A study on students' learning processes of proving within the context of problem posing by focusing on probability and diversity of argumentation

2023 Fiscal Year Final Research Report

• Project/Area Number: 20K02904
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 09040:Education on school subjects and primary/secondary education-related
• Research Institution: Chiba University
• Principal Investigator: Tsujiyama Yosuke 千葉大学, 教育学部, 准教授 (10637440)
• Co-Investigator(Kenkyū-buntansha): 榎本 哲士 信州大学, 教育学部, 講師 (60758811)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Keywords: 問題設定 / 議論 / argumentation / 証明 / 証明活動 / proving / 学習過程 / 説明

Outline of Final Research Achievements

This study examined the question, "What is the learning process of proving focusing on the probability and diversity of argumentation in mathematical problem setting?" from both theoretical and practical perspectives. As a result, we developed a learning process that consisted of proving a starting proposition, posing a problem, solving the problem, and understanding the reasons. Through practice in elementary and junior high schools, this study verified the effectiveness of the learning process and refined it, and presented the possibility of a learning process that extends proofs to "various explanations".

Free Research Field

数学教育学

Academic Significance and Societal Importance of the Research Achievements

本研究の成果の学術的意義は，証明活動を問題設定の文脈に位置付けることで，創造的・社会的な過程として証明活動を実現する手立てを明らかにしたこと，並びに，議論の蓋然性と多様性に着目することで，同じことが成り立つ場合と成り立たない場合（不具合）の両方に焦点を当てた学習過程を構築した点にある。
実践上の意義は，「問題発見・解決の過程」を重視した深い学びを，証明という算数・数学科の中核的な内容に応じて実現する手立てを，出発点の命題の証明，新たな問題の設定，その問題の解決，理由の把握からなる学習過程の形で提示した点にある。