数学学習におけるプログラミングの居場所 ―コラッツ予想を題材にした探究型学習を通して―

抄録

　　The aim of this paper is to understand the place of programming in mathematics learning.  In this study, we hypothesized that one of such places is the inquiry activity, and we designed lessons with the Collatz problem, an unsolved problem in mathematics.  The lesson design was based on the ideas of the paradigm of questioning the world, specifically Study and Research Paths (SRP).  SRP formulated within the Anthropological Theory of the Didactic (ATD) is an inquiry activity aiming at nurturing researcher’s attitude and allowing students to use any media (internet, book, etc.) and to learn mathematics according to its necessity during inquiry.  We carry out a teaching experiment for the students of grade 2 in Japanese high school, using the question related to the Collatz problem.  The data collected in this teaching experiment are analyzed by means of different concepts related to SRP.  We used a QA map that can describe the questions-answers dialectic in the inquiry activity, and we made several characterizations of the QA map to describe the dialectic between mathematics and programming.  The result of analysis showed that students engaged in inquiry activities similar to those of researchers, and they were actively using the program in their activities.  The analysis also shows that there are two different characteristics of the program developed in the inquiry process.  On the one hand, it is to ignore the economy of the program when writing it.  On the other hand, it is the use of media references to codes that have not yet been learned.  These characteristics reveal that students use programming as a tool in their mathematical inquiry.  We conclude from these results that one place for programming in mathematics learning is the mathematical inquiry.