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A Study on Teaching Geometry with an Emphasis on Learning Process to discover the property and then prove it

Research Project

Project/Area Number 22530961
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Education on school subjects and activities
Research InstitutionShizuoka University

Principal Investigator

KUNIMUNE Susumu  静岡大学, 教育学部, 教授 (50214979)

Co-Investigator(Kenkyū-buntansha) KUMAKURA Hiroyuki  静岡大学, 教育学部, 教授 (00377706)
NAKAMURA Takashi  山梨大学, 教育人間科学部, 教授 (70303394)
OTA Haruto  静岡大学, 教育学部, 教授 (40126769)
YAMADA Kozo  静岡大学, 教育学部, 教授 (00200717)
Research Collaborator KEITH Johns  サウザンプトン大学, 教育学研究科, 教授
FUJITA Taro  プリマス大学, 教育学部, 講師
MATSUMOTO Shinichiro  静岡大学, 教育学部, 准教授 (40447660)
KONDO Yutaka  奈良教育大学, 教育学部, 准教授 (80551035)
HAYAKAWA Ken  山梨大学, 教育人間科学部, 准教授 (40585387)
HATTA Hiroe  渋谷教育学園幕張中, 高等学校, 教諭
HARA Kinji  静岡県浜松市立城北小学校, 教諭
OHOHTA Ikumi  静岡県藤枝市立青島中学校, 教諭
KONDO Masao  静岡県磐田市立城山中学校, 教諭
SAKAMOTO Kenji  静岡県牧之原市立相良中学校, 教諭
SASASE Daisuke  静岡県掛川市立桜が丘中学校, 教諭
MOCHIZUKI Miki  山梨県甲府市立北中学校, 教諭
Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords数学教育 / 幾何教育 / 証明 / 授業 / 幾何学
Research Abstract

We researched the characteristics of students’ understanding about mathematical proof and proving based on literature and lessons in lower secondary schools. We indicated it is important for the students to learn geometry through the process to discover the property and then prove it, and have made many lesson plans that students learn through these processes. Moreover, cooperated with researchers in UK, we identified focus on issues of mathematical definitions, mathematical representations , and the form of instruction used by teachers.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (30 results)

All 2013 2012 2011 2010 Other

All Journal Article (15 results) (of which Peer Reviewed: 12 results) Presentation (9 results) Book (6 results)

  • [Journal Article] 補助線を引く方法を意識化させる図形指導-説明する活動を重視して-2013

    • Author(s)
      高橋達也、鈴木直、國宗進
    • Journal Title

      静岡大学教育学部附属教育実践総合センター紀要

      Volume: No.21 Pages: 21-30

    • NAID

      110009555935

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Representations and reasoning in 3-D geometry in lower secondary school2012

    • Author(s)
      Jones,K., Fujita,T. & Kunimune,S.
    • Journal Title

      Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Educatio

      Volume: Vol.2 Pages: 339-346

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Promoting Productive Reasoning in the Teaching of Geometry in Lower Secondary School: Towards A Future Research Agenda2012

    • Author(s)
      Jones, K., Fujita, T., & Kunimune, S.
    • Journal Title

      Proceedings of the 12th International Congress on Mathematical Education

      Pages: 2222-2231

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] 空間図形についての理解に関する研究-空間図形における 2 直線のなす角度に関する授業を通して-2012

    • Author(s)
      近藤裕・國宗進・熊倉啓之・八田弘恵・望月美樹
    • 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

      Pages: 593-598

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] 数学的推論能力の育成を重視した中 1 での学習指導-説明する活動を重視して-2012

    • Author(s)
      坂本健司・高橋達也・國宗進
    • Journal Title

      静岡大学教育学部教育実践総合センター紀要

      Volume: No.20 Pages: 1-10

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Promoting Productive Reasoning in the Teaching of Geometry in Lower Secondary School: Towards A Future Research Agenda.2012

    • Author(s)
      Jones, K., Fujita, T., & Kunimune, S.
    • Journal Title

      Proceedings of the 12th International Congress on Mathematical Education

      Volume: 1 Pages: 2222-2231

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Representations and reasoning in 3-D geometry in lower secondary school2012

    • Author(s)
      Jones, K., Fujita, T., & Kunimune, S.
    • Journal Title

      In T-Y Tso (Ed.), Proceedings 36th Conf. of the Int. Group for the Psychology of Mathematics Education.

      Volume: 第2巻 Pages: 339-346

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 空間図形についての理解に関する研究-2直線のなす角に関する授業を通して-2012

    • Author(s)
      近藤裕、國宗進、他
    • Journal Title

      第45回数学教育論文発表会論文集

      Volume: 第1巻 Pages: 593-598

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Proofs and Refutations in Lower Secondary School Geometry2011

    • Author(s)
      Fujita T., Jones K., Kunimune S., Kumakura H.and Matsumoto S.
    • Journal Title

      Proceeding of 7thConference of European Research in Mathematics Education

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] 空間図形についての理解に関する研究-立体の切り口の授業を通して-2011

    • Author(s)
      近藤裕・國宗進・熊倉啓之・八田弘恵・望月美樹
    • Journal Title

      日本数学教育学会第44回数学教育論文発表会論文集

      Pages: 489-494

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] イギリスの高等学校数学教科書2011

    • Author(s)
      國宗進
    • Journal Title

      日本数学教育学会誌数学教育

      Volume: 第93巻第7号 Pages: 39-42

    • NAID

      110008687181

    • Related Report
      2012 Final Research Report
  • [Journal Article] イギリスの高等学校数学教科書2011

    • Author(s)
      國宗進
    • Journal Title

      日本数学教育学会誌

      Volume: 第93巻第7号 Pages: 39-42

    • NAID

      110008687181

    • Related Report
      2011 Annual Research Report
  • [Journal Article] Students' Geometrical Construction and Proving Activities: A Case of Cognitive Unity?2010

    • Author(s)
      Fujita T., Jones K., and Kunimune S.
    • Journal Title

      Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education

      Volume: Vol.3 Pages: 9-16

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] 空間図形についての理解に関する研究-1 つの平面に着目して考えることを中心に-2010

    • Author(s)
      近藤裕・國宗進・八田弘恵・熊倉啓之・原欣司
    • Journal Title

      日本数学教育学会第43回数学教育論文発表会論文集

      Pages: 163-168

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] イギリスの算数・数学教科書2010

    • Author(s)
      國宗進
    • Journal Title

      日本数学教育学会誌数学教育

      Volume: 第92巻第5号 Pages: 13-16

    • NAID

      110007621651

    • Related Report
      2012 Final Research Report
  • [Presentation] Representations and reasoning in 3-D geometry in lower secondary school2012

    • Author(s)
      Jones,K., Fujita,T. & Kunimune,S.
    • Organizer
      The 36th Conference of the International Group for the Psychology of Mathematics Education
    • Place of Presentation
      Wesley Girls High School(Taiwan), PME
    • Year and Date
      2012-07-19
    • Related Report
      2012 Final Research Report
  • [Presentation] Promoting Productive Reasoning in the Teaching of Geometry in Lower Secondary School: Towards A Future Research Agenda2012

    • Author(s)
      Jones, K., Fujita, T., & Kunimune, S.
    • Organizer
      The 12th International Congress on Mathematical Education
    • Place of Presentation
      COEX(Korea), ICME
    • Year and Date
      2012-07-13
    • Related Report
      2012 Final Research Report
  • [Presentation] 空間図形についての理解に関する研究-立体の切り口の授業を通して-2011

    • Author(s)
      近藤裕、國宗進, 他
    • Organizer
      第44回数学教育論文発表会
    • Place of Presentation
      上越教育大学(新潟県)
    • Year and Date
      2011-11-12
    • Related Report
      2011 Annual Research Report
  • [Presentation] Proofs and Refutations in Lower Secondary School Geometry2011

    • Author(s)
      Fujita T., Jones K., Kunimune S., Kumakura H.and Matsumoto S
    • Organizer
      The 7thConference of European Research in Mathematics Education
    • Place of Presentation
      ジェシュフ大学(Poland)
    • Year and Date
      2011-02-10
    • Related Report
      2012 Final Research Report
  • [Presentation] Proofs and Refutations in Lower Secondary School Geometry2011

    • Author(s)
      Taro Fujita
    • Organizer
      Seventh Congress of the European Society for Research in Mathematics Education(CERME7)
    • Place of Presentation
      ジェシュフ大学,Poland
    • Year and Date
      2011-02-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] 空間図形についての理解に関する研究2010

    • Author(s)
      近藤裕
    • Organizer
      日本数学教育学会・数学教育論文発表会
    • Place of Presentation
      宮崎大学
    • Year and Date
      2010-11-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] Students' Geometrical Constructions and Proving Activities : A Case of Cognitive Unity2010

    • Author(s)
      Keith Jones
    • Organizer
      The 34^<th> Conference of the International Group for the Psychology of Mathematics Education (PME34)
    • Place of Presentation
      Belo Horizonte, Brasil
    • Year and Date
      2010-07-21
    • Related Report
      2010 Annual Research Report
  • [Presentation] Promoting Productive Reasoning in the Teaching of Geometry in Lower Secondary School: Towards A Future Research Agenda.

    • Author(s)
      Jones, K., Fujita, T., & Kunimune, S.
    • Organizer
      12th International Congress on Mathematical Education
    • Place of Presentation
      COEX(Seoul, Korea)
    • Related Report
      2012 Annual Research Report
  • [Presentation] Representations and reasoning in 3-D geometry in lower secondary school

    • Author(s)
      Jones, K., Fujita, T., & Kunimune, S.
    • Organizer
      36th Conf. of the Int. Group for the Psychology of Mathematics Education.
    • Place of Presentation
      Wesley Girls High School(Taiwan)
    • Related Report
      2012 Annual Research Report
  • [Book] 略案で創る中学校新数学科の授業・図形編2011

    • Author(s)
      國宗進
    • Publisher
      明治図書出版
    • Related Report
      2012 Final Research Report
  • [Book] 高等学校数学教育研究会編・高等学校数学教育の展開2011

    • Author(s)
      熊倉裕之
    • Publisher
      聖文新社
    • Related Report
      2012 Final Research Report
  • [Book] 算数科教育の基礎・基本2011

    • Author(s)
      國宗進
    • Publisher
      明治図書出版
    • Related Report
      2012 Final Research Report
  • [Book] 略案で創る中学校新数学科の授業 第2巻図形編2011

    • Author(s)
      國宗進
    • Publisher
      明治図書出版
    • Related Report
      2010 Annual Research Report
  • [Book] 高校と大学をむすぶ幾何学2010

    • Author(s)
      大田春外
    • Publisher
      日本評論社
    • Related Report
      2012 Final Research Report
  • [Book] 数学教育学研究ハンドブック2010

    • Author(s)
      國宗進
    • Publisher
      東洋館出版
    • Related Report
      2012 Final Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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