A Study of the Roles of Diagrams in Solving Word Problems for Elementary School Arithmetic

Abstract

The purpose of this study is to propose an effective utilization of diagrams in the teaching/learning of solving word problems for elementary school arithmetic. In this paper, we especially show the roles of diagrams in teaching/learning word problems of the arithmetic operations of integers and decimal numbers based on the classifications of diagrams in the textbooks. We propose a classification of diagrams for solving word problems as follows; reality diagrams, mathematical scene diagrams, structure diagrams, procedure diagrams and relation diagrams. We also show that the flow of teaching/learning calculations in the textbook matches Mayer’s process of solving word problems. Furthermore, we indicate the relation between this flow and the diagrams. Based on this relation, we show that the mathematical scene diagrams and the structure diagrams are useful for grasping quantitative relations and formularizing algebraic expressions. Utilizing these diagrams is useful for going back and forth between the step of grasping the problem and the step of getting the solution.