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Mathematics Education based on Modelism

Research Project

Project/Area Number 22500804
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Science education
Research InstitutionYokohama National University

Principal Investigator

IKEDA Toshikazu  横浜国立大学, 教育人間科学部, 教授 (70212777)

Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsモデル / 数学教育 / 数学的思考 / 表現 / 推論 / 対象 / 集合関係 / 数学第一類・二類 / 生活単元学習 / 数学教育の現代化 / オープンエンドアプローチ / 問題づくり / 数学的モデリング / モデル主義 / 数学学習 / 具体化 / 抽象化 / 数学的モデル
Research Abstract

It was pointed to at least two distinct meanings for model in respect of their epistemological assumptions and implications for teaching. The two distinct meanings we identify are: (1) models as hypothetical spaces in which we conceptualize a particular world situation in order to think about and work on it in order to solve a problem, and (2) models as physical/mental entities for comparing and contrasting which we can use to refer to a different familiar situation, and which can be compared or contrasted among themselves in terms of their capacity to represent and deepen our understanding of some particular phenomenon in the world. Two roles of models are discussed concretely both in elementary and secondary mathematics.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (27 results)

All 2013 2012 2011 2010

All Journal Article (15 results) (of which Peer Reviewed: 12 results) Presentation (8 results) (of which Invited: 2 results) Book (4 results)

  • [Journal Article] Pedagogical Reflections on the Role of Modelling in Mathematics Instruction, In Gloria Ann Stillman, Gabriele Kaiser, Wener Blum and Jill P.Brown(ed)2013

    • Author(s)
      Ikeda, T
    • Journal Title

      Mathematical Modelling : Connecting to Practice–Teaching practice and the practice of applied mathematicians, Springer

      Pages: 255-275

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] モデルに焦点を当てた数学的活動に関する研究の世界的傾向とそれらの関連2013

    • Author(s)
      池田敏和
    • Journal Title

      日本数学教育学会誌

      Volume: 第95巻第5号 Pages: 2-12

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Pedagogical Reflections on the Role of Modelling in Mathematics Instruction2013

    • Author(s)
      Toshikazu Ikeda
    • Journal Title

      Mathematical Modelling: Connecting to Practice ; Teaching practice and the practice of applied mathematicians(Springer)

      Volume: ICTMA15 Pages: 255-275

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Teaching Experiment in Modelling through Scale Reduction Methods : A Bridge to Later Trigonometric Methods2012

    • Author(s)
      Toshikazu Ikeda, Max Stephens and Yuki Wada
    • Journal Title

      Journal of Mathematics and System Science

      Volume: Vol.2 Number 6 Pages: 359-367

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] 数学的モデル化の必要性とその方法2012

    • Author(s)
      マックス・ステフェンス, 池田敏和
    • Journal Title

      日本数方の世界を互いに成長させることにつなが学教育学会誌

      Volume: 第94巻第3号 Pages: 2-8

    • NAID

      110009426076

    • Related Report
      2013 Final Research Report
  • [Journal Article] Teaching modelling through reduction methods2012

    • Author(s)
      Max Stephens, Toshikazu Ikeda and Yuki Wada
    • Journal Title

      VINCULUM(Australia)

      Volume: Vol.49 TERM1 Pages: 12-17

    • Related Report
      2013 Final Research Report
  • [Journal Article] A Teaching Experiment in Modelling through Scale Reduction Methods: A Bridge to Later Trigonometric Methods2012

    • Author(s)
      Toshikazu Ikeda
    • Journal Title

      Journal of Mathematics and System Science

      Volume: Vol.2 Number 6 Pages: 359-367

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Teaching modelling through reduction methods2012

    • Author(s)
      Max Stephens, Toshikazu Ikeda, Yuki Wada
    • Journal Title

      VINCULUM (Australia)

      Volume: Vol.49 TERM1 Pages: 12-17

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 数学的モデル化の必要性とその方法2012

    • Author(s)
      マックス・ステフェンス・池田敏和
    • Journal Title

      日本数学教育学会誌

      Volume: 第94巻第3号 Pages: 2-8

    • NAID

      110009426076

    • Related Report
      2011 Annual Research Report
  • [Journal Article] 図形領域における複数の下位体系を行き来する活動に焦点を当てた教材開発2010

    • Author(s)
      池田敏和, 渡邊公夫
    • Journal Title

      数学教育学会誌

      Volume: Vol.51 No.1, 2 Pages: 39-50

    • NAID

      10028161674

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Three teaching principles for fostering students'thinking about modelling : An experimental teaching program for 9th grade students in Japan2010

    • Author(s)
      Toshikazu Ikeda and Max Stephens
    • Journal Title

      Journal of Mathematical Modelling and Applications

      Volume: Vol.2 No.1 Pages: 49-59

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Mathematical modelling giving meaning to mathematics : A case study of Japanese textbooks seventy years ago2010

    • Author(s)
      Toshikazu Ikeda, Max Stephens and Yoshihisa Tanaka
    • Journal Title

      Proceedings of the 5th East Asia Regional Conference on Mathematics Education

      Volume: Vol.2 Pages: 591-598

    • Related Report
      2013 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Three teaching principles for fostering students' thinking about modelling : An experimental teaching program for 9^<th> grade students in Japan2010

    • Author(s)
      Toshikazu Ikeda, Max Stephens
    • Journal Title

      Journal of Mathematical Modelling and Applications

      Volume: Vol.2 No.1 Pages: 49-59

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 図形領域における複数の下位体系を行き来する活動に焦点を当てた教材開発2010

    • Author(s)
      池田敏和・渡邊公夫
    • Journal Title

      数学教育学会誌

      Volume: Vol.51 No.1-2 Pages: 39-50

    • NAID

      10028161674

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 数学的モデル化2010

    • Author(s)
      池田敏和
    • Journal Title

      数学教育学研究ハンドブック,東洋館出版社

      Pages: 272-281

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] 数学的活動を意図した授業づくり2011

    • Author(s)
      池田敏和
    • Organizer
      第93回全国算数・数学教育研究(神奈川)大会
    • Place of Presentation
      川崎市中原市民会館(招待講演)
    • Year and Date
      2011-07-30
    • Related Report
      2011 Annual Research Report
  • [Presentation] Pedagogical Reflections on the Role of Modelling in the Teaching of Mathematics2011

    • Author(s)
      Toshikazu Ikeda
    • Organizer
      15^<th> International Conference on the Teaching of Mathematical Modelling and Applications
    • Place of Presentation
      Australian Catholic University (Australia)(Plenary Lecture)(招待講演)
    • Year and Date
      2011-07-16
    • Related Report
      2011 Annual Research Report
  • [Presentation] A Teaching Experiment in Modelling through Reduction Methods : Intended as a Bridge to later Trigonometric Methods2011

    • Author(s)
      Toshikazu Ikeda, Max Stephens, Yuki Wada
    • Organizer
      15^<th> International Conference on the Teaching of Mathematical Modelling and Applications
    • Place of Presentation
      Australian Catholic University (Australia)
    • Year and Date
      2011-07-15
    • Related Report
      2011 Annual Research Report
  • [Presentation] 数学的活動を意図した授業づくり2011

    • Author(s)
      池田敏和
    • Organizer
      第93回全国算数・数学教育研究(神奈川)大会
    • Place of Presentation
      川崎市中原市民会館
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Pedagogical Reflections on the Role of Modelling in the Teaching of Mathematics(Plenary Lecture)2011

    • Author(s)
      Toshikazu Ikeda
    • Organizer
      15th Inter- national Conference on the Teaching of Mathematical Modelling and Applications
    • Place of Presentation
      Australian Catholic University (Australia)
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] A Teaching Experiment in Modelling through Reduction Methods : Intended as a Bridge to later Trigonometric Methods2011

    • Author(s)
      Toshikazu Ikeda, Max Stephens and Yuki Wada
    • Organizer
      15th Inter- national Conference on the Teaching of Mathematical Modelling and Applications
    • Place of Presentation
      Australian Catholic University (Australia)
    • Related Report
      2013 Final Research Report
  • [Presentation] 指導系列としての問題解決はいかに?-数学二類「測量」 「三角 形と三角関数」の指導系列を手掛かりに-2010

    • Author(s)
      池田敏和
    • Organizer
      日本数学教育学会
    • Place of Presentation
      広島大学
    • Year and Date
      2010-11-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] 「指導系列としての問題解決はいかに?-数学二類「測量」「三角形と三角関数」の指導系列を手掛かりに-2010

    • Author(s)
      池田敏和
    • Organizer
      日本数学教育学会
    • Related Report
      2013 Final Research Report
  • [Book] PISA 2012 Assessment and Analytical Framework2013

    • Author(s)
      OECD
    • Total Pages
      261
    • Publisher
      OECD
    • Related Report
      2012 Annual Research Report
  • [Book] 新しい教科書と授業改善, 小・中学校の学習の円滑な接続を重視した算数・数学科の授業改善(pp.90-93執筆分担)2012

    • Author(s)
      池田敏和
    • Publisher
      学校図書
    • Related Report
      2013 Final Research Report
  • [Book] 新しい教科書と授業改善(執筆内容:小・中学校の学習の円滑な接続を重視した算数・数学科の授業改善)(pp.90-93執筆分担)2012

    • Author(s)
      財団法人学校教育研究所編(執筆分担者:池田敏和)
    • Total Pages
      180
    • Publisher
      学校図書
    • Related Report
      2011 Annual Research Report
  • [Book] 数学教育学研究ハンドブック, 数学的モデル化2010

    • Author(s)
      池田敏和
    • Publisher
      東洋館出版社
    • Related Report
      2013 Final Research Report

URL: 

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

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