Contiguous Representations for Robust Learning (Aleven & Butcher)

Learning with Diagrams in Geometry: Strategic Support for Robust Learning

Vincent Aleven & Kirsten Butcher

Summary Table

STUDY 1

PIs	Vincent Aleven & Kirsten R. Butcher
Other Contributers	Graduate Students: Andy Tzou (CMU HCII), Carl Angioli (CMU HCII), Michael Nugent (Pitt, Computer Science) Research Programmers/Associates: Octav Popescu (Research Programmer, CMU HCII), Grace Lee Leonard (Research Associate, CMU HCII), Thomas Bolster (Research Associate, CMU HCII)
Study Start Date	January 24, 2006
Study End Date	February 22, 2006
LearnLab Site	Central Westmoreland Career & Technology Center (CWCTC)
LearnLab Course	Geometry
Number of Students	65
Total Participant Hours	390
DataShop	Log data is uploaded and available in the DataShop

Abstract

Does integration of visual and verbal knowledge during learning support deep understanding? Can student interactions with visual information during problem-solving support robust learning? The overall goal of this project is to gain 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.

We are using the Geometry Cognitive Tutor as a research vehicle for our project. In geometry, visual information is represented in a problem diagram and verbal/symbolic information is represented in text that contains given and goal information as well as in conceptual rules/principles of geometry. The goals of this research are to investigate how coordination between and integration of visual and verbal information influence robust learning processes, as measured by knowledge retention and transfer. By coordination, we mean the processes that support mapping between relevant visual and verbal information as well as the processes that keep relevant knowledge components active. For example, in geometry a student needs to map between text references to angles and their location in a diagram and will need to maintain the numerical (given or solved) value of that angle to use in problem solving. By integration, we mean knowledge construction events that involve both visual and verbal knowledge components. For example, in geometry a student may need to construct an understanding of linear angles that includes both a verbal definition (e.g., “two adjacent angles that form a line”) and a visual situation description (e.g., a visual representation of the two angles formed by intersection of a line).

Glossary

See Visual-Verbal Learning Project Glossary

Research question

• Do students learn more with contiguous representations that support direct students' interaction and reasoning with diagrams during practice? Is a contiguous representation sufficient to support integration of visual and verbal knowledge components?

Background & Significance

In this research, we draw upon previous work in learning with multimedia sources, self-explanations, and Cognitive Tutors. We hypothesize that two key cognitive processes support integrated knowledge development and robust learning when using visual and verbal representations. These processes are: 1) Successful mapping between visual and verbal information, and 2) Integration processes that combine visual and verbal representations into integrated knowledge components. Previous research has suggested that contiguous representations -- those that provide close temporal and physical proximity between visual and verbal elements during learning -- can support understanding of multimedia materials (e.g., Mayer, 2001); these benefits have been hypothesized to result from the easing of cognitive load required for mapping between visual and verbal information. We are investigating if these benefits can be seen during real classroom learning when students engage in extended practice with learning materials. Our research examines the potential benefits of contiguity during intelligent tutoring for robust learning in classroom environments.

In the context of the Geometry Cognitive Tutor, contiguity is achieved by placing related representations, such as a diagram and a workspace in which answers are entered, in close proximity that reduces (and in some cases, removes) the need for mapping between visual and verbal information. Although contiguous representations may reduce the initial cognitive load associated with mapping between representations, cognitive load demands may be less influential in classroom environments where practice is extended and distributed (ADD REFS). Thus, we assume that contiguous representations can support robust learning by promoting integration of visual and verbal information during practice. That is, contiguity may support students' connection between and integration of visual and verbal information leading to more robust knowledge of geometry principles. If these assumptions are true, we would expect to see similar performance on practiced problems for students who trained with contiguous vs. noncontiguous representations. However, we would expect students using the contiguous representations to demonstrate better knowledge transfer.

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)

• Log data collected during tutor use, used to assess:
  • Learning curves
  • Time on task
  • Error rates
  • Latency of responses

Independent Variables

• Contiguity of Representation

Contiguous representation (students work in diagram) vs. Non-contiguous representation (students work in separate table)

Figure 1. Noncontiguous representation: Screen shot of tutor interface.

Figure 2. Contiguous representation: Screen shot of tutor interface.

Hypotheses

• Contiguous representations increase strategic inferences and integration of visual and verbal knowledge components during problem-solving, thus supporting knowledge transfer.

Findings

Current findings suggest that interaction with visual representations during problem-solving supports deep transfer during learning.

Study 1 (In Vivo, Geometry Cognitive Tutor)

• Summary
  • In Vivo Study: 10th grade geometry classes in rural Pennsylvannia school
  • Domain: Angles curriculum in the Geometry Cognitive Tutor
  • Grade-matched pairs of students were randomly assigned to one of two conditions:
    • Diagram (Contiguous) Condition: Students interacted directly with geometry diagrams and accepted answers are displayed directly in the diagram
    • Table (Noncontiguous) Condition: Students work separate from the diagrams, in a distally located table

• Findings
  • No overall effect of experimental condition on students' performance on geometry answers or reasons at posttest
  • Although working in the Diagram condition improved lower-knowledge students' explanations at posttest, higher-knowledge students performed best when working in the Table condition. The result was evidenced by a significant 3-way interaction of Test Time (Pre- vs. Posttest) X Condition (Table vs. Diagram) X Prior Knowledge (Higher vs. Lower) for students' performance on geometry rules at posttest (F(1,39) = 6.2, p < .02).

Study 2 (In Vivo, Geometry Cognitive Tutor)

• Summary
  • In Vivo Study: 10th grade geometry classes in rural Pennsylvannia school
  • Domain: Circles curriculum in the Geometry Cognitive Tutor
  • Assessment was expanded to include not only answers and explanations for problem-solving items (as in Study 1), but also explanations on deep transfer items (explanations of unsolvable problems) and non-numerical reasoning items (true/false items that require students to judge whether a geometry rule is appropriate to relate named diagram elements).
  • Grade-matched pairs of students were randomly assigned to one of two conditions:
    • Diagram (Contiguous) Condition: Students interacted directly with geometry diagrams and accepted answers are displayed directly in the diagram
    • Table (Noncontiguous) Condition: Students work separate from the diagrams, in a distally located table

• Findings
  • Problem-solving: No condition differences for numerical answers (F(1, 89) = 1.03, p > .3) or explanations for solvable problems (F(1, 89) <1).
  • Deep Transfer Explanations: There was a significant effect of condition on students' explanations of unsolvable problems (F(1, 89) = 4.1, p = .046). Students in the Diagram (Contiguous) condition explained unsolvable problems better (M = .13, SE = .03) than students in the Table (Noncontiguous) condition (M = .06, SE = .02).

Figure 3. Mean performance on explanations for unsolvable problems by experimental condition, at pre- and posttest.

• True/False items: Although there were no condition difference for performance on "true" items (F(1,89) = 2.4, p = .13), students in the Diagram (Contiguous) condition better recognized and explained false answers at posttest (F (1, 89) = 4.3, p = .04). That is, students from both conditions were equally able to recognize statements that gave valid relationships between geometry rules and diagram elements (Diagram, M = .71, SE = .04; Table, M = .72, SE = .03). However, students who interacted with diagrams during practice were better able to recognize when and explain why given geometry rules were inappropriate to relate named diagram elements (M = .23, SE = .02) than students who worked separately from diagrams during practice (M = .17, SE = .02).

Figure 4. Mean performance on recognizing/explaining inappropriate applications of geometry rules, by experimental condition at pre- and posttest.

Explanation

The deep transfer benefits seen in Experiment 2 suggest that contiguous representations may help students integrate visual and verbal knowledge components during learning. From a Coordinative Learning perspective, the contiguous tutor interface provides implicit support for active knowledge construction during tutored problem solving. Although the same diagram (an implicit/passive form of instruction) is present in both the contiguous and the noncontiguous representations, active interaction with the diagram (an active/implicit form of instruction) supports knowledge transfer following tutored practice.

Although we cannot rule out the possibility that contiguous representations may support mapping between visual and verbal information in problem-solving, we see little evidence for substantial performance-based effects of mapping support on our normal post-test. All students performed equally well on trained problem-solving skills. Especially for higher-knowledge learners, interactive tutored practice may support mapping sufficiently to promote retention of knowledge components.

In general PSLC terms, the contiguous representations reduce the effort of deep learning paths in the learning event space (by supporting strategic inferences and reasoning directly with the diagram). Our data may also suggest that contiguous representations can have a learning path effect: students who are able to reason directly with diagram representations may attend more closely to the geometric features and relations to which geometry principles apply. This could impact meaningful learning by increasing feature validity of the visual and verbal knowledge components.

Connections

Related Studies
Visual Representations in Science Learning (Davenport, Klahr & Koedinger)

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

• Mayer, R. E. (2001). Multimedia Learning. Cambridge, Cambridge University Press.