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

Abstract

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.

Drawing Attention to Diagram Use

“…Students also need to overcome hurdles associated with thinking that drawing diagrams is too diffi cult or too costly in terms of mental effort (1,8,9). There are some projects aimed at addressing these problems (10,11).…”

Editorial Expression of Concern

“…Students also need to overcome hurdles associated with thinking that drawing diagrams is too diffi cult or too costly in terms of mental effort (1,8,9). There are some projects aimed at addressing these problems (10,11).…”

Electroencephalogram Recordings Indicate That More Abstract Diagrams Need More Mental Resources to Process

“…One explanation that has been proposed to account for such inadequacies in performance is that some forms of diagrams may entail greater cognitive cost to process—in other words, that they may demand more mental resources and effort to use (Cromley, Snyder‐Hogan, & Luciw‐Dubas, ; Manalo & Uesaka, , ; Uesaka & Manalo, ). This explanation is in part based on the fact that diagrams “distort the ‘truth’” when they “abstract, schematize, supplement, and distort the world outside onto the world of a page” (Tversky, , p. 502).…”

“…The researchers also found that students often ignored or only superficially looked over diagrams while they were going through the passages—manifesting what could have been avoidant behavior and suggesting that comprehending those diagrams might have demanded a higher cognitive cost compared to comprehending the running text. Likewise, creating diagrams that represent information in more abstract forms, such as charts, may entail higher cognitive cost compared to simply drawing what is described in the given information (Uesaka & Manalo, ). In the Uesaka and Manalo study, junior high school students were given math word problems to solve and their use of diagrams in attempts at solving those problems were examined.…”

“…The results showed that the students produced fewer diagrams in attempting to solve the problems that required the production of more abstract diagrams. Such findings suggest that, in some situations, students may not have enough mental resources available to meet the requirements of constructing some diagrammatic representations (Manalo & Uesaka, , ; Uesaka & Manalo, ).…”