「誤り」を生かす数学の授業に関する研究 : 実験授業の実践的検討

抄録

The purpose of a series of my studies is to construct the process and principles of teaching mathematics using "errors" in order to change mathematical belief of students. In this paper I practically examine the validity of the process and principles of teaching mathematics through an experimental class on "the barycenter of quadrangle" for eleventh grade students. It is based on Lakatosian theory (Quasi-empirical view of Mathematics (1978), The logic of mathematical discovery (1980), The methodology of scientific research programmes (1986)). As a result of this practice, the validity of teaching process was suggested, because many students realized the significance of using an "error". And the validity of teaching principles for posing problems (Ia, Ib, Va) was suggested, but the validity of principles for the role of teacher in class was not necessary suggested. Moreover I suggested three implications so as to more validly use the process and principles of teaching mathematics using "errors".