相互作用主義に基づく数学学習指導に関する研究 : 「三平方の定理の逆」の実践的検討

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My purpose in this paper is to obtain didactical implications for effective communicative activities in mathematics learning, mainly from the analysis of "Converse of Pythagorean Theorem" lessons in a public junior high school, Hiroshima city. To develop the rationale for this analysis, this paper uses the epistemological frameworks of Interactionisim and design research. According to Cobb (2000), "research of this type involves both instructional design and classroom-based research (p.57)", and "it is this theory that makes the results of a series of design experiments potentially generalizable even though they are empirically grounded in analyses of only a small number of classrooms (p.59)". This research finally shows us three points for improvement of teaching and learning mathematics concerning mathematics teaching and curriculum development as follows; (i) Mathematical ideas emerged from classroom, when classroom discussion and group discussion became reflexive. Moreover, signs used in discussion helped emergence of mathematical idea. (ii) The role of teacher is to make student speak of reasons, and compare their mathematical ideas, in order to develop effective communicative activities (iii) This paper illustrates student's understanding of converse of proposition and indirect proof with the practical cycles of planning, instruction, and analysis.
全国数学教育学会の論文