A Study on Teaching and Learning Using Algebraic Reasoning : Clarification of Issues in Algebraic Reasoning

Abstract

A claim of this research is to place extension to arithmetic with algebraic characteristic in the aim of arithmetic education. As for that approach, the author focused on algebraic reasoning. In such a point of view, it becomes the problem in arithmetic how algebraic reasoning is promoted. The nature of algebraic reasoning is purposeful generalization and "symbols as objects" is located as an important stage in the process of generalization. By consideration of case study on division with fraction, even if "symbols as objects" was not accompanied, algebraic reasoning worked, but it turned out that a student shows difficulty to an under-standing of generalization. Algebraic reasoning is accompanied by "symbols as objects", and going to successful generalization became clear from this. At the same time, it is clarified that successful "symbols as objects" in arithmetic is so difficult. Therefore, "a setup of learning activities suitable for a grade stage" and "recognition of quasi-variables" were key ideas that will solve the tasks of "symbols as objects".