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Development of teaching materials for facilitating students' action proof in mathematical inquiry

Research Project

Project/Area Number 22830035
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Education on school subjects and activities
Research InstitutionShinshu University

Principal Investigator

KOMATSU Xingkotaro  信州大学, 教育学部, 准教授 (40578267)

Project Period (FY) 2010 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥3,081,000 (Direct Cost: ¥2,370,000、Indirect Cost: ¥711,000)
Fiscal Year 2011: ¥1,469,000 (Direct Cost: ¥1,130,000、Indirect Cost: ¥339,000)
Fiscal Year 2010: ¥1,612,000 (Direct Cost: ¥1,240,000、Indirect Cost: ¥372,000)
Keywords数学教育 / 証明 / 操作的証明 / 数学的探究 / 教材開発
Research Abstract

Proof and proving are at the core of mathematical activities, and therefore should be the center of students' mathematical experiences at all grades. However, mathematics education researches have revealed that many students feel difficulties in learning proof and proving. In order to improve this learning situation, this study focuses on a notion of" action proof", and aims to explore how we can encourage students to utilize action proof in mathematical inquiry. In particular, this study derives some guidelines for developing teaching materials which intend to facilitate students' activities, by examining the existing researches, analyzing materials, and conducting and analyzing teaching-experiments with fifth and ninth graders.

Report

(3 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • Research Products

    (11 results)

All 2012 2011 2010

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (4 results) Book (2 results)

  • [Journal Article] ラカトシュの可謬主義から見た数学的探究とその教育的意義2011

    • Author(s)
      小松孝太郎
    • Journal Title

      『科学教育研究』(日本科学教育学会)

      Volume: 第35巻第3号 Pages: 272-286

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] How do studentsgeneralize a conjecture throughproving?: The importance of boundarycases between example andcounterexample. In B. Ubuz(Ed.)2011

    • Author(s)
      Komatsu, K.
    • Journal Title

      Proceedings of the 35th Conference ofthe International Group for thePsychology of Mathematics Education

      Volume: Vol.3 Pages: 89-96

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] How do students generalize a conjecture through proving? : The importance of boundary cases between example and counterexample2011

    • Author(s)
      Komatsu Kotaro
    • Journal Title

      Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education

      Volume: Vol.3 Pages: 89-96

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] ラカトシュの可謬主義から見た数学的探究とその教育的意義2011

    • Author(s)
      小松孝太郎
    • Journal Title

      科学教育研究

      Volume: 35(3) Pages: 272-286

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 数学的探究におけるaction proofの活用の促進:事例研究を通して2010

    • Author(s)
      小松孝太郎
    • Journal Title

      日本数学教育学会誌数学教育学論究

      Volume: 第93号 Pages: 3-29

    • NAID

      110007609878

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] How do students generalize a conjecture through proving?: The importance of boundary cases between example and counterexample.2011

    • Author(s)
      Komatsu, K.
    • Organizer
      The 35th Conference of the International Group for the Psychology of Mathematics Education
    • Place of Presentation
      Ankara, Turkey
    • Year and Date
      2011-07-14
    • Related Report
      2011 Final Research Report
  • [Presentation] How do students generalize a conjecture through proving? : The importance of boundary cases between example and counterexample2011

    • Author(s)
      Kotaro Komatsu
    • Organizer
      The 35th Conference of the International Group for the Psychology of Mathematics Education
    • Place of Presentation
      Ankara, Turkey
    • Year and Date
      2011-07-14
    • Related Report
      2011 Annual Research Report
  • [Presentation] An assessment framework for students' abilities/competencies in proving.2010

    • Author(s)
      Chino, K., Fujita, T., Komatsu, K., Makino, T., Miyakawa, T., Miyazaki, M., Mizutani, N., Nakagawa, H., Otsuka, S., & Tsujiyama, Y.
    • Organizer
      The 5th East Asia Regional Conference on Mathematics Education
    • Place of Presentation
      Tokyo, Japan
    • Year and Date
      2010-08-21
    • Related Report
      2011 Final Research Report
  • [Presentation] An assessment framework for students' abilities/competencies in proving2010

    • Author(s)
      Chino, K., Fujita, T., Komatsu, K., 他7名
    • Organizer
      The 5th East Asia Regional Conference on Mathematics Education
    • Place of Presentation
      国立オリンピック記念青少年総合センター
    • Year and Date
      2010-08-21
    • Related Report
      2010 Annual Research Report
  • [Book] 数学の学習論・学習者論,教科教育の理論と授業II2012

    • Author(s)
      小松孝太郎
    • Publisher
      東京:協同出版
    • Related Report
      2011 Final Research Report
  • [Book] 『教科教育の理論と授業II:数理編』「数学の学習論・学習者論」(第I部第5章)を執筆(大高泉・清水美憲編)2012

    • Author(s)
      小松孝太郎
    • Publisher
      協同出版
    • Related Report
      2011 Annual Research Report

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Published: 2010-08-27   Modified: 2016-04-21  

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