Analogical Scaffolding in Collaborative Learning

Soniya Gadgil & Timothy Nokes

Summary Table

PIs	Soniya Gadgil (Pitt), Timothy Nokes (Pitt)
Other Contributers	Robert Shelby (USNA)
Study Start Date	Sept. 1, 2008
Study End Date	Aug. 31, 2009
LearnLab Site	United States Naval Academy (USNA)
LearnLab Course	Physics
Number of Students	N = 72
Total Participant Hours	144 hrs.
DataShop	Anticipated

Abstract

Past research has shown that collaboration can enhance learning in certain conditions. However, not much work has explored the cognitive mechanisms that underlie such learning. Chi, Hausmann and Roy (2004) propose three mechanisms including: self-explaining, other-directed explaining, and co-construction. In the current study, we will examine the use of these mechanisms when participants learn from worked examples across different collaborative contexts. We compare the effects of adding prompts that encourage analogical comparison to prompts that focus on single examples (non-comparison) to a traditional instruction condition, as students learn to solve Physics problems in the domain of rotational kinematics. Students learning processes will be analyzed by examining their verbal protocols. Learning will be assessed via robust measures such as long-term retention and transfer.

Background and Significance

Collaborative learning Past research on collaborative learning provides compelling evidence that when students learn in groups of two or more, they show better learning gains at the group level than when working alone. Much of this research has focused on identifying conditions that underlie successful collaboration. For example, we know that factors such as presence of cognitive conflict (Schwartz, Neuman, & Biezuner, 2000), establishing of common ground (Clark, 2000) and scaffolding (or structuring) of the interaction are important factors affecting collaborative learning. Providing scripted problem solving activities (e.g., one participant plays the role of the tutor vs. tutee and then switch) have also been shown to facilitate collaborative learning compared to unscripted conditions (McLaren, Walker, Koedinger, Rummel, Spada, & Kalchman, 2007). These results are typically explained in terms of the sense making processes in which the structured collaborative environments provide the learner more opportunities to construct the relevant knowledge components. Although much work has focused on improving learning through collaboration, little research has examined the cognitive processes underlying successful collaboration. Most of the prior work has focused on the outcome or product of the group and less has been concerned with the underlying processes that give rise to the product. If we can uncover the cognitive processes underlying collaborative learning, it can further our understanding of how to improve collaborative learning environments.

Schema Acquisition and Analogical Comparison: A problem schema is a knowledge organization of the information associated with a particular problem category. Problem schemas typically include declarative knowledge of principles, concepts, and formulae, as well as the procedural knowledge for how to apply that knowledge to solve a problem. One way in which schemas can be acquired is through analogical comparison (Gick & Holyoak, 1983). Analogical comparison operates through aligning and mapping two example problem representations to one another and then extracting their commonalities (Gentner, 1983; Gick & Holyoak, 1983; Hummel & Holyoak, 2003). Research on analogy and schema learning has shown that the acquisition of schematic knowledge promotes flexible transfer to novel problems. For example, Gick and Holyoak (1983) found that transfer of a solution procedure was greater when participants’ schemas contained more relevant structural features. Analogical comparison has also been shown to improve learning even when both examples are not initially well understood (Kurtz, Miao, & Gentner, 2001; Gentner Lowenstein, & Thompson, 2003). By comparing the commonalities between two examples, students could focus on the causal structure and improve their learning about the concept. Kurtz et al. (2001) showed that students who were learning about the concept of heat transfer learned more when comparing examples than when studying each example separately. In an ongoing project in the Physics LearnLab by Nokes & VanLehn, (2008) students learned to solve problems on rotational kinematics in one of the three conditions: read worked examples, self-explain worked examples, and engage in analogical comparison of worked examples. Preliminary results showed that the groups that self-explained and engaged in analogical comparison outperformed the read-only control on the far transfer tests. Our current project builds upon these results by applying them in a collaborative setting. In summary, prior work has shown that analogical comparison can facilitate schema abstraction and transfer of that knowledge to new problems. However, this work has not examined whether analogical scaffolding can lead to effective collaboration. The current work examines how analogical comparison may help students collaborate effectively.

Glossary

Research Questions

How can analogical comparison help students collaborate effectively?
Can analogical comparison facilitate but also other learning mechanisms such as explanation, co-construction, and error-correction during collaboration?

Independent Variables

The only independent variable was Experimental Condition. There were three conditions: Compare, Non-compare, and Problem-solving.

Compare Condition: Participants in this condition first read through and explained two worked examples. The worked examples did not have explanations for the solution steps and students were encouraged to generate the explanations and justifications for each step of the problem. They then performed the analogical comparison task, in which they were told that their task was to explicitly compare each part of the solution procedure to one another noting the similarities and differences between the two (e.g., goals, concepts, and solution procedures). Prompts in the form of questions to guide them through this process were provided. After a fixed amount of time, they were given the model answers to the questions and asked to check them against their own answers.

Non-Compare Condition: Participants in this condition first read through a worked-out example. Similar to the non-compare condition, they were not given the explanations of the steps, and generated the explanations while working collaboratively. After reading through and explaining the first example they answered questions designed to act as prompts for the students to explain the worked example. These prompts were equivalent to the comparison prompts however they were only focused on a single problem (e.g., “what is the goal of this problem”). After a fixed amount of time, they were given the model answers to the questions and asked to check them against their own answers. They were then given a second worked example isomorphic to the first one. Again, students studied the example and generated explanations. They then answered questions based on the second worked example. After a fixed amount of time, they were provided answers to those questions.

Problem-Solving Condition: The problem-solving condition served as a control condition and collaborated to solve problems without any scaffolding. Students in This condition received the same worked examples as the two experimental groups, but without any prompts to guide them through the problem-solving process. They were given additional problems for practice, to equate the time on task with the other two conditions.

Hypotheses

The following hypotheses are tested in the experiment:

1. Analogical scaffolding will serve as a script to enhance learning via collaboration, therefore students in the compare condition will outperform students in the other two conditions. Students in the compare and non-compare conditions will both outperform students in the control condition.

2. Students learning gains will differ by the kinds of learning processes they engaged in. Specifically, students engaging in self-explaining, other-directed explaining, and co-construction will show differential learning gains. This is an exploratory hypothesis and will be tested by undertaking a fine-grained analysis of verbal protocols generated by students as they solve problems collaboratively.

Dependent Variables

Normal post-test: Near transfer, immediate: After training, students were given a post-test that assessed their learning on various measures. Specifically, 5 kinds of questions were included in the post-test.
Robust learning
- Long-term retention: On the student’s regular mid-term exam, one problem was similar to the training. Since this exam occurred a week after the training, and the training took place in just under 2 hours, the student’s performance on this problem is considered a test of long-term retention.
- Near and far transfer: After training, students did their regular homework problems using Andes. Students did them whenever they wanted, but most completed them just before the exam.
- Accelerated future learning: The training was on rotational kinematics, and it was followed in the course by a unit on rotational dynamics. Log data from the rotational dynamics homework will be analyzed as a measure of acceleration of future learning.

Results

Learning Results

During learning, students in all three conditions studied worked examples and solved isomorphic problems. The answers to compare questions and sequential questions were scored for students in those conditions. Students were given one point for every correct concept they mentioned while answering the analogical comparison questions in the compare condition or questions directed at studying individual examples in the sequential condition.

The sequential group answered a significantly higher percentage of questions (M = 70.28%, SE = 5%) correctly over the compare group (M = 50.66%, SE = 6%); F (1,22)= 5.60, p < 0.05. Next, we looked at the isomorphic problems students solved during learning. On the first isomorphic problem, the three conditions were not significantly different; F (2,33) = 0.88, ns. On the second isomorphic problem, the three conditions were marginally different; F (2,33) = 2.60, p < 0.1 and the effect was in a direction favoring the sequential group over the compare and the problem solving groups. High variation was observed in performance on the learning tasks, suggesting the possibility that individual differences would interact with learning outcomes. We are interested in testing the effectiveness of our intervention on test performance for when testing was successful. Therefore, we selected the best learners from each group by conducting a median split based on the learning scores (i.e., average scores on isomorphic problems from the learning phase). This was based on the assumption that there are some qualitative differences between learners who show high learning and those who show low learning during the learning intervention. This left us with six pairs in each group (high / low split for each condition).

Test Results

The test phase was administered individually; therefore all scores reported below are means of scores for individual students.The test phase was divided into three sections: multiple-choice, problem solving, and open-ended questions.

Multiple-Choice Test. Overall, all three conditions performed poorly on the multiple-choice questions. The overall mean was 3.82 (SE = 0.23) out of a total of ten points. There were no significant difference between conditions, F (2,69) = 0.05, ns. Therefore, we shall focus only on the performance of High learners. Item analysis of the multiple choice questions shows that the high learners in the compare condition performed significantly better than the high learners in the sequential and problem solving conditions on five questions. An ANOVA showed a significant difference between the three conditions, in a direction favoring the compare condition, F (2,33) = 3.86, p < 0.05 (See Fig. 1 for means and standard errors). Consistent with our predictions this result shows more conceptual learning for the compare condition than the sequential and problem solving conditions. Contrasts revealed that the compare group was significantly different from the sequential group t (1,33) = 2.56, p < 0.05 and problem-solving group; t (1,33) = 2.22, p < 0.05 but the sequential and problem-solving groups were not significantly different; t (1,33) = -0.34, ns.

Problem Solving Test. The problem-solving test consisted of two questions, one of which was isomorphic to one of the problems the students had encountered in the learning intervention, but had different surface features. The other problem had extraneous values, which required students to determine which of the values were critical to solving the problem before they plugged in the numbers. We conducted a mixed model repeated measures ANOVA with problem-type as the within subject factor, and condition as the between-subject factor. There was a significant interaction problem-type X condition interaction (F (2,33)=3.37, p < 0.05). (See Fig. 2) Specifically, the students in the compare condition and sequential conditions performed better on the extraneous information problems than on the isomorphic problems, whereas students in the problem solving condition performed better on the isomorphic problem than they did on the extraneous information problem.
Open-Ended Questions Test. The first question in this test consisted of two problems for which students had to determine whether the answer was correct or wrong and provide an explanation for the same. The second question consisted of two problems for which students had to calculate an answer and provide an explanation. Chi square tests revealed no difference between conditions on either question. All χ2s (2, N = 36) <4.8, ns.

Further Information

Annotated Bibliography

Accepted as a poster presentation to CogSci 2009, Amsterdam.
Presentation to the PSLC Industrial Affiliates, February, 2009
Presentation to the PSLC Advisory Board, January, 2009
Poster to be presented at the Second Annual Inter-Science of Learning Center Student and Post-Doc Conference (iSLC, '09) at Seattle, WA, February 2009

References

Chase, W. G., & Simon, H. A. (1973). Perception in chess. Cognitive Psychology, 4, 55-81.
Chen, Z. (1999). Schema induction in children’s analogical problem solving. Journal of Educational Psychology, 91, 703-715.
Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5, 121-152.
Chi, M. T. H., Roy, M., Hausmann, R. G. M. (2008). Observing Tutorial Dialogues Collaboratively: Insights About Human Tutoring Effectiveness From Vicarious Learning. Cognitive Science, 32, 301-341.
Cooke, N., Salas, E., Cannon-Bowers, J.A., Stout, R. (2000). Measuring team knowledge. Human Factors 42, 151-173.
Cummins, D. D. (1992). Role of analogical reasoning in the induction of problem categories. Journal of Experimental Psychology: Learning, Memory, and Cognition, 18, 1103-1124.
Dunbar, K. (1999). The Scientist InVivo: How scientists think and reason in the laboratory. In Magnani, L., Nersessian, N., & Thagard, P. Model-based reasoning in scientific discovery. Plenum Press.
Dunbar, K. (2001). The analogical paradox: Why analogy is so easy in naturalistic settings, yet so difficult in the psychology laboratory. In D. Gentner, Holyoak, K.J., & Kokinov, B. Analogy: Perspectives from Cognitive Science. MIT press.
Gentner, D., Loewenstein, J., & Thompson, L. (2003). Learning and transfer: A general role for analogical encoding. Journal of Educational Psychology, 95, 393-408.
Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15, 1-38.
Hausmann, R. G. M., Chi, M. T. H. & Roy, M. (2004). Learning from collaborative problem solving: An analysis of three dialogue patterns. In the Twenty-sixth Cognitive Science Proceedings.
Hummel, J. E., & Holyoak, K. J. (2003). A symbolic-connectionist theory of relational inference and generalization. Psychological Review, 110, 220-264.
Kurtz, K. J., Miao, C. H., & Gentner, D. (2001). Learning by analogical bootstrapping. Journal of the Learning Sciences, 10, 417-446.
Larkin, J., McDermott, J., Simon, D. P., & Simon, H. A. (1980). Expert and novice performance in solving physics problems. Science, 208, 1335-1342.
Lin, X. (2001). Designing metacognitive activities. Educational Technology Research & Development, 49, 1042-1629.
McLaren, B., Walker, E., Koedinger, K., Rummel, N., & Spada, H. (2005). Improving algebra learning and collaboration through collaborative extensions to the algebra tutor. Conference on computer supported collaborative learning.
Nokes, T. J. & VanLehn, K. (2008). Bridging principles and examples through analogy and explanation. In the Proceedings of the 8th International Conference of the Learning Sciences. Mahwah, Erlbaum.
Novick, L. R., & Holyoak, K. J. (1991). Mathematical problem solving by analogy. Journal of Experimental Psychology: Learning, Memory, and Cognition, 3, 398-415.
Ohlsson, S. (1996). Learning from performance errors. Psychological Review, 103, 241-262.
Paas, F. G. W. C., & Van Merrienboer, J. J. G. (1994). Variability of worked examples and transfer of geometrical problem solving skills: A cognitive-load approach. Journal of Educational Psychology, 86, 122-133.
Palincsar, A. S., & Brown, A. L. (1984). Reciprocal Teaching of Comprehension-Fostering and Comprehension-Monitoring Activities. Cognition and Instruction, 1, 117-175.
Schwarz, B. B., Neuman, Y., & Biezuner, S. (2000). Two Wrongs May Make a Right ... If They Argue Together! Cognition & Instruction, 18, 461-494.
Ward, M., & Sweller, J. (1990). Structuring effective worked examples. Cognition and Instruction, 7, 1-39.

Connections

This project shares features with the following research projects:

Future plans

Our future plans for January 2009 - August 2009:

Code collaborative transcripts for different learning processes
Conduct laboratory study

Analogical Scaffolding in Collaborative Learning

Contents