Task-Related Factors that Influence the Spontaneous Use of Diagrams in Math Word Problems

Diagrams are effective tools for problem solving. However, previous findings indicate that students generally do not use diagrams spontaneously. This study examined task-related factors that may influence the spontaneity of diagram use. Experiment 1 compared two possible explanations: the first, that the length-relatedness of the story context of the problem (i.e. whether it involves the measurement of length) determines the likelihood of diagram use; and the second, that the cognitive cost of transforming the situation described in the word problem to an abstract diagrammatic representation is the more important factor. Four math word problems, differing in their story context and structure, were administered to eighth-grade Japanese students (n=125) to solve. The results provide support for the cognitive transformation cost explanation. The results of experiment 2, in which the problems were administered to students in both Japan (n=291) and New Zealand (n=323), confirm this finding.