A Comparison of Sketching and Self-Explanation When Solving Math and Science Problems

• In Event: 3-219 - Exploring New Translational Science Approaches to Incorporate Spatial Thinking in Elementary Science

Integrative Statement

Sketching and self-explanation have demonstrated promising effects on problem solving performance, likely because they encourage learners to generate their own understanding (Eden & Potter, 2008). Further, they often produce more favorable results relative to other generating activities (Gagnier, Atit, Ormand, & Shipley, 2016). However, it is unclear whether either method provides unique benefits. Sketching may be useful for activities requiring enhanced spatial ability, while self-explanation may be beneficial for verbal activities. We examined the unique and joint contributions of sketching and self-explanation to explain mathematical and scientific problem solving and whether effects varied by domain (math vs. science) and problem spatialization (high vs. low).

Sixth graders (N = 156) completed prior math and science knowledge measures before condition assignment. In the read-only condition, students solved problems without prompting. If self-explaining, students were prompted to explain how the different parts work together and why. If sketching, students were reminded to sketch a diagram that includes the important parts of the problems and how they relate to each other. Combination conditions included both of the prior instructions with instruction order counterbalanced. Participants said everything they were thinking and doing aloud while solving eight math and science problems, four of which were highly spatialized (requiring a picture to conceptualize) and four were low spatialized (requiring only calculations).

Sketches were broken as elements (e.g. each individual dimension of a rectangular prism), and relationships between components (e.g., area of one plane equals one-dimension times another). Think-alouds were scored for each element and relationship scored by the type of representation: element invocation or identifying a problem feature without considering relationships between features. Accuracy scores were independent of student diagrams and think-alouds. Answers were rated as 0 (incorrect), 1 (partially correct), and 2 (correct). Problem scores were averaged across problems.

For math, the sketch – only group significantly outscored the read-only control group (χ2 [3, N = 162] = 8.716, p = .03, φ = .23, p = .019), but none of the other comparisons were significant. For science, sketching conditions significantly outscored the read-only control group (χ2 [3, N = 171] = 11.034, p = .01, φ = .31; Sketch > Read-only, p = .011, and Combination > read-only, p = .006), but self-explanation alone did not lead to significantly higher science performance. A mixed 4 (between: Condition) x 2 (within: Spatialization) x 2 (within: Domain) analysis of variance showed main effects of spatialization and domain, but no interactions. Performance was higher on questions involving low-spatialized content (M = 1.40 vs. 1.03) and was higher on science questions than on math questions (M = 1.83 vs. .60).

Students prompted to sketch demonstrated higher performance scores for both science and math problems than students in other conditions and low spatialized problems appeared to be easier for students. It may not be enough to encourage students to sketch when problem solving. Teachers may discover that attending to what students are sketching is informative, as it provides information about students’ problem comprehension, particularly if problems require visualizing in different ways.

Authors

• Dana Miller-Cotto, University of Pittsburgh
  Presenting Author

• Julie Booth, Temple University
  Non-Presenting Author

• Brianna L. Chang, The College Board
  Non-Presenting Author

• Jennifer G. Cromley, University of Illinois-Urbana Champaign
  Non-Presenting Author

• Nora S. Newcombe, Temple University
  Non-Presenting Author

• Taylor A. Williams, University of Illinois-Urbana Champaign
  Non-Presenting Author