Contiguous Representations for Robust Learning (Aleven & Butcher)

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Learning with Diagrams in Geometry: Strategic Support for Robust Learning

Vincent Aleven and Kirsten Butcher

Summary Table

Study 1

PIs Vincent Aleven & Kirsten R. Butcher
Other Contributers Graduate Students: Andy Tzou (CMU HCII)

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
Data available in DataShop

Dataset: Contiguity CWCTC Winter 2006

  • Pre/Post Test Score Data: No
  • Paper or Online Tests: Paper
  • Scanned Paper Tests: No
  • Blank Tests: No
  • Answer Key: No


Study 2

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 April 28, 2006
Study End Date May 26, 2006
LearnLab Site Central Westmoreland Career & Technology Center (CWCTC)
LearnLab Course Geometry
Number of Students 130
Total Participant Hours 780
Data available in DataShop

Dataset: Contiguity CWCTC Spring 2006

  • Pre/Post Test Score Data: No
  • Paper or Online Tests: Paper
  • Scanned Paper Tests: No
  • Blank Tests: No
  • Answer Key: No


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 research described here investigates whether implicit instruction (via direct interaction with visual information during learning) can support robust learning through visual-verbal coordination during learning. This implicit instruction is achieved via interactive instructional events in an intelligent tutoring environment, where students receive feedback on error and perform a simple (menu-based) form of self-explanation during practice.

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.

We hypothesize that implicit instruction that supports interaction with visual information will support coordination between and integration of visual and verbal information, promoting robust learning 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 visual-verbal integration, we mean knowledge construction events that involve generating a representation that includes 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).

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 (Olina, Reiser, Huang, Lim, & Park, 2006). 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.

Glossary

See Visual-Verbal Learning Project Glossary

Research questions

  1. Do contiguous representations in geometry support students' retention and transfer of knowledge components?
  2. Are the effects of contiguous representations stronger for transfer than for retention?

Dependent variables

  • Pretest, normal post-test, and transfer test measuring student performance on:
    • Problem-solving items isomorphic to the practiced problems (normal post-test)
    • Complex and demanding problem-solving items unlike those seen during problem practice (transfer)
  • Log data collected during tutor use, used to assess:
    • Learning curves
    • Time on task
    • Error rates
    • Latency of responses
  • (Planned) Log data collected during subsequent tutor use, will use to assess:
    • Accelerated future learning
      • (Note: Not available for studies conducted in "Circles" unit of the Geometry Cognitive Tutor, since the Circles unit is completed at the end of the school year.)

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.
Butcher TableScreenShot2.jpg

Figure 2. Contiguous representation: Screen shot of tutor interface.
Butcher DiagramScreenShot.jpg

Hypotheses

  • Contiguous representations increase strategic inferences and integration of visual and verbal knowledge components during problem-solving. The resulting Visual-verbal Integration will support deep learning as evidenced by transfer items the require joint analysis with geometry principles and diagrams.

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.
Butcher UnsolvableExplanations.jpg

  • 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. Butcher FalseExplanations.jpg

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 instructional support for coordination of visual-verbal knowledge 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. Active integration may cause students to attend to both representations simultaneously and thereby better distinguish relevant from irrelevant features. Enhanced attention to both representations may facilitate a process like co-training: Through easier coordination of feature interpretations across the visual and verbal representations, the student may be more likely to prune irrelevant features (e.g., the apparent size of an angle) that may be absent or inconsistent across representations and notice relevant features (e.g., the given geometric constraints on an angle) that may be present or consistent across representations. Such instructional facilitation of coordination should increase feature validity of knowledge components and promote robust learning.

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 at least near-term retention of knowledge components.

In terms of the micro-level of the theoretical framework, the contiguous representations should 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.

Further Information

Connections

Interactive Communication as Support for Visual-Verbal Integration:
Our research is investigating multiple methods with which student learning can be supported by interactions with pictorial information during geometry learning -- see also our work on Integrated Hints in geometry: Mapping Visual and Verbal Information: Integrated Hints in Geometry (Aleven & Butcher). However, our work also includes more a more explicit method for supporting student integration visual and verbal knowledge components. This method involves interactive support for students' elaborated explanations during geometry learning. Research investigating this explicit support is part of the Interactive Communication Cluster: Using Elaborated Explanations to Support Geometry Learning (Aleven & Butcher)

Visual Representations for Robust Learning in Other Domains: Our efforts to support students' integration of visual and verbal knowledge are informed by and related to efforts investigating the use of visual representations to support robust learning in other domains. A closely related PSLC project is Visual Representations in Science Learning (Davenport, Klahr, & Koedinger), in which researchers are exploring whether coordination between verbal and visual representations can help students refine initially shallow understandings into meaningful chemical concepts.

Annotated Bibliography

  • Presentation to the PSLC Advisory Board, Fall 2006. Link to Powerpoint slides
  • Butcher, K., & Aleven, V. (2007). Integrating visual and verbal knowledge during classroom learning with computer tutors. In D.S. McNamara & J.G. Trafton (Eds.), Proceedings of the 29th Annual Cognitive Science Society (pp. 137-142). Austin, TX: Cognitive Science Society. PDF File
  • Butcher, K., & Aleven, V. (2008). Diagram Interaction during Intelligent Tutoring in Geometry: Support for Knowledge Retention and Deep Understanding. In B. C. Love, K. McRae, & V. M. Sloutsky (Eds.), Proceedings of the 30th Annual Conference of the Cognitive Science Society (pp. 1736-1741). Austin, TX: Cognitive Science Society.

References

  • Mayer, R. E. (2001). Multimedia Learning. Cambridge, Cambridge University Press.
  • Olina, Z., Reiser, R., Huang, X., Lim, J., & Park, S. (2006). Problem format and presentation sequence: Effects on learning and mental effort among U.S. high school students Applied Cognitive Psychology, 20, 299-309.