中学校の図形領域における証明の教授・学習に関する考察 : 教授学的契約と委譲の概念を視座として

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The aims of this paper are to consider the causes of difficulty in the learning of geometric proofs in junior high school, and to obtain a basis for the improvement of related teaching and learning. Despite much early research into the teaching and learning of geometric proofs, difficulties of them have not been overcome. In this paper, the author considers the causes of such difficulty under the light of didactical contract, a major component of Brousseu's Theory of Didactical Situations. Especially focused on are two areas of requiring improvement to mitigate difficulties in the teaching and learning of proofs: A) Understanding the meaning of proofs B) Doing proofs in didactical situations For improvement of the difficulty of A), the didactical contract of "Generality of proof' is considered, and the proposal is that applied devolution is effective in addressing the difficulty. In respect to improvement of the difficulty of B), the didactical contract of doing proofs in didactical situations is considered, and the proposal is that teaching and learning situations that employ the negotiation of the didactical contract oriented devolution is also effective in its turn.
全国数学教育学会の論文