Experimental Use of Problem-Posing Exercise System for Efficient Calculation to Promote Relational Interpretation of Numerical Expression

Abstract

This paper reports a development and experimental use of a computer-supported posing exercise of numerical expressions that can be solved by using efficient calculation methods. In arithmetic, a learner usually interprets the numerical expression as a calculation procedure. In mathematics, relational interpretation of the expressions becomes indispensable. This difference of the interpretations causes of difficulty in introduction phase of mathematics. This exercise is aimed to promote students in an elementary school to change their procedural interpretation to relational interpretation of numerical expressions because the efficient calculation methods request learners to interpret the numerical expressions relationally. The exercise was experimentally conducted for 78 6th grade students in an elementary school. The results of comparative analysis of calculation methods between pre-test and post-test suggest that the exercise promoted the students to interpret the numerical expressions relationally.