Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers.

Abstract

It is proposed that when solving an arithmetic word problem, unsuccessful problem solvers base their solution plan on numbers and keywords that they select from the problem (the direct translation strategy), whereas successful problem solvers construct a model of the situation described in the problem and base their solution plan on this model (the problemmodel strategy). Evidence for this hypothesis was obtained in 2 experiments. In Experiment 1, the eye fixations of successful and unsuccessful problem solvers on words and numbers in the problem statement were compared. In Experiment 2, the degree to which successful and unsuccessful problem solvers remember the meaning and exact wording of word problems was examined. Why are some students successful in solving word problems whereas others are unsuccessful? To help answer this question, we begin with the well-established observation that many students from kindergarten through adulthood have difficulty in solving arithmetic word problems that contain relational statements, that is, sentences that express a numerical relation between two variables (Hegarty, Mayer, & Green, 1992; Lewis & Mayer, 1987; Riley, Greeno, & Heller, 1983; Verschaffel, De Corte, & Pauwels, 1992). For example, Appendix A shows a successful and an unsuccessful solution to a two-step word problem containing a relational statement about the price of butter at two stores. We refer to this as an inconsistent version of the problem because the relational keyword (e.g., less) primes an inappropriate arithmetic operation (subtraction rather than addition), whereas in a consistent problem, the relational term in the second problem statement primes the required arithmetic operation (e.g., more when the required operation is addition). A substantial proportion of college students, who could be called unsuccessful problem solvers, use the wrong arithmetic operation on inconsistent problems but perform correctly on consistent problems (Hegarty et al., 1992; Lewis, 1989; Lewis & Mayer, 1987; Verschaffel et al., 1992). We interpret this finding as evidence that problem comprehension processes play an important role in the solution of arithmetic word problems.