https://learnlab.org/research/wiki/api.php?action=feedcontributions&user=Julie-Booth&feedformat=atomLearnLab - User contributions [en]2024-03-28T13:39:13ZUser contributionsMediaWiki 1.31.12https://learnlab.org/wiki/index.php?title=Booth&diff=9094Booth2009-05-04T18:35:46Z<p>Julie-Booth: /* Findings from Experiments 2 and 3: */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|800px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]] (relevant instructional principle)<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Findings from Experiments 2 and 3:=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, 2009; Booth, Koedinger, & Siegler, 2008)<br />
**Improved the number of problems solved by 10%, while control group improved by 5%. No significant differnence, but experimental group students did at least as well as the control students, even though they had less practice solving problems.<br />
[[Image:procedural.jpg|500px]]<br />
**Improved their percent of conceptual questions answered correctly by 7% (control group ''decreased'' by 1%; p < .05)<br />
[[Image:conceptual.jpg|500px]]<br />
*Recieving [[Corrective self-explanation]] exercises leads to greater improvement in released items from standardized achievement tests. <br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with low and medium-level conceptual knowledge at pretest tend to perform better with [[corrective self-explanation]] than [[typical self-explanation]]<br />
**Students with high conceptual knowledge at pretest perform better with [[typical self-explanation]] than [[corrective self-explanation]].<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Presentations/Publications===<br />
*Booth, J.L. (2009). Improving Algebra Learning in Real World Classrooms with Worked Examples and Self-Explanation. Paper presented at the Presidential Symposium entitled The New Learning Sciences at the annual meeting of the Eastern Psychological Association, Pittsburgh, PA, March 5-8, 2009.<br />
*Booth, J.L., & Koedinger, K.R. (2008). Key misconceptions in algebraic problem solving. In B.C. Love, K. McRae, & V. M. Sloutsky (Eds.), Proceedings of the 30th Annual Cognitive Science Society (pp. 571-576). Austin, TX: Cognitive Science Society.<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2008, July). Using self-explanation to improve algebra learning. Poster presented at the 30th annual meeting of the Cognitive Science Society, Washington, D.C.<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). The effect of prior conceptual knowledge on procedural performance and learning in algebra. Poster presented at the 29th Annual Cognitive Science Society conference in Nashville, TN. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf Abstract]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=9093Booth2009-05-04T18:35:11Z<p>Julie-Booth: /* Findings from Experiments 2 and 3: */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|800px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]] (relevant instructional principle)<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Findings from Experiments 2 and 3:=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, 2009; Booth, Koedinger, & Siegler, 2008)<br />
**Improved the number of problems solved by 10%, while control group improved by 5%. No significant differnence, but experimental group students did at least as well as the control students, even though they had less practice solving problems.<br />
[[Image:procedural.jpg|500px]]<br />
**Improved their percent of conceptual questions answered correctly by 7% (control group ''decreased'' by 1%; p < .05)<br />
[[Image:conceptual.jpg|500px]]<br />
*Recieving [[Corrective self-explanation]] exercises leads to greater improvement in released items from standardized achievment tests. <br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with low and medium-level conceptual knowledge at pretest tend to perform better with [[corrective self-explanation]] than [[typical self-explanation]]<br />
**Students with high conceptual knowledge at pretest perform better with [[typical self-explanation]] than [[corrective self-explanation]].<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Presentations/Publications===<br />
*Booth, J.L. (2009). Improving Algebra Learning in Real World Classrooms with Worked Examples and Self-Explanation. Paper presented at the Presidential Symposium entitled The New Learning Sciences at the annual meeting of the Eastern Psychological Association, Pittsburgh, PA, March 5-8, 2009.<br />
*Booth, J.L., & Koedinger, K.R. (2008). Key misconceptions in algebraic problem solving. In B.C. Love, K. McRae, & V. M. Sloutsky (Eds.), Proceedings of the 30th Annual Cognitive Science Society (pp. 571-576). Austin, TX: Cognitive Science Society.<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2008, July). Using self-explanation to improve algebra learning. Poster presented at the 30th annual meeting of the Cognitive Science Society, Washington, D.C.<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). The effect of prior conceptual knowledge on procedural performance and learning in algebra. Poster presented at the 29th Annual Cognitive Science Society conference in Nashville, TN. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf Abstract]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=9092Booth2009-05-04T18:20:52Z<p>Julie-Booth: /* Findings from Experiments 2 and 3: */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|800px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]] (relevant instructional principle)<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Findings from Experiments 2 and 3:=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, 2009; Booth, Koedinger, & Siegler, 2008)<br />
**Improved the number of problems solved by 10%, while control group improved by 5%. No significant differnence, but experimental group students did at least as well as the control students, even though they had less practice solving problems.<br />
[[Image:procedural.jpg|500px]]<br />
**Improved their percent of conceptual questions answered correctly by 7% (control group ''decreased'' by 1%; p < .05)<br />
[[Image:conceptual.jpg|500px]]<br />
*Recieving [[Corrective self-explanation]] exercises leads to greater improvement in released items from standardized achievment tests. <br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Presentations/Publications===<br />
*Booth, J.L. (2009). Improving Algebra Learning in Real World Classrooms with Worked Examples and Self-Explanation. Paper presented at the Presidential Symposium entitled The New Learning Sciences at the annual meeting of the Eastern Psychological Association, Pittsburgh, PA, March 5-8, 2009.<br />
*Booth, J.L., & Koedinger, K.R. (2008). Key misconceptions in algebraic problem solving. In B.C. Love, K. McRae, & V. M. Sloutsky (Eds.), Proceedings of the 30th Annual Cognitive Science Society (pp. 571-576). Austin, TX: Cognitive Science Society.<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2008, July). Using self-explanation to improve algebra learning. Poster presented at the 30th annual meeting of the Cognitive Science Society, Washington, D.C.<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). The effect of prior conceptual knowledge on procedural performance and learning in algebra. Poster presented at the 29th Annual Cognitive Science Society conference in Nashville, TN. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf Abstract]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=9091Booth2009-05-04T18:20:18Z<p>Julie-Booth: /* Presentations/Publications */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|800px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]] (relevant instructional principle)<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Findings from Experiments 2 and 3:=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth & Koedinger, 2009)<br />
**Improved the number of problems solved by 10%, while control group improved by 5%. No significant differnence, but experimental group students did at least as well as the control students, even though they had less practice solving problems.<br />
[[Image:procedural.jpg|500px]]<br />
**Improved their percent of conceptual questions answered correctly by 7% (control group ''decreased'' by 1%; p < .05)<br />
[[Image:conceptual.jpg|500px]]<br />
*Recieving [[Corrective self-explanation]] exercises leads to greater improvement in released items from standardized achievment tests. <br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Presentations/Publications===<br />
*Booth, J.L. (2009). Improving Algebra Learning in Real World Classrooms with Worked Examples and Self-Explanation. Paper presented at the Presidential Symposium entitled The New Learning Sciences at the annual meeting of the Eastern Psychological Association, Pittsburgh, PA, March 5-8, 2009.<br />
*Booth, J.L., & Koedinger, K.R. (2008). Key misconceptions in algebraic problem solving. In B.C. Love, K. McRae, & V. M. Sloutsky (Eds.), Proceedings of the 30th Annual Cognitive Science Society (pp. 571-576). Austin, TX: Cognitive Science Society.<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2008, July). Using self-explanation to improve algebra learning. Poster presented at the 30th annual meeting of the Cognitive Science Society, Washington, D.C.<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). The effect of prior conceptual knowledge on procedural performance and learning in algebra. Poster presented at the 29th Annual Cognitive Science Society conference in Nashville, TN. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf Abstract]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=File:Conceptual.jpg&diff=9090File:Conceptual.jpg2009-05-04T18:18:31Z<p>Julie-Booth: </p>
<hr />
<div></div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=File:Procedural.jpg&diff=9089File:Procedural.jpg2009-05-04T18:18:08Z<p>Julie-Booth: </p>
<hr />
<div></div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=9088Booth2009-05-04T18:17:57Z<p>Julie-Booth: /* Findings from Experiments 2 and 3: */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|800px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]] (relevant instructional principle)<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Findings from Experiments 2 and 3:=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth & Koedinger, 2009)<br />
**Improved the number of problems solved by 10%, while control group improved by 5%. No significant differnence, but experimental group students did at least as well as the control students, even though they had less practice solving problems.<br />
[[Image:procedural.jpg|500px]]<br />
**Improved their percent of conceptual questions answered correctly by 7% (control group ''decreased'' by 1%; p < .05)<br />
[[Image:conceptual.jpg|500px]]<br />
*Recieving [[Corrective self-explanation]] exercises leads to greater improvement in released items from standardized achievment tests. <br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Presentations/Publications===<br />
<br />
*Booth, J.L., & Koedinger, K.R. (2008). Key misconceptions in algebraic problem solving. In B.C. Love, K. McRae, & V. M. Sloutsky (Eds.), Proceedings of the 30th Annual Cognitive Science Society (pp. 571-576). Austin, TX: Cognitive Science Society.<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2008, July). Using self-explanation to improve algebra learning. Poster presented at the 30th annual meeting of the Cognitive Science Society, Washington, D.C.<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). The effect of prior conceptual knowledge on procedural performance and learning in algebra. Poster presented at the 29th Annual Cognitive Science Society conference in Nashville, TN. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf Abstract]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=9083Booth2009-05-04T18:15:02Z<p>Julie-Booth: /* Findings */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|800px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]] (relevant instructional principle)<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Findings from Experiments 2 and 3:=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth & Koedinger, 2009)<br />
**Improved the number of problems solved by 10%, while control group improved by 5%. No significant differnence, but experimental group students did at least as well as the control students, even though they had less practice solving problems.<br />
[[Image:procedural.png|500px]]<br />
**Improved their percent of conceptual questions answered correctly by 7% (control group ''decreased'' by 1%; p < .05)<br />
[[Image:conceptual.png|500px]]<br />
*Recieving [[Corrective self-explanation]] exercises leads to greater improvement in released items from standardized achievment tests. <br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Presentations/Publications===<br />
<br />
*Booth, J.L., & Koedinger, K.R. (2008). Key misconceptions in algebraic problem solving. In B.C. Love, K. McRae, & V. M. Sloutsky (Eds.), Proceedings of the 30th Annual Cognitive Science Society (pp. 571-576). Austin, TX: Cognitive Science Society.<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2008, July). Using self-explanation to improve algebra learning. Poster presented at the 30th annual meeting of the Cognitive Science Society, Washington, D.C.<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). The effect of prior conceptual knowledge on procedural performance and learning in algebra. Poster presented at the 29th Annual Cognitive Science Society conference in Nashville, TN. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf Abstract]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=9079Booth2009-05-04T18:06:05Z<p>Julie-Booth: /* Presentations/Publications */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|800px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]] (relevant instructional principle)<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Findings from Experiment 2(pilot):=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, Koedinger, & Siegler, 2007b)<br />
**Improved the number of attempted problems solved by 18% (control group ''decreased'' percent correct by 17%)<br />
[[Image:Exp2results2.jpg|500px]]<br />
**Reduced the amount of conceptual errors made on problems by 32% (control group ''increased'' these errors by 40%) (interaction significant at p<.05)<br />
[[Image:Exp2results1.jpg|500px]]<br />
*Recieving [[Corrective self-explanation]] exercises may uniquely reduce student misconceptions about problem [[features]]<br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Presentations/Publications===<br />
<br />
*Booth, J.L., & Koedinger, K.R. (2008). Key misconceptions in algebraic problem solving. In B.C. Love, K. McRae, & V. M. Sloutsky (Eds.), Proceedings of the 30th Annual Cognitive Science Society (pp. 571-576). Austin, TX: Cognitive Science Society.<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2008, July). Using self-explanation to improve algebra learning. Poster presented at the 30th annual meeting of the Cognitive Science Society, Washington, D.C.<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). The effect of prior conceptual knowledge on procedural performance and learning in algebra. Poster presented at the 29th Annual Cognitive Science Society conference in Nashville, TN. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf Abstract]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=9078Booth2009-05-04T18:05:08Z<p>Julie-Booth: /* Further Information */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|800px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]] (relevant instructional principle)<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Findings from Experiment 2(pilot):=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, Koedinger, & Siegler, 2007b)<br />
**Improved the number of attempted problems solved by 18% (control group ''decreased'' percent correct by 17%)<br />
[[Image:Exp2results2.jpg|500px]]<br />
**Reduced the amount of conceptual errors made on problems by 32% (control group ''increased'' these errors by 40%) (interaction significant at p<.05)<br />
[[Image:Exp2results1.jpg|500px]]<br />
*Recieving [[Corrective self-explanation]] exercises may uniquely reduce student misconceptions about problem [[features]]<br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Presentations/Publications===<br />
*Booth, J.L., & Olsen, J.K. (2009, April). Encoding of equation features relates to conceptual and procedural knowledge of algebra. Poster presented at the meeting of the Society for Research in Child Development, Denver, CO.<br />
*Booth, J.L., & Koedinger, K.R. (2008). Key misconceptions in algebraic problem solving. In B.C. Love, K. McRae, & V. M. Sloutsky (Eds.), Proceedings of the 30th Annual Cognitive Science Society (pp. 571-576). Austin, TX: Cognitive Science Society.<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2008, July). Using self-explanation to improve algebra learning. Poster presented at the 30th annual meeting of the Cognitive Science Society, Washington, D.C.<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). The effect of prior conceptual knowledge on procedural performance and learning in algebra. Poster presented at the 29th Annual Cognitive Science Society conference in Nashville, TN. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf Abstract]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
<br />
<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=9077Booth2009-05-04T18:04:52Z<p>Julie-Booth: /* Presentations/Publications */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|800px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]] (relevant instructional principle)<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Findings from Experiment 2(pilot):=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, Koedinger, & Siegler, 2007b)<br />
**Improved the number of attempted problems solved by 18% (control group ''decreased'' percent correct by 17%)<br />
[[Image:Exp2results2.jpg|500px]]<br />
**Reduced the amount of conceptual errors made on problems by 32% (control group ''increased'' these errors by 40%) (interaction significant at p<.05)<br />
[[Image:Exp2results1.jpg|500px]]<br />
*Recieving [[Corrective self-explanation]] exercises may uniquely reduce student misconceptions about problem [[features]]<br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Presentations/Publications===<br />
*Booth, J.L., & Olsen, J.K. (2009, April). Encoding of equation features relates to conceptual and procedural knowledge of algebra. Poster presented at the meeting of the Society for Research in Child Development, Denver, CO.<br />
*Booth, J.L., & Koedinger, K.R. (2008). Key misconceptions in algebraic problem solving. In B.C. Love, K. McRae, & V. M. Sloutsky (Eds.), Proceedings of the 30th Annual Cognitive Science Society (pp. 571-576). Austin, TX: Cognitive Science Society.<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2008, July). Using self-explanation to improve algebra learning. Poster presented at the 30th annual meeting of the Cognitive Science Society, Washington, D.C.<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). The effect of prior conceptual knowledge on procedural performance and learning in algebra. Poster presented at the 29th Annual Cognitive Science Society conference in Nashville, TN. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf Abstract]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
<br />
===Further Information===<br />
<br />
=====Plans for January 2008-June 2008=====<br />
<br />
• Write and submit a paper to the meeting of the Cognitive Science Society (complete)<br />
<br />
• Complete data collection for Experiment 3 in two schools (complete)<br />
<br />
• Code and analyze data from Experiment 3 to determine whether [[corrective self-explanation]] improved [[robust learning]] of algebraic problem-solving. <br />
<br />
• Analyze [[individual differences]] in the effectiveness of combining [[corrective self-explanation]] with tutored [[procedural]] practice based on pretest [[conceptual knowledge]] and understanding of [[features]].<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Geometry&diff=7603Geometry2008-03-31T21:41:51Z<p>Julie-Booth: </p>
<hr />
<div>The Geometry LearnLab course is described [http://learnlab.org/learnlabs/geometry/ here].<br />
<br />
Numerous studies in the Geometry LearnLab course can be found in all three of the research clusters: [[Coordinative Learning]], [[Interactive Communication]], and [[Refinement and Fluency]].<br />
<br />
'''Geometry Learnlab Studies:'''<br />
<br />
*[[Contiguous Representations for Robust Learning (Aleven & Butcher)]]<br />
*[[Mapping Visual and Verbal Information: Integrated Hints in Geometry (Aleven & Butcher)]]<br />
**[[Training Geometry Concepts with Visual and Verbal Sources (Burchfield, Aleven, & Butcher)]]<br />
*[[Visual Feature Focus in Geometry: Instructional Support for Visual Coordination During Learning (Butcher & Aleven)]]<br />
*[[Using Elaborated Explanations to Support Geometry Learning (Aleven & Butcher)]]<br />
*[[Help_Lite (Aleven, Roll)|Hints during tutored problem solving – the effect of fewer hint levels with greater conceptual content (Aleven & Roll)]]<br />
*[[Does learning from worked-out examples improve tutored problem solving? | Does learning from worked-out examples improve tutored problem solving? (Renkl, Aleven & Salden)]]<br />
* [[The_Help_Tutor__Roll_Aleven_McLaren|Tutoring a meta-cognitive skill: Help-seeking (Roll, Aleven & McLaren)]]<br />
* [[Composition_Effect__Kao_Roll|What is difficult about composite problems? (Kao, Roll)]]<br />
* [[Using learning curves to optimize problem assignment]] (Cen & Koedinger)</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Geometry&diff=7602Geometry2008-03-31T21:41:26Z<p>Julie-Booth: </p>
<hr />
<div>The Geometry LearnLab course is described [http://learnlab.org/learnlabs/geometry/ here].<br />
<br />
Numerous studies in the Geometry LearnLab course can be found in all three of the research clusters: [[Coordinative Learning]], [[Interactive Communication]], and [[Refinement and Fluency]].<br />
<br />
'''Geometry Learnlab Studies:'''<br />
<br />
*[[Contiguous Representations for Robust Learning (Aleven & Butcher)]]<br />
*[[Mapping Visual and Verbal Information: Integrated Hints in Geometry (Aleven & Butcher)]]<br />
**[[Training Geometry Concepts with Visual and Verbal Sources (Burchfield, Aleven, & Butcher)]]<br />
*[[Visual Feature Focus in Geometry: Instructional Support for Visual Coordination During Learning (Butcher & Aleven)]]<br />
*[[Using Elaborated Explanations to Support Geometry Learning (Aleven & Butcher)]]<br />
*[[Help_Lite (Aleven, Roll)|Hints during tutored problem solving – the effect of fewer hint levels with greater conceptual content (Aleven & Roll)]]<br />
*[[Does learning from worked-out examples improve tutored problem solving? | Does learning from worked-out examples improve tutored problem solving? (Renkl, Aleven & Salden)]]<br />
* [[The_Help_Tutor__Roll_Aleven_McLaren|Tutoring a meta-cognitive skill: Help-seeking (Roll, Aleven & McLaren)]]<br />
* [[Composition_Effect__Kao_Roll|What is difficult about composite problems? (Kao, Roll)]]<br />
* [[Using learning curves to optimize problem assignment (Cen & Koedinger)]]</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Geometry&diff=7601Geometry2008-03-31T21:41:02Z<p>Julie-Booth: </p>
<hr />
<div>The Geometry LearnLab course is described [http://learnlab.org/learnlabs/geometry/ here].<br />
<br />
Numerous studies in the Geometry LearnLab course can be found in all three of the research clusters: [[Coordinative Learning]], [[Interactive Communication]], and [[Refinement and Fluency]].<br />
<br />
'''Geometry Learnlab Studies:'''<br />
<br />
*[[Contiguous Representations for Robust Learning (Aleven & Butcher)]]<br />
*[[Mapping Visual and Verbal Information: Integrated Hints in Geometry (Aleven & Butcher)]]<br />
**[[Training Geometry Concepts with Visual and Verbal Sources (Burchfield, Aleven, & Butcher)]]<br />
*[[Visual Feature Focus in Geometry: Instructional Support for Visual Coordination During Learning (Butcher & Aleven)]]<br />
*[[Using Elaborated Explanations to Support Geometry Learning (Aleven & Butcher)]]<br />
*[[Help_Lite (Aleven, Roll)|Hints during tutored problem solving – the effect of fewer hint levels with greater conceptual content (Aleven & Roll)]]<br />
*[[Does learning from worked-out examples improve tutored problem solving? | Does learning from worked-out examples improve tutored problem solving? (Renkl, Aleven & Salden)]]<br />
* [[The_Help_Tutor__Roll_Aleven_McLaren|Tutoring a meta-cognitive skill: Help-seeking (Roll, Aleven & McLaren)]]<br />
* [[Composition_Effect__Kao_Roll|What is difficult about composite problems? (Kao, Roll)]]<br />
* [[Using learning curves to optimize problem assignment]] (Cen & Koedinger)</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Geometry&diff=7600Geometry2008-03-31T21:40:18Z<p>Julie-Booth: </p>
<hr />
<div>The Geometry LearnLab course is described [http://learnlab.org/learnlabs/geometry/ here].<br />
<br />
Numerous studies in the Geometry LearnLab course can be found in all three of the research clusters: [[Coordinative Learning]], [[Interactive Communication]], and [[Refinement and Fluency]].<br />
<br />
'''Geometry Learnlab Studies:'''<br />
<br />
*[[Contiguous Representations for Robust Learning (Aleven & Butcher)]]<br />
*[[Mapping Visual and Verbal Information: Integrated Hints in Geometry (Aleven & Butcher)]]<br />
**[[Training Geometry Concepts with Visual and Verbal Sources (Burchfield, Aleven, & Butcher)]]<br />
*[[Visual Feature Focus in Geometry: Instructional Support for Visual Coordination During Learning (Butcher & Aleven)]]<br />
*[[Using Elaborated Explanations to Support Geometry Learning (Aleven & Butcher)]]<br />
*[[Help_Lite (Aleven, Roll)|Hints during tutored problem solving – the effect of fewer hint levels with greater conceptual content (Aleven & Roll)]]<br />
*[[Does learning from worked-out examples improve tutored problem solving? | Does learning from worked-out examples improve tutored problem solving? (Renkl, Aleven & Salden)]]<br />
* [[The_Help_Tutor__Roll_Aleven_McLaren|Tutoring a meta-cognitive skill: Help-seeking (Roll, Aleven & McLaren)]] [Also in Interactive Communication]<br />
* [[Composition_Effect__Kao_Roll|What is difficult about composite problems? (Kao, Roll)]]</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Geometry&diff=7599Geometry2008-03-31T21:37:35Z<p>Julie-Booth: </p>
<hr />
<div>The Geometry LearnLab course is described [http://learnlab.org/learnlabs/geometry/ here].<br />
<br />
Numerous studies in the Geometry LearnLab course can be found in all three of the research clusters: [[Coordinative Learning]], [[Interactive Communication]], and [[Refinement and Fluency]].<br />
<br />
'''Geometry Learnlab Studies:'''<br />
<br />
*[[Contiguous Representations for Robust Learning (Aleven & Butcher)]]<br />
*[[Mapping Visual and Verbal Information: Integrated Hints in Geometry (Aleven & Butcher)]]<br />
**[[Training Geometry Concepts with Visual and Verbal Sources (Burchfield, Aleven, & Butcher)]]<br />
*[[Visual Feature Focus in Geometry: Instructional Support for Visual Coordination During Learning (Butcher & Aleven)]]<br />
*[[Using Elaborated Explanations to Support Geometry Learning (Aleven & Butcher)]]<br />
*[[Help_Lite (Aleven, Roll)|Hints during tutored problem solving – the effect of fewer hint levels with greater conceptual content (Aleven & Roll)]]<br />
*[[Does learning from worked-out examples improve tutored problem solving? | Does learning from worked-out examples improve tutored problem solving? (Renkl, Aleven & Salden)]]</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Algebra&diff=7598Algebra2008-03-31T21:36:29Z<p>Julie-Booth: </p>
<hr />
<div>The Algebra LearnLab course is described [http://learnlab.org/learnlabs/algebra/ here].<br />
<br />
The Algebra LearnLab course involves teaching high school Algebra I using the textbook and tutoring system of Carnegie Learning. The curriculum combines software-based, individualized computer lessons with collaborative, real-world problem-solving activities. Students spend about 40% of their class time using the software, and the balance of their time engaged in classroom problem-solving activities. Three Pittsburgh-area high schools are currently participating as PSLC Algebra LearnLab sites, offering a diverse student population, and additional high schools around the country are anticipated for future participation. Algebra I topics include: <br />
<br />
*Organizing Single Variable Data <br />
*Simplifying Linear Expressions <br />
*Finding Linear Equations from Graphs <br />
*Solving Linear Equations and Inequalities <br />
*Standard Form <br />
*Slope Intercept Form <br />
*Mathematical Modeling <br />
*Linear Expressions and Equations <br />
*Quadratic Expressions and Equations <br />
*Solving Systems of Linear Equations Algebraically and Graphically <br />
*Solving and Graphing Equations Involving Absolute Values <br />
*Problem Solving using Proportional Reasoning <br />
*Analyzing Data and Making Predictions <br />
*Powers and Exponents <br />
<br />
Numerous studies in the algebra LearnLab course can be found in all three of the research clusters: [[Coordinative Learning]], [[Interactive Communication]], and [[Refinement and Fluency]].<br />
<br />
'''Algebra Learnlab Studies'''<br />
<br />
*[[Booth | Improving skill at solving equations through better encoding of algebraic concepts (Booth, Siegler, Koedinger & Rittle-Johnson)]]<br />
*[[Handwriting Algebra Tutor]] (Anthony, Yang & Koedinger)<br />
**[[Lab study proof-of-concept for handwriting vs typing input for learning algebra equation-solving]] (completed)<br />
**[[Effect of adding simple worked examples to problem-solving in algebra learning]] (completed, analysis in progress)<br />
**[[In vivo comparison of Cognitive Tutor Algebra using handwriting vs typing input]] (in progress)<br />
*[[Rummel_Scripted_Collaborative_Problem_Solving|Collaborative Extensions to the Cognitive Tutor Algebra: Scripted Collaborative Problem Solving (Rummel, Diziol, McLaren, & Spada)]]<br />
*[[Walker_A_Peer_Tutoring_Addition|Collaborative Extensions to the Cognitive Tutor Algebra: A Peer Tutoring Addition (Walker, McLaren, Koedinger, & Rummel)]]</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Algebra&diff=7510Algebra2008-03-25T17:12:37Z<p>Julie-Booth: </p>
<hr />
<div>The Algebra LearnLab course is described [http://learnlab.org/learnlabs/algebra/ here].<br />
<br />
The Algebra LearnLab course involves teaching high school Algebra I using the textbook and tutoring system of Carnegie Learning. The curriculum combines software-based, individualized computer lessons with collaborative, real-world problem-solving activities. Students spend about 40% of their class time using the software, and the balance of their time engaged in classroom problem-solving activities. Three Pittsburgh-area high schools are currently participating as PSLC Algebra LearnLab sites, offering a diverse student population, and additional high schools around the country are anticipated for future participation. Algebra I topics include: <br />
<br />
*Organizing Single Variable Data <br />
*Simplifying Linear Expressions <br />
*Finding Linear Equations from Graphs <br />
*Solving Linear Equations and Inequalities <br />
*Standard Form <br />
*Slope Intercept Form <br />
*Mathematical Modeling <br />
*Linear Expressions and Equations <br />
*Quadratic Expressions and Equations <br />
*Solving Systems of Linear Equations Algebraically and Graphically <br />
*Solving and Graphing Equations Involving Absolute Values <br />
*Problem Solving using Proportional Reasoning <br />
*Analyzing Data and Making Predictions <br />
*Powers and Exponents <br />
<br />
Numerous studies in the algebra LearnLab course can be found in all three of the research clusters: [[Coordinative Learning]], [[Interactive Communication]], and [[Refinement and Fluency]].<br />
<br />
'''Algebra Learnlab Studies'''<br />
<br />
*[[Booth | Improving skill at solving equations through better encoding of algebraic concepts (Booth, Siegler, Koedinger & Rittle-Johnson)]]<br />
*[[Handwriting Algebra Tutor]] (Anthony, Yang & Koedinger)<br />
**[[Lab study proof-of-concept for handwriting vs typing input for learning algebra equation-solving]] (completed)<br />
**[[Effect of adding simple worked examples to problem-solving in algebra learning]] (completed, analysis in progress)<br />
**[[In vivo comparison of Cognitive Tutor Algebra using handwriting vs typing input]] (in progress)</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Geometry&diff=7509Geometry2008-03-25T17:08:54Z<p>Julie-Booth: </p>
<hr />
<div>The Geometry LearnLab course is described [http://learnlab.org/learnlabs/geometry/ here].<br />
<br />
Numerous studies in the Geometry LearnLab course can be found in all three of the research clusters: [[Coordinative Learning]], [[Interactive Communication]], and [[Refinement and Fluency]].<br />
<br />
'''Geometry Learnlab Studies:'''<br />
<br />
*[[Contiguous Representations for Robust Learning (Aleven & Butcher)]]<br />
*[[Mapping Visual and Verbal Information: Integrated Hints in Geometry (Aleven & Butcher)]]<br />
**[[Training Geometry Concepts with Visual and Verbal Sources (Burchfield, Aleven, & Butcher)]]<br />
*[[Visual Feature Focus in Geometry: Instructional Support for Visual Coordination During Learning (Butcher & Aleven)]]<br />
*[[Help_Lite (Aleven, Roll)|Hints during tutored problem solving – the effect of fewer hint levels with greater conceptual content (Aleven & Roll)]]<br />
*[[Does learning from worked-out examples improve tutored problem solving? | Does learning from worked-out examples improve tutored problem solving? (Renkl, Aleven & Salden)]]</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Algebra&diff=7508Algebra2008-03-25T17:08:36Z<p>Julie-Booth: </p>
<hr />
<div>The Algebra LearnLab course is described [http://learnlab.org/learnlabs/algebra/ here].<br />
<br />
Numerous studies in the algebra LearnLab course can be found in all three of the research clusters: [[Coordinative Learning]], [[Interactive Communication]], and [[Refinement and Fluency]].<br />
<br />
'''Algebra Learnlab Studies'''<br />
<br />
*[[Booth | Improving skill at solving equations through better encoding of algebraic concepts (Booth, Siegler, Koedinger & Rittle-Johnson)]]<br />
*[[Handwriting Algebra Tutor]] (Anthony, Yang & Koedinger)<br />
**[[Lab study proof-of-concept for handwriting vs typing input for learning algebra equation-solving]] (completed)<br />
**[[Effect of adding simple worked examples to problem-solving in algebra learning]] (completed, analysis in progress)<br />
**[[In vivo comparison of Cognitive Tutor Algebra using handwriting vs typing input]] (in progress)</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Geometry&diff=7507Geometry2008-03-25T17:08:19Z<p>Julie-Booth: </p>
<hr />
<div>The Geometry LearnLab course is described [http://learnlab.org/learnlabs/geometry/ here].<br />
<br />
Numerous studies in the Geometry LearnLab course can be found in all three of the research clusters: [[Coordinative Learning]], [[Interactive Communication]], and [[Refinement and Fluency]].<br />
<br />
''Geometry Learnlab Studies:''<br />
<br />
*[[Contiguous Representations for Robust Learning (Aleven & Butcher)]]<br />
*[[Mapping Visual and Verbal Information: Integrated Hints in Geometry (Aleven & Butcher)]]<br />
**[[Training Geometry Concepts with Visual and Verbal Sources (Burchfield, Aleven, & Butcher)]]<br />
*[[Visual Feature Focus in Geometry: Instructional Support for Visual Coordination During Learning (Butcher & Aleven)]]<br />
*[[Help_Lite (Aleven, Roll)|Hints during tutored problem solving – the effect of fewer hint levels with greater conceptual content (Aleven & Roll)]]<br />
*[[Does learning from worked-out examples improve tutored problem solving? | Does learning from worked-out examples improve tutored problem solving? (Renkl, Aleven & Salden)]]</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Geometry&diff=7506Geometry2008-03-25T17:06:58Z<p>Julie-Booth: </p>
<hr />
<div>The Geometry LearnLab course is described [http://learnlab.org/learnlabs/geometry/ here].<br />
<br />
Numerous studies in the Geometry LearnLab course can be found in all three of the research clusters: [[Coordinative Learning]], [[Interactive Communication]], and [[Refinement and Fluency]].<br />
<br />
<br />
<br />
*[[Contiguous Representations for Robust Learning (Aleven & Butcher)]]<br />
*[[Mapping Visual and Verbal Information: Integrated Hints in Geometry (Aleven & Butcher)]]<br />
**[[Training Geometry Concepts with Visual and Verbal Sources (Burchfield, Aleven, & Butcher)]]<br />
*[[Visual Feature Focus in Geometry: Instructional Support for Visual Coordination During Learning (Butcher & Aleven)]]</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Corrective_self-explanation&diff=7505Corrective self-explanation2008-03-25T17:05:04Z<p>Julie-Booth: /* Conditions of application */</p>
<hr />
<div>==Brief statement of principle==<br />
Explaining how and why incorrect solutions are incorrect will help students to reject incorrect [[knowledge components]] and, thus, stop using incorrect strategies to solve problems.<br />
<br />
Corrective self-explanation is a kind of [[error correction support]] which is a kind of [[instructional method]].<br />
<br />
==Description of principle==<br />
<br />
===Operational definition===<br />
<br />
Corrective self-explanation is [[self-explanation]]s of ''incorrect'' [[worked examples]]; explaining how and why they are incorrect. See the study by [[Booth]].<br />
<br />
<br />
===Examples===<br />
[[Booth]]'s Corrective self-explanation exercises: [[Image:CSE3.jpg]]<br />
<br />
==Experimental support==<br />
<br />
===Laboratory experiment support===<br />
<br />
Siegler (2002) found that having students self-explain incorrect answers as well as correct answers increased learning of mathematical equality problems than explaining only correct answers. <br />
<br />
Siegler & Chen (in press) also found that asking children to explain both why correct answers were correct and why incorrect answers were incorrect was more effective for learning to solve water displacement problems than only requesting explanations of correct answers. <br />
<br />
===In vivo experiment support===<br />
<br />
Preliminary results from [[Booth]] suggest that while completing any typical or corrective self-explanation exercises improve procedural performance for solving algebraic equations (Booth, Koedinger, & Siegler, 2007), corrective self-explanation may uniquely improve conceptual knowledge about features in the equations. <br />
<br />
==Theoretical rationale== <br />
As a form of [[self-explanation]], corrective self-explanation works via making knowledge explicit. Unlike typical [[self-explanation]], however, corrective self-explanation focuses on making explicit 1) ''that'' a given [[knowledge component]] is wrong and 2) ''why'' the [[knowledge component]] is wrong (what [[features]] about the situation make the knowledge inappropriate.<br />
<br />
==Conditions of application==<br />
1. Corrective self-explanation is likely only useful when students also recieve experience that will facilitate [[construction]] of correct [[knowledge components]]. If students recieve only corrective self-explanation, they may come to reject their incorrect [[knowledge components]], but if they have nothing to replace them with, they will either flounder (having no way to solve the problem), or revert to use of the only strategy they know, even though they know it is incorrect.<br />
<br />
2. Grosse & Renkl (in press) also show that explaining incorrect examples is difficult for poor learners if the step where the error occurred is highlighted. If this is not made clear, students have difficulty detecting and explaining the error.<br />
<br />
==Caveats, limitations, open issues, or dissenting views==<br />
==Variations (descendants)==<br />
==Generalizations (ascendants)==<br />
[[Prompted Self-explanation]]<br />
<br />
==References==<br />
Booth, J.L., Koedinger, K., & Siegler, R.S. (2007, October). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC.<br />
<br />
Grosse & Renkl (in press). Finding and fixing errors in worked examples: Can this foster<br />
learning outcomes? Learning and Instruction.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), ''Microdevelopment: Transition processes in development and learning'' (pp. 31-58). New York: Cambridge University.<br />
<br />
Siegler, R.S., & Chen, Z. (in press). ''Developmental Science''.<br />
<br />
[[Category:Glossary]]<br />
[[Category:Instructional Principle]]<br />
<br />
<br />
[[Category:Glossary]]<br />
[[Category:Independent Variables]]<br />
[[Category:Booth]]</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Algebra&diff=7504Algebra2008-03-25T17:03:13Z<p>Julie-Booth: </p>
<hr />
<div>The Algebra LearnLab course is described [http://learnlab.org/learnlabs/algebra/ here].<br />
<br />
Numerous studies in the algebra LearnLab course can be found in all three of the research clusters: [[Coordinative Learning]], [[Interactive Communication]], and [[Refinement and Fluency]].<br />
<br />
'''Algebra Learnlab Studies'''<br />
<br />
*[[Booth | Improving skill at solving equations through better encoding of algebraic concepts (Booth, Siegler, Koedinger & Rittle-Johnson)]]</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Corrective_self-explanation&diff=7495Corrective self-explanation2008-03-25T16:40:43Z<p>Julie-Booth: /* References */</p>
<hr />
<div>==Brief statement of principle==<br />
Explaining how and why incorrect solutions are incorrect will help students to reject incorrect [[knowledge components]] and, thus, stop using incorrect strategies to solve problems.<br />
<br />
Corrective self-explanation is a kind of [[error correction support]] which is a kind of [[instructional method]].<br />
<br />
==Description of principle==<br />
<br />
===Operational definition===<br />
<br />
Corrective self-explanation is [[self-explanation]]s of ''incorrect'' [[worked examples]]; explaining how and why they are incorrect. See the study by [[Booth]].<br />
<br />
<br />
===Examples===<br />
[[Booth]]'s Corrective self-explanation exercises: [[Image:CSE3.jpg]]<br />
<br />
==Experimental support==<br />
<br />
===Laboratory experiment support===<br />
<br />
Siegler (2002) found that having students self-explain incorrect answers as well as correct answers increased learning of mathematical equality problems than explaining only correct answers. <br />
<br />
Siegler & Chen (in press) also found that asking children to explain both why correct answers were correct and why incorrect answers were incorrect was more effective for learning to solve water displacement problems than only requesting explanations of correct answers. <br />
<br />
===In vivo experiment support===<br />
<br />
Preliminary results from [[Booth]] suggest that while completing any typical or corrective self-explanation exercises improve procedural performance for solving algebraic equations (Booth, Koedinger, & Siegler, 2007), corrective self-explanation may uniquely improve conceptual knowledge about features in the equations. <br />
<br />
==Theoretical rationale== <br />
As a form of [[self-explanation]], corrective self-explanation works via making knowledge explicit. Unlike typical [[self-explanation]], however, corrective self-explanation focuses on making explicit 1) ''that'' a given [[knowledge component]] is wrong and 2) ''why'' the [[knowledge component]] is wrong (what [[features]] about the situation make the knowledge inappropriate.<br />
<br />
==Conditions of application==<br />
Corrective self-explanation is likely only useful when students also recieve experience that will facilitate [[construction]] of correct [[knowledge components]]. If students recieve only corrective self-explanation, they may come to reject their incorrect [[knowledge components]], but if they have nothing to replace them with, they will either flounder (having no way to solve the problem), or revert to use of the only strategy they know, even though they know it is incorrect.<br />
<br />
Grosse & Renkl (in press) also show that explaining incorrect examples is difficult for poor learners if the step where the error occurred is highlighted. If this is not made clear, students have difficulty detecting and explaining the error.<br />
<br />
==Caveats, limitations, open issues, or dissenting views==<br />
==Variations (descendants)==<br />
==Generalizations (ascendants)==<br />
[[Prompted Self-explanation]]<br />
<br />
==References==<br />
Booth, J.L., Koedinger, K., & Siegler, R.S. (2007, October). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC.<br />
<br />
Grosse & Renkl (in press). Finding and fixing errors in worked examples: Can this foster<br />
learning outcomes? Learning and Instruction.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), ''Microdevelopment: Transition processes in development and learning'' (pp. 31-58). New York: Cambridge University.<br />
<br />
Siegler, R.S., & Chen, Z. (in press). ''Developmental Science''.<br />
<br />
[[Category:Glossary]]<br />
[[Category:Instructional Principle]]<br />
<br />
<br />
[[Category:Glossary]]<br />
[[Category:Independent Variables]]<br />
[[Category:Booth]]</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Corrective_self-explanation&diff=7493Corrective self-explanation2008-03-25T16:37:28Z<p>Julie-Booth: /* Conditions of application */</p>
<hr />
<div>==Brief statement of principle==<br />
Explaining how and why incorrect solutions are incorrect will help students to reject incorrect [[knowledge components]] and, thus, stop using incorrect strategies to solve problems.<br />
<br />
Corrective self-explanation is a kind of [[error correction support]] which is a kind of [[instructional method]].<br />
<br />
==Description of principle==<br />
<br />
===Operational definition===<br />
<br />
Corrective self-explanation is [[self-explanation]]s of ''incorrect'' [[worked examples]]; explaining how and why they are incorrect. See the study by [[Booth]].<br />
<br />
<br />
===Examples===<br />
[[Booth]]'s Corrective self-explanation exercises: [[Image:CSE3.jpg]]<br />
<br />
==Experimental support==<br />
<br />
===Laboratory experiment support===<br />
<br />
Siegler (2002) found that having students self-explain incorrect answers as well as correct answers increased learning of mathematical equality problems than explaining only correct answers. <br />
<br />
Siegler & Chen (in press) also found that asking children to explain both why correct answers were correct and why incorrect answers were incorrect was more effective for learning to solve water displacement problems than only requesting explanations of correct answers. <br />
<br />
===In vivo experiment support===<br />
<br />
Preliminary results from [[Booth]] suggest that while completing any typical or corrective self-explanation exercises improve procedural performance for solving algebraic equations (Booth, Koedinger, & Siegler, 2007), corrective self-explanation may uniquely improve conceptual knowledge about features in the equations. <br />
<br />
==Theoretical rationale== <br />
As a form of [[self-explanation]], corrective self-explanation works via making knowledge explicit. Unlike typical [[self-explanation]], however, corrective self-explanation focuses on making explicit 1) ''that'' a given [[knowledge component]] is wrong and 2) ''why'' the [[knowledge component]] is wrong (what [[features]] about the situation make the knowledge inappropriate.<br />
<br />
==Conditions of application==<br />
Corrective self-explanation is likely only useful when students also recieve experience that will facilitate [[construction]] of correct [[knowledge components]]. If students recieve only corrective self-explanation, they may come to reject their incorrect [[knowledge components]], but if they have nothing to replace them with, they will either flounder (having no way to solve the problem), or revert to use of the only strategy they know, even though they know it is incorrect.<br />
<br />
Grosse & Renkl (in press) also show that explaining incorrect examples is difficult for poor learners if the step where the error occurred is highlighted. If this is not made clear, students have difficulty detecting and explaining the error.<br />
<br />
==Caveats, limitations, open issues, or dissenting views==<br />
==Variations (descendants)==<br />
==Generalizations (ascendants)==<br />
[[Prompted Self-explanation]]<br />
<br />
==References==<br />
Booth, J.L., Koedinger, K., & Siegler, R.S. (2007, October). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), ''Microdevelopment: Transition processes in development and learning'' (pp. 31-58). New York: Cambridge University.<br />
<br />
Siegler, R.S., & Chen, Z. (in press). ''Developmental Science''.<br />
<br />
[[Category:Glossary]]<br />
[[Category:Instructional Principle]]<br />
<br />
<br />
[[Category:Glossary]]<br />
[[Category:Independent Variables]]<br />
[[Category:Booth]]</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=7294Booth2008-03-18T17:08:35Z<p>Julie-Booth: /* Hypothesis */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|800px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]] (relevant instructional principle)<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Findings from Experiment 2(pilot):=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, Koedinger, & Siegler, 2007b)<br />
**Improved the number of attempted problems solved by 18% (control group ''decreased'' percent correct by 17%)<br />
[[Image:Exp2results2.jpg|500px]]<br />
**Reduced the amount of conceptual errors made on problems by 32% (control group ''increased'' these errors by 40%) (interaction significant at p<.05)<br />
[[Image:Exp2results1.jpg|500px]]<br />
*Recieving [[Corrective self-explanation]] exercises may uniquely reduce student misconceptions about problem [[features]]<br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Presentations/Publications===<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). The effect of prior conceptual knowledge on procedural performance and learning in algebra. Poster presented at the 29th Annual Cognitive Science Society conference in Nashville, TN. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf Abstract]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
<br />
===Further Information===<br />
<br />
=====Plans for January 2008-June 2008=====<br />
<br />
• Write and submit a paper to the meeting of the Cognitive Science Society (complete)<br />
<br />
• Complete data collection for Experiment 3 in two schools (complete)<br />
<br />
• Code and analyze data from Experiment 3 to determine whether [[corrective self-explanation]] improved [[robust learning]] of algebraic problem-solving. <br />
<br />
• Analyze [[individual differences]] in the effectiveness of combining [[corrective self-explanation]] with tutored [[procedural]] practice based on pretest [[conceptual knowledge]] and understanding of [[features]].<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=7293Booth2008-03-18T17:08:22Z<p>Julie-Booth: /* Hypothesis */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|800px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]](relevant instructional principle)<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Findings from Experiment 2(pilot):=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, Koedinger, & Siegler, 2007b)<br />
**Improved the number of attempted problems solved by 18% (control group ''decreased'' percent correct by 17%)<br />
[[Image:Exp2results2.jpg|500px]]<br />
**Reduced the amount of conceptual errors made on problems by 32% (control group ''increased'' these errors by 40%) (interaction significant at p<.05)<br />
[[Image:Exp2results1.jpg|500px]]<br />
*Recieving [[Corrective self-explanation]] exercises may uniquely reduce student misconceptions about problem [[features]]<br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Presentations/Publications===<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). The effect of prior conceptual knowledge on procedural performance and learning in algebra. Poster presented at the 29th Annual Cognitive Science Society conference in Nashville, TN. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf Abstract]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
<br />
===Further Information===<br />
<br />
=====Plans for January 2008-June 2008=====<br />
<br />
• Write and submit a paper to the meeting of the Cognitive Science Society (complete)<br />
<br />
• Complete data collection for Experiment 3 in two schools (complete)<br />
<br />
• Code and analyze data from Experiment 3 to determine whether [[corrective self-explanation]] improved [[robust learning]] of algebraic problem-solving. <br />
<br />
• Analyze [[individual differences]] in the effectiveness of combining [[corrective self-explanation]] with tutored [[procedural]] practice based on pretest [[conceptual knowledge]] and understanding of [[features]].<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Corrective_self-explanation&diff=7237Corrective self-explanation2008-03-13T19:30:08Z<p>Julie-Booth: /* Theoretical rationale */</p>
<hr />
<div>==Brief statement of principle==<br />
Explaining how and why incorrect solutions are incorrect will help students to reject incorrect [[knowledge components]] and, thus, stop using incorrect strategies to solve problems.<br />
<br />
Corrective self-explanation is a kind of [[error correction support]] which is a kind of [[instructional method]].<br />
<br />
==Description of principle==<br />
<br />
===Operational definition===<br />
<br />
Corrective self-explanation is [[self-explanation]]s of ''incorrect'' [[worked examples]]; explaining how and why they are incorrect. See the study by [[Booth]].<br />
<br />
<br />
===Examples===<br />
[[Booth]]'s Corrective self-explanation exercises: [[Image:CSE3.jpg]]<br />
<br />
==Experimental support==<br />
<br />
===Laboratory experiment support===<br />
<br />
Siegler (2002) found that having students self-explain incorrect answers as well as correct answers increased learning of mathematical equality problems than explaining only correct answers. <br />
<br />
Siegler & Chen (in press) also found that asking children to explain both why correct answers were correct and why incorrect answers were incorrect was more effective for learning to solve water displacement problems than only requesting explanations of correct answers. <br />
<br />
===In vivo experiment support===<br />
<br />
Preliminary results from [[Booth]] suggest that while completing any typical or corrective self-explanation exercises improve procedural performance for solving algebraic equations (Booth, Koedinger, & Siegler, 2007), corrective self-explanation may uniquely improve conceptual knowledge about features in the equations. <br />
<br />
==Theoretical rationale== <br />
As a form of [[self-explanation]], corrective self-explanation works via making knowledge explicit. Unlike typical [[self-explanation]], however, corrective self-explanation focuses on making explicit 1) ''that'' a given [[knowledge component]] is wrong and 2) ''why'' the [[knowledge component]] is wrong (what [[features]] about the situation make the knowledge inappropriate.<br />
<br />
==Conditions of application==<br />
Corrective self-explanation is likely only useful when students also recieve experience that will facilitate [[construction]] of correct [[knowledge components]]. If students recieve only corrective self-explanation, they may come to reject their incorrect [[knowledge components]], but if they have nothing to replace them with, they will either flounder (having no way to solve the problem), or revert to use of the only strategy they know, even though they know it is incorrect. <br />
<br />
==Caveats, limitations, open issues, or dissenting views==<br />
==Variations (descendants)==<br />
==Generalizations (ascendants)==<br />
[[Prompted Self-explanation]]<br />
<br />
==References==<br />
Booth, J.L., Koedinger, K., & Siegler, R.S. (2007, October). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), ''Microdevelopment: Transition processes in development and learning'' (pp. 31-58). New York: Cambridge University.<br />
<br />
Siegler, R.S., & Chen, Z. (in press). ''Developmental Science''.<br />
<br />
[[Category:Glossary]]<br />
[[Category:Instructional Principle]]<br />
<br />
<br />
[[Category:Glossary]]<br />
[[Category:Independent Variables]]<br />
[[Category:Booth]]</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=7236Booth2008-03-13T19:28:08Z<p>Julie-Booth: /* Background and Significance */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|800px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]]<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Findings from Experiment 2(pilot):=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, Koedinger, & Siegler, 2007b)<br />
**Improved the number of attempted problems solved by 18% (control group ''decreased'' percent correct by 17%)<br />
[[Image:Exp2results2.jpg|500px]]<br />
**Reduced the amount of conceptual errors made on problems by 32% (control group ''increased'' these errors by 40%) (interaction significant at p<.05)<br />
[[Image:Exp2results1.jpg|500px]]<br />
*Recieving [[Corrective self-explanation]] exercises may uniquely reduce student misconceptions about problem [[features]]<br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Presentations/Publications===<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). The effect of prior conceptual knowledge on procedural performance and learning in algebra. Poster presented at the 29th Annual Cognitive Science Society conference in Nashville, TN. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf Abstract]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
<br />
===Further Information===<br />
<br />
=====Plans for January 2008-June 2008=====<br />
<br />
• Write and submit a paper to the meeting of the Cognitive Science Society (complete)<br />
<br />
• Complete data collection for Experiment 3 in two schools (complete)<br />
<br />
• Code and analyze data from Experiment 3 to determine whether [[corrective self-explanation]] improved [[robust learning]] of algebraic problem-solving. <br />
<br />
• Analyze [[individual differences]] in the effectiveness of combining [[corrective self-explanation]] with tutored [[procedural]] practice based on pretest [[conceptual knowledge]] and understanding of [[features]].<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=7235Booth2008-03-13T19:27:29Z<p>Julie-Booth: /* Background and Significance */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|1000px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]]<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Findings from Experiment 2(pilot):=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, Koedinger, & Siegler, 2007b)<br />
**Improved the number of attempted problems solved by 18% (control group ''decreased'' percent correct by 17%)<br />
[[Image:Exp2results2.jpg|500px]]<br />
**Reduced the amount of conceptual errors made on problems by 32% (control group ''increased'' these errors by 40%) (interaction significant at p<.05)<br />
[[Image:Exp2results1.jpg|500px]]<br />
*Recieving [[Corrective self-explanation]] exercises may uniquely reduce student misconceptions about problem [[features]]<br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Presentations/Publications===<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). The effect of prior conceptual knowledge on procedural performance and learning in algebra. Poster presented at the 29th Annual Cognitive Science Society conference in Nashville, TN. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf Abstract]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
<br />
===Further Information===<br />
<br />
=====Plans for January 2008-June 2008=====<br />
<br />
• Write and submit a paper to the meeting of the Cognitive Science Society (complete)<br />
<br />
• Complete data collection for Experiment 3 in two schools (complete)<br />
<br />
• Code and analyze data from Experiment 3 to determine whether [[corrective self-explanation]] improved [[robust learning]] of algebraic problem-solving. <br />
<br />
• Analyze [[individual differences]] in the effectiveness of combining [[corrective self-explanation]] with tutored [[procedural]] practice based on pretest [[conceptual knowledge]] and understanding of [[features]].<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=7234Booth2008-03-13T19:25:58Z<p>Julie-Booth: /* Annotated Bibliography */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|1200px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]]<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Findings from Experiment 2(pilot):=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, Koedinger, & Siegler, 2007b)<br />
**Improved the number of attempted problems solved by 18% (control group ''decreased'' percent correct by 17%)<br />
[[Image:Exp2results2.jpg|500px]]<br />
**Reduced the amount of conceptual errors made on problems by 32% (control group ''increased'' these errors by 40%) (interaction significant at p<.05)<br />
[[Image:Exp2results1.jpg|500px]]<br />
*Recieving [[Corrective self-explanation]] exercises may uniquely reduce student misconceptions about problem [[features]]<br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Presentations/Publications===<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). The effect of prior conceptual knowledge on procedural performance and learning in algebra. Poster presented at the 29th Annual Cognitive Science Society conference in Nashville, TN. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf Abstract]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
<br />
===Further Information===<br />
<br />
=====Plans for January 2008-June 2008=====<br />
<br />
• Write and submit a paper to the meeting of the Cognitive Science Society (complete)<br />
<br />
• Complete data collection for Experiment 3 in two schools (complete)<br />
<br />
• Code and analyze data from Experiment 3 to determine whether [[corrective self-explanation]] improved [[robust learning]] of algebraic problem-solving. <br />
<br />
• Analyze [[individual differences]] in the effectiveness of combining [[corrective self-explanation]] with tutored [[procedural]] practice based on pretest [[conceptual knowledge]] and understanding of [[features]].<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=7233Booth2008-03-13T19:23:08Z<p>Julie-Booth: /* Preliminary findings for Experiment 2(pilot): */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|1200px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]]<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Findings from Experiment 2(pilot):=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, Koedinger, & Siegler, 2007b)<br />
**Improved the number of attempted problems solved by 18% (control group ''decreased'' percent correct by 17%)<br />
[[Image:Exp2results2.jpg|500px]]<br />
**Reduced the amount of conceptual errors made on problems by 32% (control group ''increased'' these errors by 40%) (interaction significant at p<.05)<br />
[[Image:Exp2results1.jpg|500px]]<br />
*Recieving [[Corrective self-explanation]] exercises may uniquely reduce student misconceptions about problem [[features]]<br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Annotated Bibliography ===<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). [Abstract]. The effect of prior conceptual knowledge on procedural performance and learning in algebra. In D.S. McNamara & J.G. Trafton (Eds.), Proceedings of the 29th Annual Cognitive Science Society (pp. 137-142). Austin, TX: Cognitive Science Society. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
<br />
===Further Information===<br />
<br />
=====Plans for January 2008-June 2008=====<br />
<br />
• Write and submit a paper to the meeting of the Cognitive Science Society (complete)<br />
<br />
• Complete data collection for Experiment 3 in two schools (complete)<br />
<br />
• Code and analyze data from Experiment 3 to determine whether [[corrective self-explanation]] improved [[robust learning]] of algebraic problem-solving. <br />
<br />
• Analyze [[individual differences]] in the effectiveness of combining [[corrective self-explanation]] with tutored [[procedural]] practice based on pretest [[conceptual knowledge]] and understanding of [[features]].<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=7232Booth2008-03-13T19:20:40Z<p>Julie-Booth: /* Preliminary findings for Experiment 2(pilot): */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|1200px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]]<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Preliminary findings for Experiment 2(pilot):=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, Koedinger, & Siegler, 2007b)<br />
**Improved the number of attempted problems solved by 18% (control group ''decreased'' percent correct by 17%)<br />
[[Image:Exp2results2.jpg|500px]]<br />
**Reduced the amount of conceptual errors made on problems by 32% (control group ''increased'' these errors by 40%) (interaction significant at p<.05)<br />
[[Image:Exp2results1.jpg|500px]]<br />
*Recieving [[Corrective self-explanation]] exercises may uniquely reduce student misconceptions about problem [[features]]<br />
[[Image:Exp2results3.jpg]]<br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Annotated Bibliography ===<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). [Abstract]. The effect of prior conceptual knowledge on procedural performance and learning in algebra. In D.S. McNamara & J.G. Trafton (Eds.), Proceedings of the 29th Annual Cognitive Science Society (pp. 137-142). Austin, TX: Cognitive Science Society. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
<br />
===Further Information===<br />
<br />
=====Plans for January 2008-June 2008=====<br />
<br />
• Write and submit a paper to the meeting of the Cognitive Science Society (complete)<br />
<br />
• Complete data collection for Experiment 3 in two schools (complete)<br />
<br />
• Code and analyze data from Experiment 3 to determine whether [[corrective self-explanation]] improved [[robust learning]] of algebraic problem-solving. <br />
<br />
• Analyze [[individual differences]] in the effectiveness of combining [[corrective self-explanation]] with tutored [[procedural]] practice based on pretest [[conceptual knowledge]] and understanding of [[features]].<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=7231Booth2008-03-13T19:19:56Z<p>Julie-Booth: /* Preliminary findings for Experiment 2(pilot): */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|1200px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]]<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Preliminary findings for Experiment 2(pilot):=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, Koedinger, & Siegler, 2007b)<br />
**Improved the number of attempted problems solved by 18% (control group ''decreased'' percent correct by 17%)<br />
[[Image:Exp2results2.jpg|500px]]<br />
**Reduced the amount of conceptual errors made on problems by 32% (control group ''increased'' these errors by 40%)<br />
[[Image:Exp2results1.jpg|500px]]<br />
*Recieving [[Corrective self-explanation]] exercises may uniquely reduce student misconceptions about problem [[features]]<br />
[[Image:Exp2results3.jpg]]<br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Annotated Bibliography ===<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). [Abstract]. The effect of prior conceptual knowledge on procedural performance and learning in algebra. In D.S. McNamara & J.G. Trafton (Eds.), Proceedings of the 29th Annual Cognitive Science Society (pp. 137-142). Austin, TX: Cognitive Science Society. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
<br />
===Further Information===<br />
<br />
=====Plans for January 2008-June 2008=====<br />
<br />
• Write and submit a paper to the meeting of the Cognitive Science Society (complete)<br />
<br />
• Complete data collection for Experiment 3 in two schools (complete)<br />
<br />
• Code and analyze data from Experiment 3 to determine whether [[corrective self-explanation]] improved [[robust learning]] of algebraic problem-solving. <br />
<br />
• Analyze [[individual differences]] in the effectiveness of combining [[corrective self-explanation]] with tutored [[procedural]] practice based on pretest [[conceptual knowledge]] and understanding of [[features]].<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=7230Booth2008-03-13T19:19:36Z<p>Julie-Booth: /* Preliminary findings for Experiment 2(pilot): */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|1200px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]]<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Preliminary findings for Experiment 2(pilot):=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, Koedinger, & Siegler, 2007b)<br />
**Improved the number of attempted problems solved by 18% (control group ''decreased'' percent correct by 17%)<br />
[[Image:Exp2results2.jpg|400px]]<br />
**Reduced the amount of conceptual errors made on problems by 32% (control group ''increased'' these errors by 40%)<br />
[[Image:Exp2results1.jpg|400px]]<br />
*Recieving [[Corrective self-explanation]] exercises may uniquely reduce student misconceptions about problem [[features]]<br />
[[Image:Exp2results3.jpg]]<br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Annotated Bibliography ===<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). [Abstract]. The effect of prior conceptual knowledge on procedural performance and learning in algebra. In D.S. McNamara & J.G. Trafton (Eds.), Proceedings of the 29th Annual Cognitive Science Society (pp. 137-142). Austin, TX: Cognitive Science Society. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
<br />
===Further Information===<br />
<br />
=====Plans for January 2008-June 2008=====<br />
<br />
• Write and submit a paper to the meeting of the Cognitive Science Society (complete)<br />
<br />
• Complete data collection for Experiment 3 in two schools (complete)<br />
<br />
• Code and analyze data from Experiment 3 to determine whether [[corrective self-explanation]] improved [[robust learning]] of algebraic problem-solving. <br />
<br />
• Analyze [[individual differences]] in the effectiveness of combining [[corrective self-explanation]] with tutored [[procedural]] practice based on pretest [[conceptual knowledge]] and understanding of [[features]].<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=7229Booth2008-03-13T19:07:57Z<p>Julie-Booth: /* Preliminary findings for Experiment 2(pilot): */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|1200px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]]<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Preliminary findings for Experiment 2(pilot):=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, Koedinger, & Siegler, 2007b)<br />
**Improved the number of attempted problems solved by 18% (control group ''decreased'' percent correct by 17%)<br />
[[Image:Exp2results2.jpg|800px]]<br />
**Reduced the amount of conceptual errors made on problems by 32% (control group ''increased'' these errors by 40%)<br />
[[Image:Exp2results1.jpg|800px]]<br />
*Recieving [[Corrective self-explanation]] exercises may uniquely reduce student misconceptions about problem [[features]]<br />
[[Image:Exp2results3.jpg]]<br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Annotated Bibliography ===<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). [Abstract]. The effect of prior conceptual knowledge on procedural performance and learning in algebra. In D.S. McNamara & J.G. Trafton (Eds.), Proceedings of the 29th Annual Cognitive Science Society (pp. 137-142). Austin, TX: Cognitive Science Society. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
<br />
===Further Information===<br />
<br />
=====Plans for January 2008-June 2008=====<br />
<br />
• Write and submit a paper to the meeting of the Cognitive Science Society (complete)<br />
<br />
• Complete data collection for Experiment 3 in two schools (complete)<br />
<br />
• Code and analyze data from Experiment 3 to determine whether [[corrective self-explanation]] improved [[robust learning]] of algebraic problem-solving. <br />
<br />
• Analyze [[individual differences]] in the effectiveness of combining [[corrective self-explanation]] with tutored [[procedural]] practice based on pretest [[conceptual knowledge]] and understanding of [[features]].<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=File:Exp2results1.jpg&diff=7228File:Exp2results1.jpg2008-03-13T19:07:09Z<p>Julie-Booth: </p>
<hr />
<div></div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=File:Exp2results2.jpg&diff=7227File:Exp2results2.jpg2008-03-13T19:06:38Z<p>Julie-Booth: </p>
<hr />
<div></div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=7226Booth2008-03-13T19:06:22Z<p>Julie-Booth: /* Preliminary findings for Experiment 2(pilot): */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|1200px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]]<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Preliminary findings for Experiment 2(pilot):=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, Koedinger, & Siegler, 2007b)<br />
**Improved the number of attempted problems solved by 18% (control group ''decreased'' percent correct by 17%)<br />
[[Image:Exp2results2.jpg]]<br />
**Reduced the amount of conceptual errors made on problems by 32% (control group ''increased'' these errors by 40%)<br />
[[Image:Exp2results1.jpg]]<br />
*Recieving [[Corrective self-explanation]] exercises may uniquely reduce student misconceptions about problem [[features]]<br />
[[Image:Exp2results3.jpg]]<br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Annotated Bibliography ===<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). [Abstract]. The effect of prior conceptual knowledge on procedural performance and learning in algebra. In D.S. McNamara & J.G. Trafton (Eds.), Proceedings of the 29th Annual Cognitive Science Society (pp. 137-142). Austin, TX: Cognitive Science Society. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
<br />
===Further Information===<br />
<br />
=====Plans for January 2008-June 2008=====<br />
<br />
• Write and submit a paper to the meeting of the Cognitive Science Society (complete)<br />
<br />
• Complete data collection for Experiment 3 in two schools (complete)<br />
<br />
• Code and analyze data from Experiment 3 to determine whether [[corrective self-explanation]] improved [[robust learning]] of algebraic problem-solving. <br />
<br />
• Analyze [[individual differences]] in the effectiveness of combining [[corrective self-explanation]] with tutored [[procedural]] practice based on pretest [[conceptual knowledge]] and understanding of [[features]].<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=7225Booth2008-03-13T18:35:50Z<p>Julie-Booth: /* Preliminary findings for Experiment 2(pilot): */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|1200px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]]<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Preliminary findings for Experiment 2(pilot):=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of procedural [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, Koedinger, & Siegler, 2007b)<br />
<br />
**Improved the number of attempted problems solved by 18% (control group ''decreased'' percent correct by 17%)<br />
**Reduced the amount of conceptual errors made on problems by 32% (control group ''increased'' these errors by 40%)<br />
<br />
<br />
<br />
*Recieving [[Corrective self-explanation]] exercises may uniquely reduce student misconceptions about problem [[features]]<br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Annotated Bibliography ===<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). [Abstract]. The effect of prior conceptual knowledge on procedural performance and learning in algebra. In D.S. McNamara & J.G. Trafton (Eds.), Proceedings of the 29th Annual Cognitive Science Society (pp. 137-142). Austin, TX: Cognitive Science Society. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
<br />
===Further Information===<br />
<br />
=====Plans for January 2008-June 2008=====<br />
<br />
• Write and submit a paper to the meeting of the Cognitive Science Society (complete)<br />
<br />
• Complete data collection for Experiment 3 in two schools (complete)<br />
<br />
• Code and analyze data from Experiment 3 to determine whether [[corrective self-explanation]] improved [[robust learning]] of algebraic problem-solving. <br />
<br />
• Analyze [[individual differences]] in the effectiveness of combining [[corrective self-explanation]] with tutored [[procedural]] practice based on pretest [[conceptual knowledge]] and understanding of [[features]].<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=7224Booth2008-03-13T01:45:33Z<p>Julie-Booth: /* Plans for March 2008-June 2008 */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|1200px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]]<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Preliminary findings for Experiment 2(pilot):=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of implicit (procedural) [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, Koedinger, & Siegler, 2007b)<br />
*Recieving [[Corrective self-explanation]] exercises may uniquely reduce student misconceptions about problem [[features]]<br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Annotated Bibliography ===<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). [Abstract]. The effect of prior conceptual knowledge on procedural performance and learning in algebra. In D.S. McNamara & J.G. Trafton (Eds.), Proceedings of the 29th Annual Cognitive Science Society (pp. 137-142). Austin, TX: Cognitive Science Society. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
<br />
===Further Information===<br />
<br />
=====Plans for January 2008-June 2008=====<br />
<br />
• Write and submit a paper to the meeting of the Cognitive Science Society (complete)<br />
<br />
• Complete data collection for Experiment 3 in two schools (complete)<br />
<br />
• Code and analyze data from Experiment 3 to determine whether [[corrective self-explanation]] improved [[robust learning]] of algebraic problem-solving. <br />
<br />
• Analyze [[individual differences]] in the effectiveness of combining [[corrective self-explanation]] with tutored [[procedural]] practice based on pretest [[conceptual knowledge]] and understanding of [[features]].<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=7220Booth2008-03-12T21:47:51Z<p>Julie-Booth: /* Improving skill at solving equations through better encoding of algebraic concepts */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 4 complete<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|1200px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]]<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Preliminary findings for Experiment 2(pilot):=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of implicit (procedural) [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, Koedinger, & Siegler, 2007b)<br />
*Recieving [[Corrective self-explanation]] exercises may uniquely reduce student misconceptions about problem [[features]]<br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Annotated Bibliography ===<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). [Abstract]. The effect of prior conceptual knowledge on procedural performance and learning in algebra. In D.S. McNamara & J.G. Trafton (Eds.), Proceedings of the 29th Annual Cognitive Science Society (pp. 137-142). Austin, TX: Cognitive Science Society. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
<br />
===Further Information===<br />
<br />
=====Plans for March 2008-June 2008=====<br />
<br />
• Write and submit a paper to the meeting of the Cognitive Science Society <br />
<br />
• Complete data collection for Experiment 3 in two schools<br />
<br />
• Analyze data from Experiment 3 to determine whether [[corrective self-explanation]] improved [[robust learning]] of algebraic problem-solving. <br />
<br />
• Analyze [[individual differences]] in the effectiveness of combining [[corrective self-explanation]] with tutored [[procedural]] practice based on pretest [[conceptual knowledge]] and understanding of [[features]].<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=7219Booth2008-03-12T21:40:58Z<p>Julie-Booth: /* Improving skill at solving equations through better encoding of algebraic concepts */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 2 complete, 1 in progress<br />
[[Image:StudyTable-Booth.jpg|800px]]<br />
<br />
<br />
===Abstract===<br />
<br />
This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
<br />
===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
<br />
===Research Question===<br />
<br />
Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
<br />
===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
<br />
Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
<br />
Examples of corresponding misconceptions and incorrect knowledge components:<br />
<br />
[[Image:misconceptions2.jpg|1200px]]<br />
<br />
===Dependent Variables===<br />
<br />
''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
<br />
=====Robust Learning Measures:=====<br />
<br />
''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
<br />
''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
<br />
''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
<br />
===Independent Variables===<br />
<br />
<br />
Two types of self-explanation exercises: <br />
<br />
1) Typical self-explanation (explanation of correct [[worked examples]])<br />
<br />
[[Image:TSE2.jpg]]<br />
<br />
2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
<br />
[[Image:CSE3.jpg]]<br />
<br />
The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
<br />
===Hypothesis===<br />
<br />
[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]]<br />
<br />
===Findings===<br />
<br />
=====Findings for Experiments 1a and 1b:=====<br />
<br />
*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
<br />
=====Preliminary findings for Experiment 2:=====<br />
<br />
*Students who received any kind of [[self-explanation]] exercises show greater learning of implicit (procedural) [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, Koedinger, & Siegler, 2007b)<br />
*Recieving [[Corrective self-explanation]] exercises may uniquely reduce student misconceptions about problem [[features]]<br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
<br />
===Explanation===<br />
<br />
Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
<br />
===Descendents===<br />
<br />
None<br />
<br />
=== Annotated Bibliography ===<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). [Abstract]. The effect of prior conceptual knowledge on procedural performance and learning in algebra. In D.S. McNamara & J.G. Trafton (Eds.), Proceedings of the 29th Annual Cognitive Science Society (pp. 137-142). Austin, TX: Cognitive Science Society. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
<br />
===Further Information===<br />
<br />
=====Plans for January 2008-June 2008=====<br />
<br />
• Write and submit a paper to the meeting of the Cognitive Science Society <br />
<br />
• Complete data collection for Experiment 2 in two schools<br />
<br />
• Analyze data from Experiment 2 to determine whether [[corrective self-explanation]] improved [[robust learning]] of algebraic problem-solving. <br />
<br />
• Analyze [[individual differences]] in the effectiveness of combining [[corrective self-explanation]] with tutored [[procedural]] practice based on pretest [[conceptual knowledge]] and understanding of [[features]].<br />
<br />
===References===<br />
<br />
Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
<br />
Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
<br />
Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
<br />
Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
<br />
Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
<br />
Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
<br />
Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=File:StudyTable-Booth.jpg&diff=7218File:StudyTable-Booth.jpg2008-03-12T21:40:03Z<p>Julie-Booth: uploaded a new version of "Image:StudyTable-Booth.jpg"</p>
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<div></div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=File:StudyTable-Booth.jpg&diff=7217File:StudyTable-Booth.jpg2008-03-12T21:38:43Z<p>Julie-Booth: uploaded a new version of "Image:StudyTable-Booth.jpg": Reverted to version as of 21:37, 12 March 2008</p>
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<div></div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=File:StudyTable-Booth.jpg&diff=7216File:StudyTable-Booth.jpg2008-03-12T21:38:14Z<p>Julie-Booth: uploaded a new version of "Image:StudyTable-Booth.jpg"</p>
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<div></div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=File:StudyTable-Booth.jpg&diff=7215File:StudyTable-Booth.jpg2008-03-12T21:37:43Z<p>Julie-Booth: uploaded a new version of "Image:StudyTable-Booth.jpg"</p>
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<div></div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Coordinative_Learning&diff=6685Coordinative Learning2008-01-09T15:47:03Z<p>Julie-Booth: /* Examples and Explanations */</p>
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<div>= The PSLC Coordinative Learning cluster =<br />
<br />
== Abstract ==<br />
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:<br />
<br />
*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.<br />
*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. <br />
<br />
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.<br />
<br />
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.<br />
<br />
<br><center>[[Image:cl-theory.jpg]]</center><br />
<br />
== Glossary ==<br />
[[:Category:Coordinative Learning|Coordinative Learning]] glossary.<br />
<br />
*'''[[Co-training]]'''<br />
*'''[[Complementary]]'''<br />
*'''[[Conceptual tasks]]''' <br />
*'''[[Contiguity]]'''<br />
*'''[[Coordination]]'''<br />
*'''[[Ecological control group]]'''<br />
*'''[[External representations]]'''<br />
*'''[[Input sources ]]'''<br />
*'''[[Instructional method]]'''<br />
*'''[[Multimedia sources]]'''<br />
*'''[[Procedural tasks]]''' <br />
*'''[[Self-explanation]]'''<br />
*'''[[Self-supervised learning]]'''<br />
*'''[[Sources]]'''<br />
*'''[[Strategies]]'''<br />
*'''[[Unlabeled examples]]'''<br />
<br />
== Research questions ==<br />
<br />
When and how does coordinating multiple sources of information or lines of reasoning increase robust learning?<br />
<br />
Two sub-groups of coordinative learning studies are exploring these more specific questions:<br />
<br />
=== Visualizations and Multi-modal sources ===<br />
<br />
When does adding visualizations or other multi-modal input enhance robust learning and how do we best support students in coordinating these sources?<br />
<br />
=== Examples and Explanations ===<br />
<br />
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?<br />
<br />
== Independent variables ==<br />
<br />
*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<br />
<br />
*Instructional activities designed to engage students in [[coordination]] (e.g., conceptual vs. [[procedural]] exercises, contiguous presentation of sources, [[self-explanation]])<br />
<br />
See [[:Category:Independent Variables]]<br />
<br />
== Dependent variables ==<br />
[[Normal post-test]] and measures of [[robust learning]].<br />
<br />
== Hypotheses ==<br />
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.<br />
<br />
== Explanation ==<br />
<br />
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]].<br />
<br />
== Descendents ==<br />
<br />
=== Visualizations and Multi-modal sources ===<br />
*[[Contiguous Representations for Robust Learning (Aleven & Butcher)]]<br />
**[[Static vs. Animated Visual Representations for Science Learning (Kaye, Small, Butcher, & Chi)]]<br />
*[[Mapping Visual and Verbal Information: Integrated Hints in Geometry (Aleven & Butcher)]]<br />
**[[Training Geometry Concepts with Visual and Verbal Sources (Burchfield, Aleven, & Butcher)]]<br />
*[[Visual Representations in Science Learning | Visual Representations in Science Learning (Davenport, Klahr & Koedinger)]]<br />
*[[Co-training of Chinese characters| Co-training of Chinese characters (Liu, Perfetti, Dunlap, Zi, Mitchell)]]<br />
*[[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]<br />
<br />
=== Examples and Explanations ===<br />
*[[Booth | Improving skill at solving equations through better encoding of algebraic concepts (Booth, Siegler, Koedinger & Rittle-Johnson)]]<br />
*[[Stoichiometry_Study | Studying the Learning Effect of Personalization and Worked Examples in the Solving of Stoichiometry Problems (McLaren, Koedinger & Yaron)]]<br />
*[[Note-Taking_Technologies | Note-taking Project Page (Bauer & Koedinger)]]<br />
**[[Note-Taking: Restriction and Selection]] (completed)<br />
**[[Note-Taking: Coordination]] (planned)<br />
*[[REAP_main | The REAP Project: Implicit and explicit instruction on word meanings (Juffs & Eskenazi)]]<br />
*[[Help_Lite (Aleven, Roll)|Hints during tutored problem solving – the effect of fewer hint levels with greater conceptual content (Aleven & Roll)]]<br />
*[[Handwriting Algebra Tutor]] (Anthony, Yang & Koedinger)<br />
**[[Lab study proof-of-concept for handwriting vs typing input for learning algebra equation-solving]] (completed)<br />
**[[Effect of adding simple worked examples to problem-solving in algebra learning]] (completed, analysis in progress)<br />
**[[In vivo comparison of Cognitive Tutor Algebra using handwriting vs typing input]] (in progress)<br />
*[[Bridging_Principles_and_Examples_through_Analogy_and_Explanation | Bridging Principles and Examples through Analogy and Explanation (Nokes & VanLehn)]]<br />
*[[Does learning from worked-out examples improve tutored problem solving? | Does learning from worked-out examples improve tutored problem solving? (Renkl, Aleven & Salden)]] [Also in Interactive Communication]<br />
*[[Ringenberg_Examples-as-Help | Scaffolding Problem Solving with Embedded Example to Promote Deep Learning (Ringenberg & VanLehn)]]<br />
*[[Baker_Choices_in_LE_Space | How Content and Interface Features Influence Student Choices Within the Learning Space (Baker, Corbett, Koedinger, & Rodrigo)]]<br />
<br />
== Annotated Bibliography ==<br />
Much research in human and machine learning research has advocated various kinds of “multiples” to assist learning: <br />
* multiple data sources (e.g., human learning (HL): Mayer, 2001; machine learning (ML): Blum & Mitchell, 1998; Collins & Singer, 1999). <br />
* multiple representations (e.g., HL: Ainsworth & Van Labeke, 2004; ML: Liere & Tadepalli, 1997), <br />
* multiple strategies (e.g., HL: Klahr & Siegler, 1978; ML: Michalski & Tecucci 1997; Saitta, Botta, & Neri, 1993); <br />
* multiple learning tasks (e.g., HL: Holland, Holyoak, Nisbett, & Thagard, 1986; ML: Caruana, 1997; Case, Jain, Ott, Sharma, & Stephan, 1998); <br />
<br />
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). <br />
<br />
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.<br />
<br />
An ambitious goal of PSLC is provide a rigorous causal theory of human learning results at the level of precision of machine learning research. <br />
<br />
* 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.<br />
* Ainsworth, S.E. & Van Labeke (2004) Multiple forms of dynamic representation. Learning and Instruction, 14(3), 241-255. <br />
* 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<br />
* Caruana, R. (1997). Multitask learning. Machine Learning 28(1), 41-75. Available: citeseer.nj.nec.com/caruana97multitask.html.<br />
* 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.<br />
* 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).<br />
* 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.<br />
* Holland, J. H., Holyoak, K. J., Nisbett, R. E., & Thagard, P. R. (1986). Induction: Processes of inference, learning, and discovery. Cambridge, MA: MIT Press.<br />
* 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.<br />
* 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.<br />
* Mayer, R. E. (2001). Multimedia learning. New York: Cambridge University Press.<br />
* Michalski, R., & Tecuci, G. (Eds.) (1997). Machine learning: A multi-strategy approach. Morgan Kaufmann.<br />
* Muslea, I., Minton, S., & Knoblock, C. (2002). Active + semi-supervised learning = robust multi-view learning. In Proceedings of ICML-2002. Sydney, Australia.<br />
* 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.<br />
* 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.<br />
* Saitta, L., Botta, M., & Neri, F. (1993). Multi-strategy learning and theory revision. Machine Learning, 11(2/3), 153–172.<br />
[[Category:Cluster]]</div>Julie-Boothhttps://learnlab.org/wiki/index.php?title=Booth&diff=6684Booth2008-01-09T15:46:38Z<p>Julie-Booth: /* Knowledge component construction vs. recall */</p>
<hr />
<div>==Improving skill at solving equations through better encoding of algebraic concepts==<br />
<br />
Julie Booth, Robert Siegler, Ken Koedinger & Bethany Rittle-Johnson <br />
<br />
*PI: Julie Booth <br />
*Key faculty: Ken Koedinger, Robert Siegler, Bethany Rittle-Johnson<br />
<br />
*Studies: 2 complete, 1 in progress<br />
[[Image:StudyTable-Booth.jpg|600px]]<br />
<br />
<br />
===Abstract===<br />
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This project examines the effectiveness of corrective [[self-explanation]], or explanation of [[incorrect worked examples]], for improving students' [[knowledge components]] for solving algebraic equations. Students in classrooms which are using the Algebra Cognitive Tutor curriculum will complete such exercises during their otherwise typical experience solving equations with the Tutor to determine whether [[coordination]] of the two instructional methods increases [[robust learning]]; as a control, other students in the classroom will receive typical [[self-explanation]] exercises (explanation of correct worked examples) or no [[self-explanation]] exercises amid their tutor problems ([[Ecological control group]]). [[Robust learning]] will be assessed using measures of [[long-term retention]], [[transfer]], and [[accelerated future learning]].<br />
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===Glossary===<br />
*Corrective Self-Explanations: [[Self-explanation]]s of incorrect worked examples; explaining how and why they are incorrect<br />
*Incorrect [[worked examples]]: Examples that include errors<br />
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===Research Question===<br />
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Students tend to learn overgeneralized [[knowledge components]] and apply them when attempting to solve algebra problems with incorrect [[features]]. How can we help them to learn correct [[knowledge components]]? And when is combining exercises designed to improve [[conceptual knowledge]] with tutored [[procedural]] exercises effective for improving [[robust learning]] of algebraic problem-solving?<br />
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===Background and Significance===<br />
Errors are inevitable when individuals are first learning any skill; solving algebraic equations is no exception. Students often use incorrect [[knowledge components]] when learning Algebra (Lerch, 2004; Sebrechts, Enright, Bennett, & Martin, 1996), and use of incorrect [[knowledge components]] has been attributed to misunderstandings or gaps in students’ [[conceptual knowledge]] of Algebra (Anderson, 1989; Van Lehn & Jones, 1993). Results from Experiment 1 in Booth et al.’s current PSLC project confirm this hypothesis; a lack of knowledge about certain [[features]] in the problems (e.g., negatives, equals sign, like terms) was associated with use of related incorrect [[knowledge components]] on the problem-solving task. For example, students who do not see negatives as integral parts of terms in algebraic equations, or who believe that negatives can enter and exit equations without consequence tend to apply knowledge components with incorrect (or incomplete) [[features]] when solving equations, such as behaving in accordance with “to remove a term from an equation, subtract it from both sides” rather than with a [[knowledge component]] with [[feature validity]] that specifies “positive term” in the predicate, Thus, improving students’ knowledge of the conceptual [[features]] that underlie Algebra may be necessary for [[robust learning]] to occur. <br />
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Siegler’s overlapping waves theory suggests that there are two important steps that are necessary to improve knowledge (Siegler, 1996): 1) Weaken the incorrect [[knowledge component]], and 2)Construct and strengthen correct [[knowledge component]]. One way to accomplish this is through [[self-explanation]], or generating explanations about instructional material. Chi and her colleagues (e.g., Chi, 2000; Roy & Chi, 2005) have shown that [[self-explanation]] is useful for a variety of purposes, including generating new knowledge to fill gaps and repairing faulty knowledge. Siegler (2002) suggests that one particular type of [[self-explanation]] may be especially useful for repairing faulty knowledge: explaining why the procedures used in [[incorrect worked examples]] are wrong. This [[self-explanation]] of [[incorrect worked examples]] (why they’re wrong) can weaken students’ overgeneralized [[knowledge components]] by helping them to understand both that the [[knowledge components]] are incorrect and what relevant [[features]] make them incorrect.<br />
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Examples of corresponding misconceptions and incorrect knowledge components:<br />
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[[Image:misconceptions2.jpg|1200px]]<br />
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===Dependent Variables===<br />
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''[[Normal post-test]]''. Near transfer—immediate posttest in which isomorphic problems to instruction are included for students to solve. (e.g., 3x + 10 = 20, 4x/3 + 4 = 16, 2/(-5x) = 14)<br />
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=====Robust Learning Measures:=====<br />
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''[[Long-term retention]]''. Embedded assessment within instruction by the Cognitive Tutor. We will collect log data from the review portion of the next equation-solving Tutor unit to determine whether correct knowledge components are applied. <br />
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''[[Transfer]]''. Problems included on the posttest in two forms: 1)Procedural format with more difficult problems/problems with additional features (e.g., 2x - 7 = -5x + 9, 4/(6x) – 7 = 32). 2) Conceptual format assessing knowledge of features (e.g., State whether each of the following is the same as 3 – 4x: a. 3 + 4x b. 3 + (-4x) c. 4x – 3 d. 4x + 3)<br />
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''[[Accelerated future learning]]''. We will collect log data during tutor instruction in the next equation-solving Tutor unit when treatment is no longer in place to determine whether the slope of the learning curve is greater for students who received the [[corrective self-explanation]] treatment.<br />
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===Independent Variables===<br />
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Two types of self-explanation exercises: <br />
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1) Typical self-explanation (explanation of correct [[worked examples]])<br />
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[[Image:TSE2.jpg]]<br />
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2) [[Corrective self-explanation]] (explanation of [[incorrect worked examples]])<br />
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[[Image:CSE3.jpg]]<br />
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The design is a 2 x 2 factorial with two levels of typical self-explanation (yes or no) and two levels of [[corrective self-explanation]] (yes and no). The result is that within any participating classroom, one fourth of students received typical self-explanation, one fourth received [[corrective self-explanation]], one fourth received both, and one fourth received neither (the current tutor as-is, the [[Ecological control group]].<br />
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===Hypothesis===<br />
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[[Self-explanation]] of [[incorrect worked examples]] (why they’re wrong) combined with [[procedural]] practice can lead to [[robust learning]] through two processes: 1) Weaken low-[[feature validity]] [[knowledge components]] (know that they’re wrong and why they’re wrong) 2) Facilitate construction of high-[[feature validity]] [[knowledge components]]. See [[Corrective self-explanation]]<br />
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===Findings===<br />
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=====Findings for Experiments 1a and 1b:=====<br />
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*Pretest misconceptions about [[features]] are related to use of specific incorrect [[knowledge components]] to solve problems Concepts related to specific buggy procedures<br />
**Students with incorrect or missing equality or terms [[features]] are more likely to make errors of those types (p’s < .05 and .01); nonsignificant trend in the same direction for negative feature<br />
*Having knowledge of the [[features]] of negativity and equality predicts correctness on [[procedural]] problems (p’s < .05 and .01)<br />
*Students do improve from pretest to posttest, but roughly 1/3 of students still lack each of the [[features]] at posttest<br />
*Pretest [[conceptual knowledge]] predicts students' pretest to posttest gain in [[procedural]] knowledge after using the Algebra Tutor as is<br />
*Improvement in [[conceptual knowledge]] of the equals sign feature leads to more learning on the [[procedural]] problems than if that knowledge was not improved.<br />
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=====Preliminary findings for Experiment 2:=====<br />
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*Students who received any kind of [[self-explanation]] exercises show greater learning of implicit (procedural) [[knowledge components]] for solving algebraic equations compared with students who did not get any type of [[self-explanation]] exercises ([[Ecological control group]]). (Booth, Koedinger, & Siegler, 2007b)<br />
*Recieving [[Corrective self-explanation]] exercises may uniquely reduce student misconceptions about problem [[features]]<br />
*[[Corrective self-explanation]] may affect students differently based on the amount and quality of their [[knowledge components]] prior to beginning the treatment. <br />
**Students with high-[[feature validity]] [[knowledge components]] may not require [[corrective self-explanation]] for success, and introduction of incorrect strategies in the exercises may actually impair learning.<br />
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===Explanation===<br />
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Students who receive [[corrective self-explanation]] exercises are expected to gain improved explicit [[conceptual knowledge]] about the [[features]] in problems that make certain [[knowledge components]] inappropriate. This expected to lead to greater [[robust learning]] compared with the other conditions that gain only implicit knowledge or explicit knowledge but do not have this additional knowledge about when it is appropriate to apply their [[knowledge components]].<br />
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===Descendents===<br />
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None<br />
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=== Annotated Bibliography ===<br />
*Presentation to the PSLC Advisory Board, Fall 2006. [http://www.learnlab.org/uploads/mypslc/talks/booth%202006%20advisory%20board%20talk%20slides.ppt Link to Powerpoint slides]<br />
*Booth, J.L., Koedinger, K.R., & Siegler, R.S. (2007a). [Abstract]. The effect of prior conceptual knowledge on procedural performance and learning in algebra. In D.S. McNamara & J.G. Trafton (Eds.), Proceedings of the 29th Annual Cognitive Science Society (pp. 137-142). Austin, TX: Cognitive Science Society. [http://www.learnlab.org/uploads/mypslc/publications/ma206-booth.pdf]<br />
*Booth, J.L., Koedinger, K., & Siegler, R.S. (2007b). The effect of corrective and typical self-explanation on algebraic problem solving. Poster presented at the Science of Learning Centers Awardee’s Meeting in Washington, DC, October, 2007.<br />
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===Further Information===<br />
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=====Plans for January 2008-June 2008=====<br />
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• Write and submit a paper to the meeting of the Cognitive Science Society <br />
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• Complete data collection for Experiment 2 in two schools<br />
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• Analyze data from Experiment 2 to determine whether [[corrective self-explanation]] improved [[robust learning]] of algebraic problem-solving. <br />
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• Analyze [[individual differences]] in the effectiveness of combining [[corrective self-explanation]] with tutored [[procedural]] practice based on pretest [[conceptual knowledge]] and understanding of [[features]].<br />
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===References===<br />
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Anderson, J.R. (1989). The analogical origins of errors in problem solving. In D. Klahr & K. Kotovsky (Eds). Complex information processing: The impact of Herbert A. Simon. (pp. 343-371). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc.<br />
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Chi, M.T.H. (2000) Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In Glaser, R. (Ed.) Advances in Insturctional Psychology, Mahwah, NJ: Lawrence Erlbaum Associates, pp. 161-238. <br />
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Lerch, C. M. (2004). Control decisions and personal beliefs: Their effect on solving mathematical problems. Journal of Mathematical Behavior, 23, 21-36. <br />
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Roy, M. & Chi, M.T.H. (2005). Self-explanation in a multi-media context. In R. Mayer (Ed.), Cambridge Handbook of Multimedia Learning (pp. 271-286). Cambridge Press.<br />
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Siegler, R.S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.<br />
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Siegler, R. S. (2002). Microgenetic studies of self-explanations. In N. Granott & J. Parziale (Eds.), Microdevelopment: Transition processes in development and learning (pp. 31-58). New York: Cambridge University.<br />
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Van Lehn, K., & Jones, R.M. (1993). What mediates the self-explanation effect? Knowledge gaps, schemas, or analogies? In M. Polson (Ed.) Proceedings of the Fifteenth Annual Conference of the Cognitive Science Society (pp. 1034-1039).</div>Julie-Booth