Visual Support for Instructional Analogy: Context Matters

Abstract

Instructional analogies can overload children’s executive function and working memory resources (see Richland, Morrison & Holyoak, 2006), though structure-mapping lies at the core of recommended pedagogy in mathematics instruction (National Mathematics Panel, 2008; NRC, 2001). Videotaped mathematics instruction was manipulated to test the role of visual representations in instructional analogy. Pretest, posttest, and delayed posttest measures assessed 11- 13 year old children’s learning from one of three versions of the same lesson in which three solution strategies (one a misconception) were compared. Analogs were either a) Not Visible (NV) - presented only orally, b) Partially Visible (PV) – only the most recent solution was visible, or 3) All Visible (AV) - all solutions were visible throughout the instruction. Overall, AV students experienced greater learning gains in procedural knowledge, procedural flexibility, and conceptual/ schematic knowledge compared to PV students. These results persist after one-week delay. Apart from procedural knowledge, the same trend is evident when comparing AV students’ to NV students’ immediate learning gains. Overall, visual representations of analogs within an instructional analogy appear to support schema formation only when they are all visible simultaneously and throughout structuremapping. Showing students visual representations of analogs but not enabling them to be simultaneously visible led to the lowest performance overall, suggesting this may lead to more object-level encoding than schema formation.


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