数学的概念の形成を図る集団解決の在り方に関する研究(1) : 数学的概念のモデル及びその評価

抄録

This research is related to the group discussion method to promote the formation of the mathematical concept. Especially, this research applies the focus to the proposal and the evaluation of the model of a mathematical concept as a basic research. The main contents of this research are as follows. (1) It is mentioned that there is a tendency that the teaching of elementary school mathematics leans toward instrumentalism as a result of the preceding research. (2) The characteristics of the mathematical concept are discussed from the aspect of "instrument", "representation", "definition" and "relationship". Moreover we classified "relationship" into "functional relationship", "conceptual relationship" and "social relationship". (3) The characteristics of the formation of the mathematical concept are discussed from the point of view of "development" and "hierarchy". We described the lesson as the transformation process of private mathematical concepts into public mathematical concepts. In this discussion "relationship" played an important role. (4) We proposed the model of the mechanism of the formation of the mathematical concepts and referred "teacher", "learning materials" and "children" as factors to promote the formation of the mathematical concepts. (5) Finally we tried to evaluate the effectiveness of the model proposed in this paper by appling it to a lesson.