An Attempt to Cultivate Students' Autonomy through Mathematics Experiments and Experimental Mathematics Using ICT

2021 Fiscal Year Final Research Report

• Project/Area Number: 20K22245
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Multi-year Fund
• Review Section: :Education and related fields
• Research Institution: Iwate Prefectural University
• Principal Investigator: TAMURA Atsushi 岩手県立大学, ソフトウェア情報学部, 准教授 (00882002)
• Project Period (FY): 2020-09-11 – 2022-03-31
• Keywords: 数学教育 / 非ユークリッド幾何学 / 動的幾何学ソフトウェア / 探究学習 / 主体性 / 思考実験

Outline of Final Research Achievements

I developed teaching materials on projective geometry, spherical geometry, and taxicab geometry. All of them are designed to deepen students' understanding through experiments using GeoGebra.
For projective geometry, I believe that I have made a new proposal that has not been reported before in Japan, which stimulates students' imagination and helps them to cultivate their logical thinking. This proposal has been accepted as a refereed paper.
The teaching materials on spherical geometry and taxicab geometry were taught to first- and second-year high school students at a local school in the prefecture by two students. Both students reported their results at conference of the Japan Society for Educational Technology. A questionnaire survey was conducted in the classes conducted by the students, and the results indicated that the software was effective and that each of the materials could reach out to students with low academic ability and elicit their interest and initiative.

Free Research Field

数学教育学

Academic Significance and Societal Importance of the Research Achievements

従来から学校現場では「日本の生徒は数学の現実場面への適用力が弱い」と指摘されており，主体性の涵養や数学的に考える資質・能力の育成も課題になっていた。実際，新学習指導要領でも「生徒の主体的・対話的で深い学びの実現を図る」，「日常生活や社会の事象の数学化」等が求められている。この現状を踏まえ，新課程では「理数探究」等が設置され，上記の課題の解決が期待されている。
本研究では，射影幾何や球面幾何等のある種の現実場面を，生徒がGeoGebraを用いた実験数学によって解決する教材を開発した。現実場面の課題を解決する授業への変換を見据え，新課程・理数探究に対応した1つの問題提起ができたと考えている。