Prospects for Didactics of Mathematics as Mathematics Education Research: A Study on a Research Method in Terms of Curriculum Development in Mathematical Induction

Abstract

　　Previous Japanese studies on mathematics education have been focussed on primary education.  This is because learning has been prioritised over teaching.  Yet if we consider how contemporary society is lifelong learning, then it is upper secondary education that we ought to concern ourselves with and must uncover the prospects from the vantage point of didactics.  Thus, we aimed to establish a research method in the form of didactics of mathematics in terms of curriculum development in mathematical induction.  

　　As teaching is central to didactics of mathematics, the study of teaching materials becomes the most important core of this research method.  In order to bring together the various backgrounds relating to the study of teaching materials, we turned to Prof. Dr. Wittmann’s SLEs and Prof. Dr. Chevallard’s didactic paradigm of questioning the world.  While the former emphasises mathematical contents themselves as well as their systematisation, the latter takes an interest in methods of mathematical questioning.  As such, we developed an SLE and designed its implementation according to the didactic paradigm of questioning the world before conducting a teaching experiment.   

　　This paper concludes that such a study of teaching materials can itself be framed as a research method in the form of didactics of mathematics.  This is a case study on mathematical induction, where we developed ‘cut & paste problems’ by mixing isometric and isoperimetric problems and conducted a teaching experiment through questioning-the-world teaching.  The paper also reports on the results thereof.