Investigation of Analogical Reasoning in Mathematics Education : An Analysis of Interviews on Analogical Reasoning for Third, Fourth, and Fifth Graders

Abstract

The purpose of this paper is to investigate the developmental aspects of analogical reasoning from 3rd to 5th graders, which is focused on the function of cognition/understanding. In order to analyze their analogical reasoning, five viewpoints are established as follows: (1) Representations of the targets; (2) Choices of the bases; (3) Mappings between the targets and bases; (4) Adaptation processes; and (5) Knowledge related to both the targets and bases. As a result, the following implications are found out. Firstly, when children fail to represent the targets, they fail to reason by analogy successfully. Secondly, children's knowledge related to both the targets and bases has an influence on successful analogical reasoning. Thirdly, the major point of successful analogical reasoning in this investigation is the adaptation processes. It is classified as follows: (a) Applications of relational features of the bases to the targets without any transformations; (b) Transformations of the targets for applicable; and (c) Transformations of the bases for applicable. This classification becomes difficult in turn. Finally, while 3rd graders tend to pay attention to similarities between the targets and bases, 4th and 5th graders pay attention to not only the similarities but also differences between the targets and bases. 4th graders, however, tend to give rise to cognitive conflict between the targets and bases because of the differences.