A Cognitive Component Analysis in Solving Arithmetic Word Problems

Abstract

When understanding processes of arithmetic word problem solving are broken down into two components, translation and integration components, we explored which of the two cognitive components is more closely associated with solution accuracy in arithmetic word problems. Subjects were one hundred and seventy-four fifth-grade children. Two independent variables were experimental condition (the relational picture group, the diagram group, or the control group) and problem type (easy problems or hard problems). Three problems evaluating the translation component asked students to identify the contents of each statement of each word problem. Problems for the integration component consisted of two types of questions: diagrams and relational pictures. Prior to solving each of eight word problems, subjects under each group were asked to perform each task. The results showed that subjects in the relational picture group performed best. The results indicated that the students who solved problems involving relational pictures, that is, problems emphasizing the integration component, performed best on arithmetic word problem solving. We interpreted the results of this experiment in terms of the problem solving components.