPrinciples|instructional principle]] indicated in the column. When a cell contains a "b" it indicates that '''both''' the experimental and control conditions use this instructional method (or employ this instructional principle). In this case, the study is not a true experimental test of the principle.

 <center>[[Image:Cl.JPG]]</center>

== Glossary ==
[[:Category:Coordinative Learning|Coordinative Learning]] glossary.

*'''[[Analogical comparison]]'''
*'''[[Co-training]]'''
*'''[[Complementary]]'''
*'''[[Conceptual tasks]]'''
*'''[[Contiguity]]'''
*'''[[Coordination]]'''
*'''[[Ecological control group]]'''
*'''[[External representations]]'''
*'''[[Input sources ]]'''
*'''[[Instructional method]]'''
*'''[[Multimedia sources]]'''
*'''[[Procedural tasks]]'''
*'''[[Self-explanation]]'''
*'''[[Self-supervised learning]]'''
*'''[[Sources]]'''
*'''[[Strategies]]'''
*'''[[Unlabeled examples]]'''

== Research questions ==

When and how does coordinating multiple sources of information or lines of reasoning increase robust learning?

Two sub-groups of coordinative learning studies are exploring these more specific questions:

=== Visualizations and Multi-modal sources ===

When does adding visualizations or other multi-modal input enhance robust learning and how do we best support students in coordinating these sources?

=== Examples and Explanations ===

When and how should example study be combined and coordinated with problem solving to increase robust learning? When and how should explicit explanations be added or requested of students before, during, or after example study and problem solving practice?

== Independent variables ==

*Content of the sources (e.g., pictures, diagrams, written text, audio, animation) or the encouraged lines of reasoning (e.g., example study, self-explanation, conceptual task, procedural task) and combinations

*Instructional activities designed to engage students in [[coordination]] (e.g., conceptual vs. [[procedural]] exercises, contiguous presentation of sources, [[self-explanation]])

See [[:Category:Independent Variables]]

== Dependent variables ==
[[Normal post-test]] and measures of [[robust learning]].

== Hypotheses ==
When students are given sources/methods whose [[sense making]] difficulties are complementary and they are engaged in coordinating the sources/methods, then their learning will be more robust than it would otherwise be.

== Explanation ==

There are both [[sense making]] and [[foundational skill building]] explanations. From the sense making perspective, if the sources/methods yield complementary content and the student is engaged in coordinating them, then the student is more likely to successfully understand the instruction because if a student fails to understand one of the sources/methods, he can use the second to make sense of the first. From a foundational skill building perspective, attending to both sources/methods simultaneously associates [[features]] from both with the learned knowledge components, thus potentially increasing [[feature validity]] and hence [[robust learning]].

== Descendents ==

=== Visualizations and Multi-modal sources ===
*[[Contiguous Representations for Robust Learning (Aleven & Butcher)]]
**[[Static vs. Animated Visual Representations for Science Learning (Kaye, Small, Butcher, & Chi)]]
*[[Mapping Visual and Verbal Information: Integrated Hints in Geometry (Aleven & Butcher)]]
**[[Training Geometry Concepts with Visual and Verbal Sources (Burchfield, Aleven, & Butcher)]]
*[[Visual Representations in Science Learning | Visual Representations in Science Learning (Davenport, Klahr & Koedinger)]]
* Cotraining in language learning
**[[Co-training of Chinese characters| Co-training of Chinese characters (Liu, Perfetti, Dunlap, Zi, Mitchell)]]
**[[Co-training and pairing| The pairing effect in Chinese cotraining (Liu, Perfetti, Dunlap, Wu, Mitchell)]]
*[[Learning Chinese pronunciation from a “talking head”| Learning Chinese pronunciation from a “talking head” (Liu, Massaro, Dunlap, Wu, Chen,Chan, Perfetti)]] [Was in Refinement and Fluency]
*[[Visual Feature Focus in Geometry: Instructional Support for Visual Coordination During Learning (Butcher & Aleven)]]
*[[Learning About Emergence and Heat Transfer (Chi)]]

=== Examples and Explanations ===
*[[Booth | Improving skill at solving equations through better encoding of algebraic concepts (Booth, Siegler, Koedinger & Rittle-Johnson)]]
*[[McLaren_et_al_-_Studying_the_Learning_Effect_of_Personalization_and_Worked_Examples_in_the_Solving_of_Stoich_Problems | Studying the Learning Effect of Personalization and Worked Examples in the Solving of Stoichiometry Problems (McLaren, Koedinger & Yaron)]]
*[[Note-Taking_Technologies | Note-taking Project Page (Bauer & Koedinger)]]
**[[Note-Taking: Restriction and Selection]] (completed)
**[[Note-Taking: Coordination]] (planned)
*[[REAP_main | The REAP Project: Implicit and explicit instruction on word meanings (Juffs & Eskenazi)]]
*[[Help_Lite (Aleven, Roll)|Hints during tutored problem solving – the effect of fewer hint levels with greater conceptual content (Aleven & Roll)]]
*[[Handwriting Algebra Tutor]] (Anthony, Yang & Koedinger)
**[[Lab study proof-of-concept for handwriting vs typing input for learning algebra equation-solving]] (completed)
**[[Effect of adding simple worked examples to problem-solving in algebra learning]] (completed, analysis in progress)
**[[In vivo comparison of Cognitive Tutor Algebra using handwriting vs typing input]] (in progress)
*[[Bridging_Principles_and_Examples_through_Analogy_and_Explanation | Bridging Principles and Examples through Analogy and Explanation (Nokes & VanLehn)]]
*[[Does learning from worked-out examples improve tutored problem solving? | Does learning from worked-out examples improve tutored problem solving? (Renkl, Aleven & Salden)]]
*[[Ringenberg_Examples-as-Help | Scaffolding Problem Solving with Embedded Example to Promote Deep Learning (Ringenberg & VanLehn)]]
* [[The_Help_Tutor__Roll_Aleven_McLaren|Tutoring a meta-cognitive skill: Help-seeking (Roll, Aleven & McLaren)]]
*[[Roll_IPL | Invention as Preparation for Learning (Roll, Aleven, Koedinger & Schwartz)]]
*[[Baker_Choices_in_LE_Space | How Content and Interface Features Influence Student Choices Within the Learning Space (Baker, Corbett, Koedinger, & Rodrigo)]]
*[[Mayer_and_McLaren_-_Social_Intelligence_And_Computer_Tutors | Building Social Intelligence into Computer-Based Tutors (Mayer & McLaren)]]

== Annotated Bibliography ==
Much research in human and machine learning research has advocated various kinds of “multiples” to assist learning:
* multiple data sources (e.g., human learning (HL): Mayer, 2001; machine learning (ML): Blum & Mitchell, 1998; Collins & Singer, 1999).
* multiple representations (e.g., HL: Ainsworth & Van Labeke, 2004; ML: Liere & Tadepalli, 1997),
* multiple strategies (e.g., HL: Klahr & Siegler, 1978; ML: Michalski & Tecucci 1997; Saitta, Botta, & Neri, 1993);
* multiple learning tasks (e.g., HL: Holland, Holyoak, Nisbett, & Thagard, 1986; ML: Caruana, 1997; Case, Jain, Ott, Sharma, & Stephan, 1998);

Experiments in human learning have demonstrated, for instance, that instruction that combines rules or principles and [[example]]s yields better results than either alone (Holland, Holyoak, Nisbett, & Thagard, 1986) or, for instance, iterative instruction of both [[Procedural tasks|procedures]] and [[Conceptual tasks|concepts]] better learning (Rittle-Johnson & Koedinger, 2002; Rittle-Johnson, Siegler, & Alibali, 2001). See also the [http://www.psyc.memphis.edu/learning/principles/lp5.shtml variable learning principle.]

Experiments in machine learning have demonstrated how more robust, generalizable learning can be achieved by training a single learner on ''multiple'' related tasks (Caruana 1997) or by training ''multiple'' learning systems on the same task (Blum & Mitchell 1998; Collins & Singer 1999; Muslea, Minton, & Knoblock, 2002). Blum and Mitchell (1998) provide both empirical results and a proof of the circumstances under which strategy combinations enhance learning. In particular, the [[co-training]] approach for combining multiple learning strategies yields better learning to the extent that the learning strategies produce “uncorrelated errors” – when one is wrong the other is often right. As an example of PSLC work, Donmez et al. (2005) demonstrate, using a multi-dimensional collaborative process analysis, that regularities across ''multiple'' codings of the same data can be exploited for the purpose of improving text classification accuracy for difficult codings.

An ambitious goal of PSLC is provide a rigorous causal theory of human learning results at the level of precision of machine learning research.

* Ainsworth, S., Bibby, P., & Wood, D. (2002). Examining the effects of different multiple representational systems in learning primary mathematics. The Journal of the Learning Sciences, 11(1), 25–61.
* Ainsworth, S.E. & Van Labeke (2004) Multiple forms of dynamic representation. Learning and Instruction, 14(3), 241-255.
* Blum, A., & Mitchell, T. (1998). Combining labeled and unlabeled data with co-training. In Proceedings of Eleventh Annual Conference on Computational Learning Theory (COLT), (pp. 92–100). New York: ACM Press. Available: citeseer.nj.nec.com/blum98combining.html
* Caruana, R. (1997). Multitask learning. Machine Learning 28(1), 41-75. Available: citeseer.nj.nec.com/caruana97multitask.html.
* Case, J., Jain, S., Ott, M., Sharma, A., & Stephan, F. (1998). Robust learning aided by context. In Proceedings of Eleventh Annual Conference on Computational Learning Theory (COLT), (pp. 44-55). New York: ACM Press.
* Collins, M., & Singer, Y. (1999). Unsupervised models for named entity classification. In Proceedings of the Joint SIGDAT Conference on Empirical Methods in Natural Language Processing and Very Large Corpora (pp. 189–196).
* Donmez, P., Rose, C. P., Stegmann, K., Weinberger, A., and Fischer, F. (2005). Supporting CSCL with Automatic Corpus Analysis Technology, to appear in the Proceedings of Computer Supported Collaborative Learning.
* Holland, J. H., Holyoak, K. J., Nisbett, R. E., & Thagard, P. R. (1986). Induction: Processes of inference, learning, and discovery. Cambridge, MA: MIT Press.
* Klahr D., and Siegler R.S. (1978). The Representation of Children's Knowledge. In H.W. Reese and L.P. Lipsitt (Eds.), Advances in Child Development and Behavior, Academic Press, New York, NY, pp. 61-116.
* Liere, R., & Tadepalli, P. (1997). Active learning with committees for text categorization. In Proceedings of AAAI-97, 14th Conference of the American Association for Artificial Intelligence (pp. 591—596). Menlo Park, CA: AAAI Press.
* Mayer, R. E. (2001). Multimedia learning. New York: Cambridge University Press.
* Michalski, R., & Tecuci, G. (Eds.) (1997). Machine learning: A multi-strategy approach. Morgan Kaufmann.
* Muslea, I., Minton, S., & Knoblock, C. (2002). Active + semi-supervised learning = robust multi-view learning. In Proceedings of ICML-2002. Sydney, Australia.
* Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346–262.
* Rittle-Johnson, B., & Koedinger, K. R. (2002). Comparing instructional strategies for integrating conceptual and procedural knowledge. Paper presented at the Psychology of Mathematics Education, National, Athens, GA.
* Saitta, L., Botta, M., & Neri, F. (1993). Multi-strategy learning and theory revision. Machine Learning, 11(2/3), 153–172.
[[Category:Cluster]]

Coordinative Learning

2008-05-27T21:29:40Z

Timothy Nokes: /* Glossary */

= The PSLC Coordinative Learning cluster =

== Abstract ==
The studies in the Coordinative Learning cluster tend to focus on varying ''a)'' the types of information available to learning or ''b)'' the instructional methods that they employ. In particular, the studies focus on the impact of having learners coordinate two or more types. Given that the student has multiple [[sources]]/methods available, two factors that might impact learning are:

*What is the relationship between the content in the two sources or the content generated by the two methods? Our hypothesis is that the two sources or methods facilitate [[robust learning]] when a [[knowledge component]] is difficult to understand or absent in one and is present or easier to understand in the other.
*When and how does the student coordinate between the two sources or methods? Our hypothesis is that students should be encouraged to compare the two, perhaps by putting them close together in space or time.

At the micro-level, the overall hypothesis is that robust learning occurs when the [[learning event space]] has target paths whose [[sense making]] difficulties complement each other (as expressed in the first bullet above) and the students make path choices that take advantage of these [[complementary]] paths (as in the second bullet, above). This hypothesis is just a specialization of the [[Root_node|general PSLC hypothesis]] to this cluster.

The matrix below shows how studies in this cluster (pages for these studies can be found Descendants section below) either test or make use of various [[instructional method|instructional methods]] or treatments. When a study tests an instructional method a "v" is one shown in the appropriate cell to indicate that that method is '''varied''' in the study, that is, the [[robust learning]] gains of an experimental condition that receives this method are contrasted with those of an otherwise equivalent control condition that does not receive this method. In this case (when a "v" is present), the study tests the [[InstructionalPrinciples|instructional principle]] indicated in the column. When a cell contains a "b" it indicates that '''both''' the experimental and control conditions use this instructional method (or employ this instructional principle). In this case, the study is not a true experimental test of the principle.

 <center>[[Image:Cl.JPG]]</center>

== Glossary ==
[[:Category:Coordinative Learning|Coordinative Learning]] glossary.

*'''[[Analogical Comparison]]'''
*'''[[Co-training]]'''
*'''[[Complementary]]'''
*'''[[Conceptual tasks]]'''
*'''[[Contiguity]]'''
*'''[[Coordination]]'''
*'''[[Ecological control group]]'''
*'''[[External representations]]'''
*'''[[Input sources ]]'''
*'''[[Instructional method]]'''
*'''[[Multimedia sources]]'''
*'''[[Procedural tasks]]'''
*'''[[Self-explanation]]'''
*'''[[Self-supervised learning]]'''
*'''[[Sources]]'''
*'''[[Strategies]]'''
*'''[[Unlabeled examples]]'''

== Research questions ==

When and how does coordinating multiple sources of information or lines of reasoning increase robust learning?

Two sub-groups of coordinative learning studies are exploring these more specific questions:

=== Visualizations and Multi-modal sources ===

When does adding visualizations or other multi-modal input enhance robust learning and how do we best support students in coordinating these sources?

=== Examples and Explanations ===

When and how should example study be combined and coordinated with problem solving to increase robust learning? When and how should explicit explanations be added or requested of students before, during, or after example study and problem solving practice?

== Independent variables ==

*Content of the sources (e.g., pictures, diagrams, written text, audio, animation) or the encouraged lines of reasoning (e.g., example study, self-explanation, conceptual task, procedural task) and combinations

*Instructional activities designed to engage students in [[coordination]] (e.g., conceptual vs. [[procedural]] exercises, contiguous presentation of sources, [[self-explanation]])

See [[:Category:Independent Variables]]

== Dependent variables ==
[[Normal post-test]] and measures of [[robust learning]].

== Hypotheses ==
When students are given sources/methods whose [[sense making]] difficulties are complementary and they are engaged in coordinating the sources/methods, then their learning will be more robust than it would otherwise be.

== Explanation ==

There are both [[sense making]] and [[foundational skill building]] explanations. From the sense making perspective, if the sources/methods yield complementary content and the student is engaged in coordinating them, then the student is more likely to successfully understand the instruction because if a student fails to understand one of the sources/methods, he can use the second to make sense of the first. From a foundational skill building perspective, attending to both sources/methods simultaneously associates [[features]] from both with the learned knowledge components, thus potentially increasing [[feature validity]] and hence [[robust learning]].

== Descendents ==

=== Visualizations and Multi-modal sources ===
*[[Contiguous Representations for Robust Learning (Aleven & Butcher)]]
**[[Static vs. Animated Visual Representations for Science Learning (Kaye, Small, Butcher, & Chi)]]
*[[Mapping Visual and Verbal Information: Integrated Hints in Geometry (Aleven & Butcher)]]
**[[Training Geometry Concepts with Visual and Verbal Sources (Burchfield, Aleven, & Butcher)]]
*[[Visual Representations in Science Learning | Visual Representations in Science Learning (Davenport, Klahr & Koedinger)]]
* Cotraining in language learning
**[[Co-training of Chinese characters| Co-training of Chinese characters (Liu, Perfetti, Dunlap, Zi, Mitchell)]]
**[[Co-training and pairing| The pairing effect in Chinese cotraining (Liu, Perfetti, Dunlap, Wu, Mitchell)]]
*[[Learning Chinese pronunciation from a “talking head”| Learning Chinese pronunciation from a “talking head” (Liu, Massaro, Dunlap, Wu, Chen,Chan, Perfetti)]] [Was in Refinement and Fluency]
*[[Visual Feature Focus in Geometry: Instructional Support for Visual Coordination During Learning (Butcher & Aleven)]]
*[[Learning About Emergence and Heat Transfer (Chi)]]

=== Examples and Explanations ===
*[[Booth | Improving skill at solving equations through better encoding of algebraic concepts (Booth, Siegler, Koedinger & Rittle-Johnson)]]
*[[McLaren_et_al_-_Studying_the_Learning_Effect_of_Personalization_and_Worked_Examples_in_the_Solving_of_Stoich_Problems | Studying the Learning Effect of Personalization and Worked Examples in the Solving of Stoichiometry Problems (McLaren, Koedinger & Yaron)]]
*[[Note-Taking_Technologies | Note-taking Project Page (Bauer & Koedinger)]]
**[[Note-Taking: Restriction and Selection]] (completed)
**[[Note-Taking: Coordination]] (planned)
*[[REAP_main | The REAP Project: Implicit and explicit instruction on word meanings (Juffs & Eskenazi)]]
*[[Help_Lite (Aleven, Roll)|Hints during tutored problem solving – the effect of fewer hint levels with greater conceptual content (Aleven & Roll)]]
*[[Handwriting Algebra Tutor]] (Anthony, Yang & Koedinger)
**[[Lab study proof-of-concept for handwriting vs typing input for learning algebra equation-solving]] (completed)
**[[Effect of adding simple worked examples to problem-solving in algebra learning]] (completed, analysis in progress)
**[[In vivo comparison of Cognitive Tutor Algebra using handwriting vs typing input]] (in progress)
*[[Bridging_Principles_and_Examples_through_Analogy_and_Explanation | Bridging Principles and Examples through Analogy and Explanation (Nokes & VanLehn)]]
*[[Does learning from worked-out examples improve tutored problem solving? | Does learning from worked-out examples improve tutored problem solving? (Renkl, Aleven & Salden)]]
*[[Ringenberg_Examples-as-Help | Scaffolding Problem Solving with Embedded Example to Promote Deep Learning (Ringenberg & VanLehn)]]
* [[The_Help_Tutor__Roll_Aleven_McLaren|Tutoring a meta-cognitive skill: Help-seeking (Roll, Aleven & McLaren)]]
*[[Roll_IPL | Invention as Preparation for Learning (Roll, Aleven, Koedinger & Schwartz)]]
*[[Baker_Choices_in_LE_Space | How Content and Interface Features Influence Student Choices Within the Learning Space (Baker, Corbett, Koedinger, & Rodrigo)]]
*[[Mayer_and_McLaren_-_Social_Intelligence_And_Computer_Tutors | Building Social Intelligence into Computer-Based Tutors (Mayer & McLaren)]]

== Annotated Bibliography ==
Much research in human and machine learning research has advocated various kinds of “multiples” to assist learning:
* multiple data sources (e.g., human learning (HL): Mayer, 2001; machine learning (ML): Blum & Mitchell, 1998; Collins & Singer, 1999).
* multiple representations (e.g., HL: Ainsworth & Van Labeke, 2004; ML: Liere & Tadepalli, 1997),
* multiple strategies (e.g., HL: Klahr & Siegler, 1978; ML: Michalski & Tecucci 1997; Saitta, Botta, & Neri, 1993);
* multiple learning tasks (e.g., HL: Holland, Holyoak, Nisbett, & Thagard, 1986; ML: Caruana, 1997; Case, Jain, Ott, Sharma, & Stephan, 1998);

Experiments in human learning have demonstrated, for instance, that instruction that combines rules or principles and [[example]]s yields better results than either alone (Holland, Holyoak, Nisbett, & Thagard, 1986) or, for instance, iterative instruction of both [[Procedural tasks|procedures]] and [[Conceptual tasks|concepts]] better learning (Rittle-Johnson & Koedinger, 2002; Rittle-Johnson, Siegler, & Alibali, 2001). See also the [http://www.psyc.memphis.edu/learning/principles/lp5.shtml variable learning principle.]

Experiments in machine learning have demonstrated how more robust, generalizable learning can be achieved by training a single learner on ''multiple'' related tasks (Caruana 1997) or by training ''multiple'' learning systems on the same task (Blum & Mitchell 1998; Collins & Singer 1999; Muslea, Minton, & Knoblock, 2002). Blum and Mitchell (1998) provide both empirical results and a proof of the circumstances under which strategy combinations enhance learning. In particular, the [[co-training]] approach for combining multiple learning strategies yields better learning to the extent that the learning strategies produce “uncorrelated errors” – when one is wrong the other is often right. As an example of PSLC work, Donmez et al. (2005) demonstrate, using a multi-dimensional collaborative process analysis, that regularities across ''multiple'' codings of the same data can be exploited for the purpose of improving text classification accuracy for difficult codings.

An ambitious goal of PSLC is provide a rigorous causal theory of human learning results at the level of precision of machine learning research.

* Ainsworth, S., Bibby, P., & Wood, D. (2002). Examining the effects of different multiple representational systems in learning primary mathematics. The Journal of the Learning Sciences, 11(1), 25–61.
* Ainsworth, S.E. & Van Labeke (2004) Multiple forms of dynamic representation. Learning and Instruction, 14(3), 241-255.
* Blum, A., & Mitchell, T. (1998). Combining labeled and unlabeled data with co-training. In Proceedings of Eleventh Annual Conference on Computational Learning Theory (COLT), (pp. 92–100). New York: ACM Press. Available: citeseer.nj.nec.com/blum98combining.html
* Caruana, R. (1997). Multitask learning. Machine Learning 28(1), 41-75. Available: citeseer.nj.nec.com/caruana97multitask.html.
* Case, J., Jain, S., Ott, M., Sharma, A., & Stephan, F. (1998). Robust learning aided by context. In Proceedings of Eleventh Annual Conference on Computational Learning Theory (COLT), (pp. 44-55). New York: ACM Press.
* Collins, M., & Singer, Y. (1999). Unsupervised models for named entity classification. In Proceedings of the Joint SIGDAT Conference on Empirical Methods in Natural Language Processing and Very Large Corpora (pp. 189–196).
* Donmez, P., Rose, C. P., Stegmann, K., Weinberger, A., and Fischer, F. (2005). Supporting CSCL with Automatic Corpus Analysis Technology, to appear in the Proceedings of Computer Supported Collaborative Learning.
* Holland, J. H., Holyoak, K. J., Nisbett, R. E., & Thagard, P. R. (1986). Induction: Processes of inference, learning, and discovery. Cambridge, MA: MIT Press.
* Klahr D., and Siegler R.S. (1978). The Representation of Children's Knowledge. In H.W. Reese and L.P. Lipsitt (Eds.), Advances in Child Development and Behavior, Academic Press, New York, NY, pp. 61-116.
* Liere, R., & Tadepalli, P. (1997). Active learning with committees for text categorization. In Proceedings of AAAI-97, 14th Conference of the American Association for Artificial Intelligence (pp. 591—596). Menlo Park, CA: AAAI Press.
* Mayer, R. E. (2001). Multimedia learning. New York: Cambridge University Press.
* Michalski, R., & Tecuci, G. (Eds.) (1997). Machine learning: A multi-strategy approach. Morgan Kaufmann.
* Muslea, I., Minton, S., & Knoblock, C. (2002). Active + semi-supervised learning = robust multi-view learning. In Proceedings of ICML-2002. Sydney, Australia.
* Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346–262.
* Rittle-Johnson, B., & Koedinger, K. R. (2002). Comparing instructional strategies for integrating conceptual and procedural knowledge. Paper presented at the Psychology of Mathematics Education, National, Athens, GA.
* Saitta, L., Botta, M., & Neri, F. (1993). Multi-strategy learning and theory revision. Machine Learning, 11(2/3), 153–172.
[[Category:Cluster]]

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T21:25:13Z

Timothy Nokes: /* Abstract */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008; Analysis on-going
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through [[self-explain]]ing how [[worked examples]] are related to the principles. The second path is learning a schema through [[analogical comparison]] of two examples and then relating that schema to the principle. These hypotheses are tested in both a [[in vivo experiment]] in the [[Physics]] LearnLab as well as laboratory studies.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables the reliable retrieval and use of those concepts to solve novel problems and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two [[worked examples]]. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two [[worked examples]] and are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance
===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T21:23:24Z

Timothy Nokes: /* Abstract */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008; Analysis on-going
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through explaining how [[worked examples]] are related to the principles. The second path is learning a schema through analogical comparison of two examples and then relating that schema to the principle. These hypotheses are tested in both a [[in vivo experiment]] in the [[Physics]] LearnLab as well as laboratory studies.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables the reliable retrieval and use of those concepts to solve novel problems and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two [[worked examples]]. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two [[worked examples]] and are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance
===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T21:22:42Z

Timothy Nokes: /* Abstract */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008; Analysis on-going
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through explaining how worked examples are related to the principles. The second path is learning a schema through analogical comparison of two examples and then relating that schema to the principle. These hypotheses are tested in both a [[in vivo experiment]] in the [[Physics]] LearnLab as well as laboratory studies.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables the reliable retrieval and use of those concepts to solve novel problems and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two [[worked examples]]. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two [[worked examples]] and are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance
===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T21:21:38Z

Timothy Nokes: /* Abstract */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008; Analysis on-going
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through explaining how worked examples are related to the principles. The second path is learning a schema through analogical comparison of two examples and then relating that schema to the principle. These hypotheses are tested in both a [[in vivo experiment]] in the Physics LearnLab as well as laboratory studies.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables the reliable retrieval and use of those concepts to solve novel problems and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two [[worked examples]]. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two [[worked examples]] and are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance
===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T21:20:21Z

Timothy Nokes: /* Study 1 (In Vivo) */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008; Analysis on-going
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through explaining how worked examples are related to the principles. The second path is learning a schema through analogical comparison of two examples and then relating that schema to the principle. These hypotheses are tested in two [[in vivo experiment]]s in the Physics LearnLab.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables the reliable retrieval and use of those concepts to solve novel problems and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two [[worked examples]]. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two [[worked examples]] and are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance
===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2008-05-27T21:19:44Z

Timothy Nokes: /* Study 2 (In Vivo) */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || October, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || 78
|-
| '''Total Participant Hours''' || 312
|-
| '''Data Shop''' || Expected Spring, 2008
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through explaining how worked examples are related to the principles. The second path is learning a schema through analogical comparison of two examples and then relating that schema to the principle. These hypotheses are tested in two [[in vivo experiment]]s in the Physics LearnLab.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables the reliable retrieval and use of those concepts to solve novel problems and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two [[worked examples]]. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two [[worked examples]] and are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance
===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2008-05-26T00:57:03Z

Timothy Nokes: /* Study 1 */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 2 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || September, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || na
|-
| '''Total Participant Hours''' || na
|-
| '''Data Shop''' || Expected January, 2008
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through explaining how worked examples are related to the principles. The second path is learning a schema through analogical comparison of two examples and then relating that schema to the principle. These hypotheses are tested in two [[in vivo experiment]]s in the Physics LearnLab.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables the reliable retrieval and use of those concepts to solve novel problems and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two [[worked examples]]. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two [[worked examples]] and are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance
===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Analogical comparison principle

2008-03-25T16:57:48Z

Timothy Nokes: /* Theoretical rationale */

==Brief statement of principle==
Analogical comparison can facilitate schema abstraction and transfer of that knowledge to new problem. By comparing the commonalities between two examples, students can focus on the causal structure and improve their learning about the concept.

==Description of principle==
===Operational definition===
===Examples===
==Experimental support==
===Laboratory experiment support===
Analogical comparison has also been shown to improve learning even when both examples are not initially well understood (Kurtz, Miao, & Gentner, 2001; Gentner Lowenstein, & Thompson, 2003). By comparing the commonalities between two examples, students could focus on the causal structure and improve their learning about the concept. Kurtz et al. (2001) showed that students who were learning about the concept of heat transfer learned more when comparing examples than when studying each example separately.

===In vivo experiment support===
==Theoretical rationale==
Comparing and contrasting problems can facilitate [[analogical comparison]].
(These entries should link to one or more [[:Category:Learning Processes|learning processes]].)

==Conditions of application==
==Caveats, limitations, open issues, or dissenting views==
==Variations (descendants)==
==Generalizations (ascendants)==
==References==
[[Category:Glossary]]
[[Category:Instructional Principle]]

Analogical comparison principle

2008-03-25T16:57:29Z

Timothy Nokes: /* Theoretical rationale */

==Brief statement of principle==
Analogical comparison can facilitate schema abstraction and transfer of that knowledge to new problem. By comparing the commonalities between two examples, students can focus on the causal structure and improve their learning about the concept.

==Description of principle==
===Operational definition===
===Examples===
==Experimental support==
===Laboratory experiment support===
Analogical comparison has also been shown to improve learning even when both examples are not initially well understood (Kurtz, Miao, & Gentner, 2001; Gentner Lowenstein, & Thompson, 2003). By comparing the commonalities between two examples, students could focus on the causal structure and improve their learning about the concept. Kurtz et al. (2001) showed that students who were learning about the concept of heat transfer learned more when comparing examples than when studying each example separately.

===In vivo experiment support===
==Theoretical rationale==
Comparing and contrasting problems can facilitate [analogical comparison].
(These entries should link to one or more [[:Category:Learning Processes|learning processes]].)

==Conditions of application==
==Caveats, limitations, open issues, or dissenting views==
==Variations (descendants)==
==Generalizations (ascendants)==
==References==
[[Category:Glossary]]
[[Category:Instructional Principle]]

Analogical comparison principle

2008-03-25T16:47:36Z

Timothy Nokes: /* Theoretical rationale */

==Brief statement of principle==
Analogical comparison can facilitate schema abstraction and transfer of that knowledge to new problem. By comparing the commonalities between two examples, students can focus on the causal structure and improve their learning about the concept.

==Description of principle==
===Operational definition===
===Examples===
==Experimental support==
===Laboratory experiment support===
Analogical comparison has also been shown to improve learning even when both examples are not initially well understood (Kurtz, Miao, & Gentner, 2001; Gentner Lowenstein, & Thompson, 2003). By comparing the commonalities between two examples, students could focus on the causal structure and improve their learning about the concept. Kurtz et al. (2001) showed that students who were learning about the concept of heat transfer learned more when comparing examples than when studying each example separately.

===In vivo experiment support===
==Theoretical rationale==
Problem comparison facilitates analogical learning processes.
(These entries should link to one or more [[:Category:Learning Processes|learning processes]].)

==Conditions of application==
==Caveats, limitations, open issues, or dissenting views==
==Variations (descendants)==
==Generalizations (ascendants)==
==References==
[[Category:Glossary]]
[[Category:Instructional Principle]]

Analogical comparison principle

2008-03-25T16:39:16Z

Timothy Nokes: /* Laboratory experiment support */

==Brief statement of principle==
Analogical comparison can facilitate schema abstraction and transfer of that knowledge to new problem. By comparing the commonalities between two examples, students can focus on the causal structure and improve their learning about the concept.

==Description of principle==
===Operational definition===
===Examples===
==Experimental support==
===Laboratory experiment support===
Analogical comparison has also been shown to improve learning even when both examples are not initially well understood (Kurtz, Miao, & Gentner, 2001; Gentner Lowenstein, & Thompson, 2003). By comparing the commonalities between two examples, students could focus on the causal structure and improve their learning about the concept. Kurtz et al. (2001) showed that students who were learning about the concept of heat transfer learned more when comparing examples than when studying each example separately.

===In vivo experiment support===
==Theoretical rationale==
(These entries should link to one or more [[:Category:Learning Processes|learning processes]].)
==Conditions of application==
==Caveats, limitations, open issues, or dissenting views==
==Variations (descendants)==
==Generalizations (ascendants)==
==References==
[[Category:Glossary]]
[[Category:Instructional Principle]]

Analogical comparison principle

2008-03-25T16:36:26Z

Timothy Nokes: /* Brief statement of principle */

==Brief statement of principle==
Analogical comparison can facilitate schema abstraction and transfer of that knowledge to new problem. By comparing the commonalities between two examples, students can focus on the causal structure and improve their learning about the concept.

==Description of principle==
===Operational definition===
===Examples===
==Experimental support==
===Laboratory experiment support===
Several factors have been shown to improve schema acquisition including: increasing the number of examples (Gick & Holyoak, 1983), increasing the variability of the examples (Chen, 1999; Paas & Merrienboer, 1994), using instructions that focus the learner on structural commonalities (Cummins, 1992; Gentner et al., 2003), focusing the learner on the subgoals of the problems (Catrambone, 1996, 1998), and using examples that minimize students cognitive load (Ward & Sweller, 1990).

===In vivo experiment support===
==Theoretical rationale==
(These entries should link to one or more [[:Category:Learning Processes|learning processes]].)
==Conditions of application==
==Caveats, limitations, open issues, or dissenting views==
==Variations (descendants)==
==Generalizations (ascendants)==
==References==
[[Category:Glossary]]
[[Category:Instructional Principle]]

Analogical comparison principle

2008-03-25T16:33:04Z

Timothy Nokes: /* Laboratory experiment support */

==Brief statement of principle==
Analogical comparison can facilitate schema abstraction and transfer of that knowledge to new problem. By comparing the commonalities between two examples, students could focus on the causal structure and improve their learning about the concept.

==Description of principle==
===Operational definition===
===Examples===
==Experimental support==
===Laboratory experiment support===
Several factors have been shown to improve schema acquisition including: increasing the number of examples (Gick & Holyoak, 1983), increasing the variability of the examples (Chen, 1999; Paas & Merrienboer, 1994), using instructions that focus the learner on structural commonalities (Cummins, 1992; Gentner et al., 2003), focusing the learner on the subgoals of the problems (Catrambone, 1996, 1998), and using examples that minimize students cognitive load (Ward & Sweller, 1990).

===In vivo experiment support===
==Theoretical rationale==
(These entries should link to one or more [[:Category:Learning Processes|learning processes]].)
==Conditions of application==
==Caveats, limitations, open issues, or dissenting views==
==Variations (descendants)==
==Generalizations (ascendants)==
==References==
[[Category:Glossary]]
[[Category:Instructional Principle]]

Analogical comparison principle

2008-03-25T16:31:40Z

Timothy Nokes: /* Brief statement of principle */

Analogical comparison principle

2008-03-25T16:28:37Z

Timothy Nokes: /* Brief statement of principle */

==Brief statement of principle==
Analogical comparison operates through aligning and mapping two example problem representations to one another and then extracting their commonalities (Gentner, 1983; Gick & Holyoak, 1983; Hummel & Holyoak, 2003). This process discards the elements of the knowledge representation that do not overlap between two examples but preserves the common elements. The resulting knowledge organization typically consists of fewer superficial similarities (than the examples) but retains the deep causal structure of the problems.
Research on analogy and schema learning has shown that the acquisition of schematic knowledge promotes flexible transfer to novel problems. Many researchers have found a positive relationship between the quality of the abstracted schema and transfer to a novel problem that is an instance of that schema (Catrambone & Holyoak, 1989; Gick & Holyoak, 1983; Novick & Holyoak, 1991).

==Description of principle==
===Operational definition===
===Examples===
==Experimental support==
===Laboratory experiment support===
===In vivo experiment support===
==Theoretical rationale==
(These entries should link to one or more [[:Category:Learning Processes|learning processes]].)
==Conditions of application==
==Caveats, limitations, open issues, or dissenting views==
==Variations (descendants)==
==Generalizations (ascendants)==
==References==
[[Category:Glossary]]
[[Category:Instructional Principle]]

Analogical comparison principle

2008-03-25T16:22:31Z

Timothy Nokes: New page: ==Brief statement of principle== ==Description of principle== ===Operational definition=== ===Examples=== ==Experimental support== ===Laboratory experiment support=== ===In vivo experiment...

==Brief statement of principle==
==Description of principle==
===Operational definition===
===Examples===
==Experimental support==
===Laboratory experiment support===
===In vivo experiment support===
==Theoretical rationale==
(These entries should link to one or more [[:Category:Learning Processes|learning processes]].)
==Conditions of application==
==Caveats, limitations, open issues, or dissenting views==
==Variations (descendants)==
==Generalizations (ascendants)==
==References==
[[Category:Glossary]]
[[Category:Instructional Principle]]

Analogical comparison

2007-05-21T15:02:54Z

Timothy Nokes:

Analogical comparison operates through aligning and mapping two example problem representations to one another and then extracting their commonalities (Gentner, 1983; Gick & Holyoak, 1983; Hummel & Holyoak, 2003). This process discards the elements of the knowledge representation that do not overlap between two examples but preserves the common elements. The resulting knowledge organization typically consists of fewer superficial similarities (than the examples) but retains the deep causal structure of the problems.

===References===
*Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy, ''Cognitive Science, 7'', 155-170.
*Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. ''Cognitive Psychology, 15'', 1-38.
*Hummel, J. E., & Holyoak, K. J. (2003). A symbolic-connectionist theory of relational inference and generalization. ''Psychological Review, 110'', 220-264.

[[Category: Glossary]]
[[Category: Coordinative Learning]]

Analogical comparison

2007-05-21T15:02:34Z

Timothy Nokes:

Analogical comparison operates through aligning and mapping two example problem representations to one another and then extracting their commonalities (Gentner, 1983; Gick & Holyoak, 1983; Hummel & Holyoak, 2003). This process discards the elements of the knowledge representation that do not overlap between two examples but preserves the common elements. The resulting knowledge organization typically consists of fewer superficial similarities (than the examples) but retains the deep causal structure of the problems.

==References==
*Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy, ''Cognitive Science, 7'', 155-170.
*Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. ''Cognitive Psychology, 15'', 1-38.
*Hummel, J. E., & Holyoak, K. J. (2003). A symbolic-connectionist theory of relational inference and generalization. ''Psychological Review, 110'', 220-264.

[[Category: Glossary]]
[[Category: Coordinative Learning]]

Analogical comparison

2007-05-21T14:58:25Z

Timothy Nokes:

Analogical comparison

2007-05-21T14:56:44Z

Timothy Nokes:

Analogical comparison

2007-05-21T14:55:55Z

Timothy Nokes:

Bridging Principles and Examples through Analogy and Explanation

2007-05-21T14:49:51Z

Timothy Nokes:

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || May, 2007
|-
| '''Study End Date''' || June, 2007
|-
| '''LearnLab Site''' || University of Pittsburgh
|-
| '''Number of Students''' || 60 (planned)
|-
| '''Total Participant Hours''' || 180 (planned)
|-
| '''Data Shop''' || na
|}
 

====Study 2 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || September, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || na
|-
| '''Total Participant Hours''' || na
|-
| '''Data Shop''' || Expected January, 2008
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through explaining how worked examples are related to the principles. The second path is learning a schema through analogical comparison of two examples and then relating that schema to the principle. These hypotheses are tested in two [[in vivo experiment]]s in the Physics LearnLab.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables the reliable retrieval and use of those concepts to solve novel problems and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. [[Self-explanation]] has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and [[worked examples]] will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through [[analogical comparison]]. Prior work has shown that [[analogical comparison]] can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two [[worked examples]]. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two [[worked examples]] and are instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on [[Andes]] problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

*[[Accelerated future learning]]
**Performance on subsequent topics (e.g., rotational dynamics) as measured by [[Andes]] performance
===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Analogical comparison

2007-05-08T02:38:58Z

Timothy Nokes:

Bridging Principles and Examples through Analogy and Explanation

2007-04-03T13:31:46Z

Timothy Nokes: /* Study 1 */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || May, 2007
|-
| '''Study End Date''' || June, 2007
|-
| '''LearnLab Site''' || University of Pittsburgh
|-
| '''Number of Students''' || 60 (planned)
|-
| '''Total Participant Hours''' || 180 (planned)
|-
| '''Data Shop''' || na
|}
 

====Study 2 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || September, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || na
|-
| '''Total Participant Hours''' || na
|-
| '''Data Shop''' || Expected January, 2008
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through explaining how worked examples are related to the principles. The second path is learning a schema through analogical comparison of two examples and then relating that schema to the principle. These hypotheses are tested in two [[in vivo experiment]]s in the Physics LearnLab.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables the reliable retrieval and use of those concepts to solve novel problems and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. Self-explanation has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and worked examples will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through analogical comparison. Prior work has shown that analogical comparison can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two worked-out examples. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two worked examples and instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on ANDES problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Coordinative Learning

2007-04-03T13:30:57Z

Timothy Nokes: /* Descendents */

== The PSLC Coordinative Learning cluster ==

=== Abstract ===
The studies in the Coordinative Learning cluster tend to focus on varying ''a)'' the types of information available to learning or ''b)'' the instructional methods that they employ. In particular, the studies focus on the impact of having learners coordinate two or more types. Given that the student has multiple [[sources]]/methods available, two factors that might impact learning are:

*What is the relationship between the content in the two sources or the content generated by the two methods? Our hypothesis is that the two sources or methods facilitate [[robust learning]] when a [[knowledge component]] is difficult to understand or absent in one and is present or easier to understand in the other.
*When and how does the student coordinate between the two sources or methods? Our hypothesis is that students should be encouraged to compare the two, perhaps by putting them close together in space or time.

At the micro-level, the overall hypothesis is that robust learning occurs when the [[learning event space]] has target paths whose [[sense making]] difficulties complement each other (as expressed in the first bullet above) and the students make path choices that take advantage of these [[complementary]] paths (as in the second bullet, above). This hypothesis is just a specialization of the [[Root_node|general PSLC hypothesis]] to this cluster.

=== Glossary ===
[[:Category:Coordinative Learning|Coordinative Learning]] glossary.

*'''[[Co-training]]'''
*'''[[Complementary]]'''
*'''[[Conceptual tasks]]'''
*'''[[Contiguity]]'''
*'''[[Coordination]]'''
*'''[[Ecological Control Group]]'''
*'''[[External representations]]'''
*'''[[Input sources ]]'''
*'''[[Instructional method]]'''
*'''[[Multimedia sources]]'''
*'''[[Procedural tasks]]'''
*'''[[Self-explanation]]'''
*'''[[Self-supervised learning]]'''
*'''[[Sources]]'''
*'''[[Strategies]]'''
*'''[[Unlabeled examples]]'''

=== Research question ===

When and how does coordinating multiple sources of information or lines of reasoning increase robust learning?

Two sub-groups of coordinative learning studies are exploring these more specific questions:

1) Visualizations and Multi-modal sources

When does adding visualizations or other multi-modal input enhance robust learning and how do we best support students in coordinating these sources?

2) Examples and Explanations

When and how should example study by combined and coordinated with problem solving to increase robust learning? When and how should explicit explanations be added or requested of students before, during, or after example study and problem solving practice?

=== Independent variables ===

*Content of the sources (e.g., pictures, diagrams, written text, audio, animation) or the encouraged lines of reasoning (e.g., example study, self-explanation, conceptual task, procedural task) and combinations

*Instructional activities designed to engage students in [[coordination]] (e.g., conceptual vs. [[procedural]] exercises, contiguous presentation of sources, [[self-explanation]])

=== Dependent variables ===
[[Normal post-test]] and measures of [[robust learning]].

=== Hypotheses ===
When students are given sources/methods whose [[sense making]] difficulties are complementary and they are engaged in coordinating the sources/methods, then their learning will be more robust than it would otherwise be.

=== Explanation ===

There are both [[sense making]] and [[foundational skill building]] explanations. From the sense making perspective, if the sources/methods yield complementary content and the student is engaged in coordinating them, then the student is more likely to successfully understand the instruction because if a student fails to understand one of the sources/methods, he can use the second to make sense of the first. From a foundational skill building perspective, attending to both sources/methods simultaneously associates [[features]] from both with the learned knowledge components, thus potentially increasing feature validity and hence robust learning.

=== Descendents ===

Visualizations and Multi-modal sources
*[[Contiguous Representations for Robust Learning (Aleven & Butcher)]]
*[[Mapping Visual and Verbal Information: Integrated Hints in Geometry (Aleven & Butcher)]]
*[[Visual Representations in Science Learning | Visual Representations in Science Learning (Davenport, Klahr & Koedinger)]]
*[[Co-training of Chinese characters| Co-training of Chinese characters (Liu, Perfetti, Dunlap, Zi, Mitchell)]]
*[[Learning Chinese pronunciation from a “talking head”| Learning Chinese pronunciation from a “talking head” (Liu, Massaro, Dunlap, Wu, Chen,Chan, Perfetti)]] [Was in Fluency]

Examples and Explanations
*[[Booth | Knowledge component construction vs. recall (Booth, Siegler, Koedinger & Rittle-Johnson)]]
*[[Stoichiometry_Study | Studying the Learning Effect of Personalization and Worked Examples in the Solving of Stoichiometry Problems (McLaren, Koedinger & Yaron)]]
*[[Note-Taking_Technologies | Note-taking Project Page (Bauer & Koedinger)]]
**[[Note-Taking: Restriction and Selection]] (completed)
**[[Note-Taking: Coordination]] (planned)
*[[REAP_main | The REAP Project: Implicit and explicit instruction on word meanings (Juffs & Eskenazi)]]
*[[Help_Lite (Aleven, Roll)|Hints during tutored problem solving – the effect of fewer hint levels with greater conceptual content (Aleven & Roll)]]
*[[Effect of adding simple worked examples to problem-solving in algebra learning (Anthony, Yang & Koedinger)]]
*[[Bridging_Principles_and_Examples_through_Analogy_and_Explanation | Bridging Principles and Examples through Analogy and Explanation (Nokes & VanLehn)]]

=== Annotated Bibliography ===
Forthcoming

[[Category:Cluster]]

Bridging Principles and Examples through Analogy and Explanation

2007-04-03T13:29:40Z

Timothy Nokes: /* Study 2 (In Vivo) */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1====
(Laboratory Experiment)
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || May, 2007
|-
| '''Study End Date''' || June, 2007
|-
| '''LearnLab Site''' || University of Pittsburgh
|-
| '''Number of Students''' || 60 (planned)
|-
| '''Total Participant Hours''' || 180 (planned)
|-
| '''Data Shop''' || na
|}
 

====Study 2 (In Vivo)====
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || September, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || na
|-
| '''Total Participant Hours''' || na
|-
| '''Data Shop''' || Expected January, 2008
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through explaining how worked examples are related to the principles. The second path is learning a schema through analogical comparison of two examples and then relating that schema to the principle. These hypotheses are tested in two [[in vivo experiment]]s in the Physics LearnLab.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables the reliable retrieval and use of those concepts to solve novel problems and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. Self-explanation has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and worked examples will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through analogical comparison. Prior work has shown that analogical comparison can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two worked-out examples. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two worked examples and instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on ANDES problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2007-04-03T13:29:23Z

Timothy Nokes: /* Study 1 */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

====Study 1====
(Laboratory Experiment)
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || May, 2007
|-
| '''Study End Date''' || June, 2007
|-
| '''LearnLab Site''' || University of Pittsburgh
|-
| '''Number of Students''' || 60 (planned)
|-
| '''Total Participant Hours''' || 180 (planned)
|-
| '''Data Shop''' || na
|}
 

===Study 2 (In Vivo)===
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || September, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || na
|-
| '''Total Participant Hours''' || na
|-
| '''Data Shop''' || Expected January, 2008
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through explaining how worked examples are related to the principles. The second path is learning a schema through analogical comparison of two examples and then relating that schema to the principle. These hypotheses are tested in two [[in vivo experiment]]s in the Physics LearnLab.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables the reliable retrieval and use of those concepts to solve novel problems and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. Self-explanation has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and worked examples will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through analogical comparison. Prior work has shown that analogical comparison can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two worked-out examples. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two worked examples and instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on ANDES problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2007-04-03T13:28:53Z

Timothy Nokes: /* Study 1 */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

==Study 1==
(Laboratory Experiment)
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || May, 2007
|-
| '''Study End Date''' || June, 2007
|-
| '''LearnLab Site''' || University of Pittsburgh
|-
| '''Number of Students''' || 60 (planned)
|-
| '''Total Participant Hours''' || 180 (planned)
|-
| '''Data Shop''' || na
|}
 

===Study 2 (In Vivo)===
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || September, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || na
|-
| '''Total Participant Hours''' || na
|-
| '''Data Shop''' || Expected January, 2008
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through explaining how worked examples are related to the principles. The second path is learning a schema through analogical comparison of two examples and then relating that schema to the principle. These hypotheses are tested in two [[in vivo experiment]]s in the Physics LearnLab.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables the reliable retrieval and use of those concepts to solve novel problems and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. Self-explanation has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and worked examples will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through analogical comparison. Prior work has shown that analogical comparison can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two worked-out examples. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two worked examples and instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on ANDES problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2007-04-03T13:27:40Z

Timothy Nokes: /* Bridging Principles and Examples through Analogy and Explanation */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

===Study 1===
(Laboratory Experiment)
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || May, 2007
|-
| '''Study End Date''' || June, 2007
|-
| '''LearnLab Site''' || University of Pittsburgh
|-
| '''Number of Students''' || 60 (planned)
|-
| '''Total Participant Hours''' || 180 (planned)
|-
| '''Data Shop''' || na
|}
 

===Study 2 (In Vivo)===
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || September, 2007
|-
| '''Study End Date''' || December, 2007
|-
| '''LearnLab Site''' || United States Naval Academy
|-
| '''Number of Students''' || na
|-
| '''Total Participant Hours''' || na
|-
| '''Data Shop''' || Expected January, 2008
|}
 

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through explaining how worked examples are related to the principles. The second path is learning a schema through analogical comparison of two examples and then relating that schema to the principle. These hypotheses are tested in two [[in vivo experiment]]s in the Physics LearnLab.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables the reliable retrieval and use of those concepts to solve novel problems and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. Self-explanation has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and worked examples will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through analogical comparison. Prior work has shown that analogical comparison can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two worked-out examples. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two worked examples and instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on ANDES problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2007-04-03T13:25:23Z

Timothy Nokes: /* Bridging Principles and Examples through Analogy and Explanation */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

===Study 1=== (Laboratory Experiment)
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || May, 2007
|-
| '''Study End Date''' || June, 2007
|-
| '''LearnLab Site''' || University of Pittsburgh
|-
| '''Number of Students''' || 60 (planned)
|-
| '''Total Participant Hours''' || 180 (planned)
|-
| '''Data Shop''' || na
|}
 

Study 2 (In Vivo)
{| border="1" cellpadding="5" cellspacing="0"
!PIs
|Timothy Nokes and Kurt VanLehn
|-
!Study Start Date
|September 2007
|-
!Study End Date
|December, 2007
|-
!LearnLab Site
| United States Naval Academy
|-
!Number of Students
|na
|-
!Total Participant Hours
|na
|-
!Data Shop
| January, 2008
|}

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through explaining how worked examples are related to the principles. The second path is learning a schema through analogical comparison of two examples and then relating that schema to the principle. These hypotheses are tested in two [[in vivo experiment]]s in the Physics LearnLab.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables the reliable retrieval and use of those concepts to solve novel problems and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. Self-explanation has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and worked examples will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through analogical comparison. Prior work has shown that analogical comparison can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two worked-out examples. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two worked examples and instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on ANDES problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2007-04-03T13:22:47Z

Timothy Nokes: /* Bridging Principles and Examples through Analogy and Explanation */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

===Study 1=== (Laboratory Experiment)
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || May, 2007
|-
| '''Study End Date''' || June, 2007
|-
| '''LearnLab Site''' || University of Pittsburgh
|-
| '''Number of Students''' || 60 (planned)
|-
| '''Total Participant Hours''' || 180 (planned)
|-
| '''Data Shop''' || na
|}
<br

Study 2 (In Vivo)
{| border="1" cellpadding="5" cellspacing="0"
!PIs
|Timothy Nokes and Kurt VanLehn
|-
!Study Start Date
|September 2007
|-
!Study End Date
|December, 2007
|-
!LearnLab Site
| United States Naval Academy
|-
!Number of Students
|na
|-
!Total Participant Hours
|na
|-
!Data Shop
| January, 2008
|}

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through explaining how worked examples are related to the principles. The second path is learning a schema through analogical comparison of two examples and then relating that schema to the principle. These hypotheses are tested in two [[in vivo experiment]]s in the Physics LearnLab.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables the reliable retrieval and use of those concepts to solve novel problems and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. Self-explanation has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and worked examples will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through analogical comparison. Prior work has shown that analogical comparison can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two worked-out examples. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two worked examples and instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on ANDES problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2007-04-03T13:22:28Z

Timothy Nokes: /* Bridging Principles and Examples through Analogy and Explanation */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

===Study 1=== (Laboratory Experiment)
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left;"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || May, 2007
|-
| '''Study End Date''' || June, 2007
|-
| '''LearnLab Site''' || University of Pittsburgh
|-
| '''Number of Students''' || 60 (planned)
|-
| '''Total Participant Hours''' || 180 (planned)
|-
| '''Data Shop''' || na
|}

Study 2 (In Vivo)
{| border="1" cellpadding="5" cellspacing="0"
!PIs
|Timothy Nokes and Kurt VanLehn
|-
!Study Start Date
|September 2007
|-
!Study End Date
|December, 2007
|-
!LearnLab Site
| United States Naval Academy
|-
!Number of Students
|na
|-
!Total Participant Hours
|na
|-
!Data Shop
| January, 2008
|}

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through explaining how worked examples are related to the principles. The second path is learning a schema through analogical comparison of two examples and then relating that schema to the principle. These hypotheses are tested in two [[in vivo experiment]]s in the Physics LearnLab.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables the reliable retrieval and use of those concepts to solve novel problems and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. Self-explanation has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and worked examples will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through analogical comparison. Prior work has shown that analogical comparison can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two worked-out examples. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two worked examples and instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on ANDES problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2007-04-03T13:18:58Z

Timothy Nokes: /* Bridging Principles and Examples through Analogy and Explanation */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

===Study 1=== (Laboratory Experiment)
{| border="1" cellpadding="5" cellspacing="0" style="text-align: left"
| '''PIs''' || Timothy Nokes and Kurt VanLehn
|-
| '''Study Start Date''' || May, 2007
|-
| '''Study End Date''' || June, 2007
|-
| '''LearnLab Site''' || University of Pittsburgh
|-
| '''Number of Students''' || 60 (planned)
|-
| '''Total Participant Hours''' || 180 (planned)
|-
| '''Data Shop''' || na
|}

Study 2 (In Vivo)
{| border="1" cellpadding="5" cellspacing="0"
!PIs
|Timothy Nokes and Kurt VanLehn
|-
!Study Start Date
|September 2007
|-
!Study End Date
|December, 2007
|-
!LearnLab Site
| United States Naval Academy
|-
!Number of Students
|na
|-
!Total Participant Hours
|na
|-
!Data Shop
| January, 2008
|}

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through explaining how worked examples are related to the principles. The second path is learning a schema through analogical comparison of two examples and then relating that schema to the principle. These hypotheses are tested in two [[in vivo experiment]]s in the Physics LearnLab.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables the reliable retrieval and use of those concepts to solve novel problems and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. Self-explanation has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and worked examples will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through analogical comparison. Prior work has shown that analogical comparison can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two worked-out examples. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two worked examples and instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on ANDES problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===

Bridging Principles and Examples through Analogy and Explanation

2007-04-03T13:13:06Z

Timothy Nokes: /* Summary Table */

==Bridging Principles and Examples through Analogy and Explanation==

Timothy J. Nokes and Kurt VanLehn

===Summary Table===

===Study 1=== (Laboratory Experiment)
{| border="1" cellpadding="5" cellspacing="0"
!PIs ||Timothy Nokes and Kurt VanLehn
|-
! '''Study Start Date''' || May, 2007
|-
!Study End Date
|June, 2007
|-
!LearnLab Site
| University of Pittsburgh
|-
!Number of Students
|60 (planned)
|-
!Total Participant Hours
|180 (planned)
|-
!Data Shop
| na
|}

Study 2 (In Vivo)
{| border="1" cellpadding="5" cellspacing="0"
!PIs
|Timothy Nokes and Kurt VanLehn
|-
!Study Start Date
|September 2007
|-
!Study End Date
|December, 2007
|-
!LearnLab Site
| United States Naval Academy
|-
!Number of Students
|na
|-
!Total Participant Hours
|na
|-
!Data Shop
| January, 2008
|}

===Abstract===
The purpose of the current work is to test the hypothesis that learning the relations between principles and examples is critical to deep understanding and [[transfer]]. It is proposed that there are at least two paths to acquiring these relations. The first path is through explaining how worked examples are related to the principles. The second path is learning a schema through analogical comparison of two examples and then relating that schema to the principle. These hypotheses are tested in two [[in vivo experiment]]s in the Physics LearnLab.

===Research Question===
The central problem addressed in this work is how to facilitate students’ deep learning of new concepts. Of particular interest is to determine what learning paths lead to a deep understanding of new concepts that enables the reliable retrieval and use of those concepts to solve novel problems and [[accelerated future learning]].

===Background and Significance===
Much research in cognitive science has shown that when students first learn a new domain such as statistics or physics they rely heavily on prior examples to solve new problems (Anderson, Greeno, Kline, & Neves, 1981; Ross, 1984; VanLehn, 1998). Furthermore, laboratory studies indicate that students prefer to use examples even when they have access to written instructions or principles (LeFerve & Dixon, 1986; Ross, 1987). For example, LeFerve and Dixon (1986) showed that when learning to solve induction problems, students preferred to use the solution procedure illustrated in the example over the one described in the written instructions. Although using examples enables novices to make progress when solving new problems they are often only able to apply such knowledge to near transfer problems with similar surface features (see Reeves & Weissberg, 1994 for a review). It is principally through extended practice in the domain that students begin to develop more ‘expert-like’ abilities such as being able to ‘perceive’ and use the deep structural features of the problem (Chi, Feltovich, & Glaser, 1981) or use a forwards-working problem solving strategy (Sweller, Mawer, & Ward, 1983).

One reason that students may rely so heavily on prior examples to solve new problems is that they lack a deep understanding for how the principles are instantiated in the examples. That is, they may lack the knowledge and skills required for relating the principle components to the problem features. Some prior research by Nisbett and colleagues (Fong, Krantz, & Nisbett, 1986; Fong & Nisbett, 1991) has shown that when students are given brief training on an abstract rule (the statistical principle for the Law of Large Numbers) with illustrating examples they perform better than students trained on the rule or examples alone. This result was shown in a domain where the students were hypothesized to have an intuitive understanding of the principle prior to training. One plausible interpretation of this result is that the students used their intuitive understanding of the principle to relate the abstract rule to the illustrating examples. This possibility is intriguing and suggests that a training procedure designed to facilitate understanding of the relations between principles and examples may result in deep learning.

The current research builds on this result by postulating that learning activities designed to focus students on learning the relations between examples and principles should improve their conceptual understanding and lead to [[robust learning]]. We examine two learning paths to acquiring these relations: [[self-explanation]] and [[analogical comparison]]. Self-explanation has been shown to facilitate both procedural and conceptual learning and [[transfer]] of that knowledge to new contexts. Prior work by Chi, Bassok, Lewis, Reimann, and Glaser (1989) showed that good learners were more likely than poor learners to generate inferences relating the worked examples to the principles and concepts of the problem. This result suggests that ''prompting'' students to self-explain the relations between principles and worked examples will further facilitate learning. Of central interest to the current work is to understand how students learn to coordinate the knowledge representations of principles and examples through explanation. The second path is learning a schema through analogical comparison. Prior work has shown that analogical comparison can facilitate schema abstraction and [[transfer]] to new problems (Gentner, Lowenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001). However, this work has not examined how learning from problem comparison impacts understanding of an abstract principle. The current work examines how analogical comparison may help bridge students’ learning of the relations between principles and examples.

===Independent Variables===
'''Type of instruction'''
*Problem solving
**Participants read through a principle description and two worked-out examples. After reading through the learning materials they solve practice problems.
*Explanation
**Participants read the principle. Next they read the first example problem and are instructed to explain how each solution step relates to the principle / concepts. After completing the first example they perform the same task for the second example.
*Analogy+explanation
**Participants first read the principle and then perform the analogical comparison task. They are given the two worked examples and instructed to compare each part of the examples writing a summary of the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Next, participants are asked to explain how each component of their written summary relates to the principle.

===Dependent Variables===
'''Learning Measures''' (manipulation check)
*Control group: Performance on practice problems
*Explanation group: Content of explanations
*Analogy+explanation group: Comparison summaries and content of explanations
'''Test Measures'''
*[[Normal post-test]]
**Problem solving both with equations given (articulating the solution) and without (determine the correct principle, then solve)
*[[Transfer]]
**Judgment task
***The similarity judgment task consists of a target word problem and three comparison problems (similar to those used by Dufresne, Gerace, Hardiamnn, & Mestre, 1992). The students’ goal in this task is to determine which of the three comparison problems can be solved most similarly to the target problem. The comparison problems will vary in their similarity to the target problem and will have similar surface features (e.g., inclined planes), deep features (e.g., Newton’s Second Law), both surface and deep features, or neither.
**Problem posing
***The problem posing task consists of a problem principle to be tested, set-up, and diagram (adapted from Mestre, 2002). The students’ goal is to generate a statement or question that correctly completes the problem and then explain how their problem tests the basic principle.

*Performance on ANDES problems
**Learning curves
**Solution times
**Error rates

*[[Long-term retention]]
**Tests given after a 1-month delay that include both the [[normal post-test]] and [[transfer]] tasks mentioned above

===Hypotheses===
*Learning the ''relations'' between principles and examples is critical to deep understanding and [[transfer]].
**Generating explanations can serve as one mechanism to facilitate this learning.
**Problem schemas may help bridge the student's understanding between principles and examples.
**Analogical comparison can serve as one mechanism to facilitate schema acquisition.

===Expected Findings===
*If learning the relations is critical for deep understanding and transfer then the groups prompted to explain relations should perform better on the test tasks than the unprompted group.
*If schema acquisition helps bridge this understanding then the Analogy+explanation group should perform best.

*Variety of test tasks will help identify what knowledge components are learned:
**Judgment task: Analogy+explanation > Explanation > Control; more likely to choose problems that match on deep features than surface features.
**Problem solving with equations: Analogy+explanation = Explanation = Control; accuracy
**Problem solving without equations: Analogy+explanation > Explanation > Control; accuracy
**Problem posing: Analogy+explanation > Explanation > Control; accuracy and justifications

*Andes performance: Analogy+explanation > Explanation > Control; errors rates

===Explanation===
Prompting students to explain how each step of a worked example is related to the principles facilitates the generation of inferences connecting the physics principles and concepts to the procedures and equations in the problem. These inferences serve to highlight the importance of the concepts in problem solving and increase the likelihood of future activation when solving novel problems. Furthermore, they serve as the critical links integrating and coordinating the principle [[knowledge components]] with the problem [[features]].

By comparing similarities and differences of worked examples students have an opportunity to identify the important [[features]] of the problems. After having identified the important features they can be related to the principle description through explanation.

===Descendents===
None
=== Annotated Bibliography ===
*Anderson, J. R., Greeno, J. G., Kline, P. J., & Neves, D. M. (1981). Acquisition of problem-solving skill. In J. R. Anderson (Ed.), ''Cognitive skills and their acquisition'' (pp. 191-230). Hillsdale, NJ: Erlbaum.
*Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. ''Cognitive Science, 13'', 145-182.
*Chi, M. T. H., De Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. ''Cognitive Science, 18'', 439-477.
*Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. ''Cognitive Science, 5'', 121-152.
*Dufresne, R. J., Gerace, W. J., Hardiman, P. T., & Mestre, J. P. (1992). Constraining novices to perform expertlike analyses: effects on schema acquisition. ''Journal of the Learning Sciences, 2'', 307-331.
*Fong, G. T., & Nisbett, R. E. (1991). Immediate and delayed transfer of training effects in statistical reasoning. ''Journal of Experimental Psychology: General, 120'', 34-45.
*Fong, G. T., Krantz, D. H., & Nisbett, R. E. (1986). The effects of statistical training on thinking about everyday problems. ''Cognitive Psychology, 18'', 253-292.
*Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. ''Journal of Educational Psychology, 95'', 393-408.
*Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. ''Journal of the Learning Sciences, 10'', 417-446.
*LeFerve, J., & Dixon, P. (1986). Do written instructions need examples? Cognition and Instruction, 3, 1-30.
*Mestre, J. P. (2002). Probing adults’ conceptual understanding and transfer of learning via problem posing. ''Applied Developmental Psychology, 23'', 9-50.
*Reeves, L. M., & Weissberg, W. R. (1994). The role of content and abstract information in analogical transfer. ''Psychological Bulletin, 115'', 381-400.
*Ross, B. H. (1984). Remindings and their effects in learning a cognitive skill. ''Cognitive Psychology, 16'', 371-416.
*Sweller, Mawer, & Ward (1983). Development of expertise in mathematical problem solving. ''Journal of Experimental Psychological: General, 112'', 639-661.
*VanLehn, K. (1998). Analogy events: How examples are used during problem solving. ''Cognitive Science, 22'', 347-388.

===Further Information===