高等学校数学Ⅰ「２次関数」における知識の再文脈化の検討 ―教えられるべき知識のプラクセオロジー分析を通して―

抄録

　　The authors are concerned that, with regard to the textbook for the unit “quadratic functions” in Mathematics I at senior high school, the contents are “decontextualized” and presented axiomatically, so that the need to study each of them is not clear. It is hoped that teachers will “recontextualize” the contents to be learnt so that they arise with necessity.

　　In this paper, the authors clarify what knowledge and skills learning is required in a unit on quadratic functions, and what knowledge learning is covered by several examples for recontextualization.

　　To achieve this objective, the knowledge of the textbook is first organised through a praxeological analysis using the Anthropological Theory of the Didactic (ATD) as a theoretical framework to clarify its structure and the sequence of instruction. The author then analyses examples of lessons incorporating applied questions from the textbook and the author’s own practice of inquiry.

　　As a result, the knowledge of both the pracxis block and the logos block was organised and diagrammed in a tree structure. The results were further used to analyse two types of case studies and to organise whether and how knowledge arises. From these analyses, a discussion was held on the recontextualization of knowledge and the realisation of inquiry.