Finding similarities and differences in the solutions of word problems.

Abstract

This study extends the Rittle-Johnson and Star (2009) research agenda of identifying when solution comparisons are effective by combining their quantitative approach with the qualitative descriptive approach advocated by Lobato (2008). In Experiment 1 university students described similarities and differences between detailed solutions of arithmetic or algebra word problems so we could determine whether such comparisons support learning of the combine and compare schema that represent semantic components of these solutions. Comparison of arithmetic solutions improved the selection of arithmetic equations to model word problems but did not transfer to algebra equations. Comparisons of the more complex algebra solutions did not result in either learning or transfer. A more scaffolded variation of the arithmetic comparisons in Experiment 2 replicated the Experiment 1 findings (learning but no transfer), but students identified more schematic components in their comparisons. Comparing a pair of arithmetic solutions followed by a pair of algebra solutions in Experiment 3 replicated the previous findings of improvement on arithmetic, but not algebra, problems. The results connect reported similarities and differences to learning (Lobato, Ellis, & Munoz, 2003) and support the conclusion that complexity can limit the potential benefits of solution comparisons (Rittle-Johnson, Star, & Durkin, 2009)