Computational Thinking as a Subject of Research in the Field of Mathematics Education: Mutual Development of Mathematical and Computational Thinking

Abstract

　　In international educational discourses, economic and political driving forces are introducing computational thinking, which was originally advocated by an information scientist J. M. Wing, for mathematics education. Introduction of programming education in Japanese primary education in 2020 can be considered as a step toward this movement.  However, existing studies on mathematics education have put less emphasis on the idea of computational thinking as a subject of research, although it has the potential to radically change the national curriculum of mathematics education.  The purpose of this study is to argue why we need to consider the idea of computational thinking in mathematics education research, and to elaborate on its potential impact on educational practices and curriculum development of mathematics.  

　　The structure of this paper is as follows: 1) an overview of international research trend on computational thinking; 2) theoretical consideration of the reciprocal relationship between developmental paths of mathematical and computational thinking; 3) illustration of concrete mathematical contents to exemplify the reciprocal relationship; and 4) further consideration on a distinction between mathematical and computational thinking in mathematical activities.  

　　The results reveal the reciprocal relationship, that is, in mathematical activities, a kind of computational thinking can be developed using mathematical thinking, and conversely, a different kind of mathematical thinking can be developed using computational thinking.  In addition, three new roots of mathematical topics through mathematical activities with computational thinking were identified: A) reification of mathematical procedures by creating new mathematical objects; B) methodological consideration of mathematical methods as theoretical ways of problem solving in the idealized mathematical world; and C) methodological consideration of mathematical methods as practical ways of problem solving in the real world.  Based on these findings, future research directions are discussed.