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The role of geometric figure of which "variable" and "constant"underlie hidden in junior high school geometric proving

Research Project

Project/Area Number 24653279
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Education on school subjects and activities
Research InstitutionKagawa University

Principal Investigator

KIMIE KAZAMA  香川大学, 教育学部, 教授 (00552374)

Co-Investigator(Kenkyū-buntansha) HASHIMOTO Yoshihiro  大阪教育大学, 教区学部, 名誉教授 (00030479)
Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords図形命題 / 図の変数性 / 図の定数性 / 証明活動 / 図の役割
Outline of Final Research Achievements

For the purpose of improvement of geometrical proof teaching, this study has two aims; (A) to clarify how junior high school students understand two geometrical viewpoints i.e. "variable" and "constant" of figure used in a proposition, and, (B) to suggest the development of teaching materials and the improvement of proof teaching. This study makes the improvement plan of proof teaching.
①It clarifies how junior high school students understand a geometrical figure.② Teaching materials that are developed on the basis of the data of ① are used in the classroom, its validity is confirmed empirically.③ The results of the comparative analysis of student’s understanding between before and after teaching, revealed that they can do better.④ It is determined that the new idea of teaching material development: to increase the number of "variable" from one to two and three that is appended to a figure used in a propositional, works effectively in proof teaching.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (10 results)

All 2015 2014 2013 2012

All Journal Article (5 results) (of which Open Access: 3 results,  Acknowledgement Compliant: 3 results,  Peer Reviewed: 2 results) Presentation (5 results)

  • [Journal Article] 証明と図の関係の中学生の捉え方2015

    • Author(s)
      風間 喜美江
    • Journal Title

      近畿数学教育学会

      Volume: 28 Pages: 30-40

    • NAID

      40021757642

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] 図形課題「はとめ返し」の探究-レポート学習の活用を通して-2015

    • Author(s)
      風間 喜美江,杉本 紘野
    • Journal Title

      香川大学教育学部研究報告第Ⅱ部

      Volume: 第65巻第1号 Pages: 19-37

    • NAID

      120007014139

    • Related Report
      2014 Annual Research Report
    • Open Access / Acknowledgement Compliant
  • [Journal Article] 所与の課題を解決し,そこから探究・発展させる図形学習-レポート学習の活用を通して-2014

    • Author(s)
      風間 喜美江,杉本 紘野
    • Journal Title

      香川大学教育学部研究報告第Ⅱ部

      Volume: 第64巻第2号 Pages: 61-77

    • NAID

      120007014144

    • Related Report
      2014 Annual Research Report
    • Open Access / Acknowledgement Compliant
  • [Journal Article] 「数学を学ぶ意味」を実感させるための教師のかかわりあいのあり方2014

    • Author(s)
      風間 喜美江
    • Journal Title

      香川大学教育学部附属教育実践センターニュース

      Volume: No.39 Pages: 3-3

    • Related Report
      2013 Research-status Report
  • [Journal Article] 図形命題の仮定を図で思考する証明活動2012

    • Author(s)
      風間 喜美江
    • Journal Title

      日本数学教育学会 第45回数学教育論文発表会論文集

      Volume: 第2巻 Pages: 845-850

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] 幾何的な豊饒の「図」を顕在させる図形指導2014

    • Author(s)
      風間 喜美江
    • Organizer
      全国数学教育学会
    • Place of Presentation
      大阪教育大学天王寺キャンパス
    • Year and Date
      2014-06-14 – 2014-06-15
    • Related Report
      2014 Annual Research Report
  • [Presentation] 証明活動における図の役割2014

    • Author(s)
      風間 喜美江
    • Organizer
      近畿数学教育学会
    • Place of Presentation
      兵庫教育大学ハーバーランドキャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] 「数学を学ぶ意味」を実感させるための教師のかかわりあいのあり方2014

    • Author(s)
      風間 喜美江
    • Organizer
      第14回学部・附属学校園合同研究集会
    • Place of Presentation
      香川大学教育学部
    • Related Report
      2013 Research-status Report
  • [Presentation] 図から図形をくみ尽くす力2013

    • Author(s)
      風間 喜美江
    • Organizer
      近畿数学教育学会第53回発表会
    • Place of Presentation
      神戸女子大学
    • Related Report
      2012 Research-status Report
  • [Presentation] 図形命題の仮定を図で思考する証明活動2012

    • Author(s)
      風間 喜美江
    • Organizer
      日本数学教育第45回論文発表会
    • Place of Presentation
      奈良教育大学
    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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