Analogy Use in Eighth-Grade Mathematics Classrooms

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Compared With What? The Effects of Different Comparisons on Conceptual Knowledge and Procedural Flexibility for Equation Solving (2009, methodology): “…these features are 1) a written record of all to-be-compared solution methods, with the solution steps aligned (Fraivillig, Murphy, & Fuson, 1999; Richland et al., 2004; Richland et al., 2007) 2) explicit opportunities to identify similarities and differences in methods (Catrambone & Holyoak,…”
Middle school children’s cognitive perceptions of constructive and deconstructive generalizations involving linear figural patterns (2008, background): “Performing analogy involves ‘‘perceiv[ing] and operat[ing] on the basis of corresponding structural similarity in objects whose surface features are not necessarily similar’’ ( Richland, Holyoak, & Stigler, 2004, pp. 37 ‐38).”
Learning by analogy: Discriminating between potential analogs (2010, background): “Second, we sought to generalize across the two most common types of mathematical analogies in US instruction (Richland et al., 2004).”
Learning by Mapping Across Situations (2012, methodology): “An example is the previously cited case from the Third International Mathematics and Science Study (Richland et al., 2004).”