Using Elaborated Explanations to Support Geometry Learning (Aleven & Butcher)

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Using Elaborated Explanations to Support Geometry Learning

Vincent Aleven & Kirsten Butcher

NOTE: This page is IN-PROGRESS as of February 27, 2007.

Abstract

Does integration of visual and verbal knowledge during learning support deep understanding? Can visually-related explanations during student learning promote robust learning in geometry? In our research, we are exploring how student explanations in an intelligent tutoring environment can support learning. We are investigating the use of elaborated explanations. Elaborated explanations are a form of interactive communication in which students justify problem solving steps by giving an explanation that connects to both visual and verbal knowledge components. In our studies, students give a verbal explanation by stating a geometry rule as well as a visual explanation by stating the diagram features that are being used by the stated rule. We hypothesize that explanations that reference visual and verbal knowledge components will support the integration of visual and verbal knowledge during learning, leading to better understanding of geometry principles.

This study is part of a larger project targeted toward developing a better understanding of 1) visual and verbal knowledge components in a problem-solving environment and, 2) how interacting with visual information can support the development of deep understanding. Ultimately, we are interested in coordination and integration processes in learning with visual and verbal knowledge components, and how these processes may support robust learning.

Glossary

See Visual-Verbal Learning Project Glossary

Research question

  1. Can explanations that connect visual and verbal knowledge components support learning better than explanations that reference verbal information only?
  2. What robust learning processes are affected by elaborated explanations during problem-solving?

Background & Significance

A rich body of prior research has demonstrated that students develop deeper understanding of instructional materials when they self-explain to themselves during learning (e.g., Bielaczyc, Pirolli, & Brown, 1995; Chi, Bassok, Lewis, Reimann, & Glaser, 1989; Chi, de Leeuw, Chiu, & LaVancher, 1994). An existing version of the Geometry Cognitive Tutor implements student self-explanations of their problem solving using a very simple process: after correctly answering a geometry problem step, students must select the geometry rule or theorem that justifies their answer from a glossary menu of terms. Despite the limitations of the menu-based explanations, they have been shown to promote student learning in the Geometry Cognitive Tutor (Aleven & Koedinger, 2002). Thus, our question is whether more explicit forms of communication that link verbal and visual knowledge components can be more successful at promoting robust learning. We argue that scaffolds that promote sense making using both visual and verbal knowledge may be of greater benefit to students than scaffolds that require student explanations using only verbal declarative knowledge.

Dependent variables

  • Pretest, normal post-test, and immediate transfer test measuring student performance on:
    • Problem-solving items isomorphic to the practiced problems (near-term knowledge retention)
    • Problem-solving items unlike those seen during problem practice (near-term knowledge transfer)
  • Delayed posttest, measuring student performance on:
    • Problem-solving items isomorphic to the practiced problems (far-term knowledge retention)
    • Problem-solving items unlike those seen during problem practice (far-term knowledge transfer)
  • Log data collected during tutor use, used to assess:
    • Learning curves
    • Time on task
    • Error rates
    • Latency of responses

Independent Variables

2. Type of Explanation
Verbal explanations (students state geometry principles only) vs. Elaborated Explanations (students state geometry principles and their application to the diagram)

ADD SCREEN SHOTS

Hypothesis

  • Elaborated explanations promote integration of visual and verbal knowledge components during problem-solving, thus supporting knowledge transfer.

Findings

Paper-based Difficulty Factors Analysis

  • Summary
    • In Vivo Study: 10th grade geometry classes in rural Pennsylvannia school
    • Format: Paper-based Difficulty Factors Analysis (DFA) covering Angles content from the Geometry Cognitive Tutor
    • Problems varied along two dimensions:
      • Problem Format: Diagram vs. Table. In Diagram-format problems, students entered answers within the geometry diagram. In the Table format, students entered answers in a table separate from the geometry diagram.
      • Explanation Type: Simple vs. Elaborated Explanations. Simple explanations required students to name only the geometry rule that justified their problem-solving steps. Elaborated explanations required students to name the geometry rule and the known diagram elements that allowed them to use the rule for each problem-solving step.
    • Students using the standard version of the Geometry Cognitive Tutor took the paper-based DFA test midway through their completion of the Angles unit on the tutor.
  • Findings
    • Although there is an overall trend that, with no practice, students perform best in the familiar Table format (F (1, 88) = 3.47, p = .07), the type of explanations required significantly impacted performance (F (1, 88), = 6.75, p = .01). Students performed better on problem-solving when required to provide elaborated explanations (M = 42., SE = .04) compared to when they produced only simple, rule-based explanations (M = .34, SE = .04).

In-vivo Study of Elaborated Explanations

This data is currently being uploaded to the Datashop. We anticipate that elaborated explanations will support students' performance on transfer tasks, especially the ability to reason about conceptual relationships in a geometry diagram.

KB: Expand this section!!

Explanation

We have evidence from the (paper-based) difficulty factors analysis that elaborated explanations support problem solving performance. We hypothesize that the classroom test of elaborated explanations will show support for robust learning. That is, we anticipate that the classroom test will show not only support for retention but also transfer of geometry knowledge.

From an Interactive Communication Cluster perspective, the elaborated explanations help students focus on the right content for problem solving. Students will be less likely to engage in shallow strategies or to focus on irrelevant features in problem solving when tutored to make these explanations.

From a broader PSLC perspective, elaborated explanations support coordination through self-explanation of visual and verbal information. Communication that makes use of multiple representations during learning likely affects path choice. For example, when students are required to explain the application of geometry principles using diagrams, there will be only small differences in estimated effort of shallow and deep strategies since shallow strategies are unlikely to achieve the correct answer. Further, we anticipate that elaborated explanations also produce path effects: the processes that students employ via path choice are more effective when the materials support use of visual and verbal information during sense making. Specifically, scaffolds or materials that support sense making with visual and verbal information should promote integration.

Annotated Bibliography

  • Presentation to the PSLC Advisory Board, Fall 2006. Link to Powerpoint slides
  • Butcher, K. B., & Aleven, V. A. (submitted). Integrating Visual and Verbal Knowledge During Classroom Learning with Computer Tutors. Paper submitted to Cognitive Science 2007 Conference.

References

  • Bielaczyc, K., Pirolli, P. L., & Brown, A. L. (1995). Training in self-explanation and self-regulation strategies: Investigating the effects of knowledge acquisition activities on problem solving. Cognition & Instruction, 13, 221-252.
  • Chi, M. T., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. Cognitive Science, 13, 145-182.
  • Chi, M. T. H., de Leeuw, N., Chiu, M.-H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. Cognitive Science, 18, 439-477.
  • Koedinger, K. R., & Anderson, J. R. (1990). Abstract planning and perceptual chunks: Elements of expertise in geometry. Cognitive Science, 14, 511-550.
  • Lovett, M. C., & Anderson, J. R. (1994). Effects of solving related proofs on memory and transfer in geometry problem solving. Journal of Experimental Psychology: Learning, Memory, and Cognition, 20, 366-378.
  • Mayer, R. E. (2001). Multimedia Learning. Cambridge, Cambridge University Press.
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