数学的な方法知の育成へ向けた発問行為を設計するための理論的枠組の開発 ―高校数学Ⅰにおける２次関数の応用場面を題材として ―

抄録

　　 If we want to teach mathematics more effectively, we need more elaborated questioning with epistemological backgrounds for enhancing students’ mathematical reasoning.  The purpose of this paper is to develop a theoretical framework for designing teachers’ questioning in classrooms toward fostering mathematical know-hows.  The present paper extended a radical constructivist methodology: Conceptual analysis.  Through theoretical considerations, two important extended ideas were proposed for designing teachers’ questioning.  The first one is where it is difficult for learners to proceed on their learning trajectories, and the second one is what interpretation of social situations learners may make.  For these two viewpoints, the use of the two theoretical frameworks were proposed from previous theoretical studies: Instantiationdescription-chain model and radical constructivism with motivational assumptions.

　　  As a result, the paper developed and proposed a theoretical heuristics for designing teachers’ questioning, like Polya’s heuristics for problem solving.  In addition, as an example, the author tried to use the heuristics for designing teachers’ questioning, focusing on “an application task of quadratic functions” in Japanese high school mathematics.  Through the example-based consideration, the value and the limitation of the proposed theoretical heuristics is discussed.