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Clarification and control of the transition of the "modes of expansion of the discourse" in generating "incomplete proofs"

Research Project

Project/Area Number 19K02805
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 09040:Education on school subjects and primary/secondary education-related
Research InstitutionUtsunomiya University

Principal Investigator

MAKINO Tomohiko  宇都宮大学, 共同教育学部, 准教授 (10450157)

Project Period (FY) 2019-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords証明学習 / 未完成な証明 / 命題の認識値 / 命題のステータス / ディスコースの拡張 / 中学校数学 / ディスコースの拡張モード
Outline of Research at the Start

我が国の多くの中学生は証明の学習に困難を抱えている。今なお,学習状況の改善の兆しは見えない。そこで,本研究は,完成に至らなかった解答である「未完成な証明」に焦点を当てる。教育現場では,「未完成な証明」の存在は認められているも,改善のための手立てがないため,個々の教師による経験的,直観的な判断に基づいて,試行錯誤的に実践が行われている。
そこで,本研究は「未完成な証明」の生成過程の解明に取り組んでいる。とりわけ,「未完成な証明」の生成に影響を与える中学生の認識の特徴を探っている。

Outline of Final Research Achievements

In the process of generating incomplete proofs, when making an argument using the collected information, if there is enough information to grasp the whole picture of the theory, the reasoning can be understood, and it is not necessary to show the details in detail, so a leap of reasoning is generated.
In addition, two patterns were found for the generation of proofs including inversive inference, and the aspects of understanding the epistemic values and status of the propositions influencing each generation were clarified.
Finally, the key to making a complete proof for a student is to recognize the degree of gap or leap in the step of reasoning and how to organize propositions into the proof. Moreover, since the students' ideas are gradually modified and improved, it is becoming clear how to improve and modify the incomplete proof.

Academic Significance and Societal Importance of the Research Achievements

本研究で「未完成な証明」の生成過程での「ディスコースの拡張」の転換の「きっかけ」,「ディスコースの拡張」の転換に影響する中学生の認識が解明されることで,「未完成な証明」の生成過程の理解が進み,数学教育研究上大きな価値がある.これらの知見によって,
生徒が「未完成な証明」を改善・修正する手立ての開発に貢献できる.その結果,未完成な証明の生成に留まっていた生徒が,自力で証明を完成させることができるようになる.

Report

(4 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Research-status Report
  • 2019 Research-status Report
  • Research Products

    (7 results)

All 2021 2020 2019

All Journal Article (4 results) (of which Peer Reviewed: 2 results) Presentation (3 results) (of which Int'l Joint Research: 2 results,  Invited: 1 results)

  • [Journal Article] A Cognitive Characteristic in Generating Incomplete Proofs with Inversive Inference in Geometrical Proof Problems: Analyzing Epistemic Value and Status of Proposition in Deductive Organization2021

    • Author(s)
      牧野 智彦
    • Journal Title

      Journal of Science Education in Japan

      Volume: 45 Issue: 4 Pages: 406-420

    • DOI

      10.14935/jssej.45.406

    • NAID

      130008139876

    • ISSN
      0386-4553, 2188-5338
    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cognitive Characteristics Generating Incomplte Proof: Analyzing the Solving Process of a Geometrical Problem by Japanese Ninth Graders2021

    • Author(s)
      Tomohiko Makino
    • Journal Title

      Proceedings of The 14th International Congress on Mathematical Education

      Volume: -

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] 未完成な証明を生成する命題の「認識値」の特徴-「論理的に誤った命題」に関するグループインタビューの分析を通して2020

    • Author(s)
      牧野智彦
    • Journal Title

      宇都宮大学教育学部研究紀要

      Volume: 70 Pages: 209-220

    • NAID

      120006813570

    • Related Report
      2019 Research-status Report
  • [Journal Article] 未完成な証明を生成する命題の「認識値」の様相-証明の中の「論理的な誤り」に着目して-2019

    • Author(s)
      牧野智彦
    • Journal Title

      日本数学教育学会第52回秋期研究大会発表集録

      Volume: - Pages: 431-434

    • NAID

      40022493833

    • Related Report
      2019 Research-status Report
  • [Presentation] Cognitive Characteristics Generating Incomplete Proof: Analyzing the Solving Process of a Geometrical Problem by Japanese Ninth Graders2021

    • Author(s)
      MAKINO Tomohiko
    • Organizer
      14th International Congress on Mathematical Education
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Cognitive Characteristics Generating Incomplte Proof: Analyzing the Solving Process of a Geometrical Problem by Japanese Ninth Graders2021

    • Author(s)
      Tomohiko Makino
    • Organizer
      The 14th International Congress on Mathematical Education, TSG-16 - Reasoning, argumentation and proof in mathematics education
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 未完成な証明を生成する命題の「認識値」の様相-証明の中の「論理的な誤り」に着目して-2019

    • Author(s)
      牧野智彦
    • Organizer
      日本数学教育学会
    • Related Report
      2019 Research-status Report

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Published: 2019-04-18   Modified: 2023-01-30  

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