「必要条件」という概念の本来の機能の発生とその顕在化 ―論理概念の高校数学における生息可能性―

抄録

　　In Anthropological Theory of Didactic, it is often questioned what is the condition under which specific knowledge can “live” in a given institution, and also what will happen if the condition varies.  In this paper, we focus on the logical concepts such as “necessary condition” in secondary mathematics.  It has been reported that notions of “necessary condition” and “sufficient condition” are often just memorized in a contextless way by students and lose their raison d’être in studying.  We point out that this loss of their raison d’être comes from the missing of the niche of logical notions.  Therefore, in this paper, we propose a practical course of lessons in which the raison d’être of the logical notion “necessary condition” can be actualized.  The theme of the class is to search for similarly-dissectable triangles, that is, triangles which can be dissected into two figures which are similar each other.  Then we show the results of this practice and discuss the possibility that logical notions can “live” in the institution of secondary mathematics.