Solution processes of arithmetic word problems generally involve two steps, language understanding and problem solution (Kintsch & Greeno, 1985; Mayer, 1986; Riley, Greeno, & Heller, 1983). Language understanding refers to reading arithmetic word problems and understanding the information conveyed by arithmetic word problems. Problem solution refers to applying a solution plan to problem representation which subjects have generated and to executing a planned operation. The present study focuses on language understanding of arithmetic word problems. The experiment was designed to extend the finding of Tajika & Ishida (1989) that subjects understood the integrated semantic structure in solving word problems. Tajika & Ishida (1989) presented rate word problems to subjects under three conditions. The subjects were six graders in an elementary school and were assigned to one of three groups. Subjects in the 'memory condition' group memorized word problems presented to them. Subjects in the 'writing condition' group wrote down word problems. Subjects in the 'solving condition' group solved word problems. Word problems contained three types of propositions: Assignments, relations, and questions (See Mayer, 1986; Mayer, Larkin, & Kadane, 1984). Assignments were propositions which assigned a value to a variable. Relations were propositions which expressed a quantitative rate relation. Questions were propositions which asked for a numerical value of a variable. Then, each subject recalled word problems. The results showed that subjects who solved word problems recalled as many relations as those who memorized them, and that subjects who solved hard word problems incorrectly made more recall errors of relations than those with correct performance. The results suggest that subjects with correct performance understand the integrated semantic structure which consists of a unified representation of each proposition and the relation among propositions. The question of whether subjects understand the integrated semantic structure in solving word problems is of some interest. The purpose of the present experiment is to test our claim further. If subjects were presented word problems without relations and could generate relations when they were asked to generate relations, this would constitute powerful evidence for understanding the integrated semantic structure in solving rate word problems.
View full abstract