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Curriculum development on vertical sequence of mathematics based on model-oriented approach

Research Project

Project/Area Number 26350188
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Science education
Research InstitutionYokohama National University

Principal Investigator

IKEDA Toshikazu  横浜国立大学, 教育学部, 教授 (70212777)

Project Period (FY) 2014-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywordsモデル / 算数・数学 / カリキュラム / 図形 / 複数の世界 / 教材開発 / 数学的知識 / 再帰的活動
Outline of Final Research Achievements

The values of interactive translations among plural worlds were discussed by developing the concrete materials focused on interactive translations among plural worlds. Targeting the curriculum development on vertical sequences of mathematics, nine phases to deepen students’mathematical knowledge concerning Geometry through interactive translations among plural worlds are identified from two viewpoints “objects” and “actions”. Concerning objects, equivalence relationships of geometric figures are identified, and concerning actions, operations and transformations of geometric figures are identified.

Academic Significance and Societal Importance of the Research Achievements

本論では,応用志向と構造志向といった二つの考えを二律背反的に考えるのではなく,両者が共に影響を与えることによって,現実の世界,数学の世界が共に成長していくとともに,二つの世界をつなぐ関係自体も成長していくという考えを基にしている,そして,現実の世界,数学の世界を拡張して複数の世界として捉え直し,複数の世界間において,互いが互いを成長させるという考えに基づくカリキュラム開発に焦点を当てている.こうような方針は,持続的な数学的知識の成長を促すカリキュラムを開発していく上で,一つの指針に成り得ると考える。

Report

(6 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (24 results)

All 2018 2017 2016 2015 2014 Other

All Int'l Joint Research (2 results) Journal Article (8 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 5 results) Presentation (9 results) (of which Int'l Joint Research: 2 results,  Invited: 2 results) Book (5 results)

  • [Int'l Joint Research] The University of Melbourne(Australia)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] Melborne University/Australian Catholic University(Australia)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Evaluating student perceptions of the roles of mathematics in society following an experimental teaching program2018

    • Author(s)
      Toshikazu Ikeda
    • Journal Title

      ZDM

      Volume: 50 Pages: 259-271

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Modelling as interactive translations among plural worlds: Experimental teaching using the night-time problem2017

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

      Mathematical modelling and applications-Crossing and researching boundaries in mathematics education

      Volume: 17 Pages: 399-409

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] 陶冶的目的からみた数学教育における汎用的能力の育成とその課題2017

    • Author(s)
      池田敏和
    • Journal Title

      第5回春期研究大会論文集,日本数学教育学会

      Volume: 5 Pages: 249-254

    • Related Report
      2017 Research-status Report
  • [Journal Article] 数学教育における汎用的能力の育成を考えるための枠組みとその歴史的展望2016

    • Author(s)
      池田敏和
    • Journal Title

      日本数学教育学会第4回春期研究大会論文集

      Volume: 4 Pages: 289-292

    • NAID

      40022277933

    • Related Report
      2016 Research-status Report
  • [Journal Article] Mathematical Applications and Modelling in the Teaching and Learning of Mathematics2015

    • Author(s)
      Jill Brown and Toshikazu Ikeda
    • Journal Title

      The Proceedings of the 12th International Congress on Mathematical Education

      Volume: 12 Pages: 469-473

    • DOI

      10.1007/978-3-319-12688-3_42

    • ISBN
      9783319106854, 9783319126883
    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Applying PISA Ideas to Classroom Teaching of Mathematical Modelling2015

    • Author(s)
      Toshikazu Ikeda
    • Journal Title

      Assessing Mathematical Literacy

      Volume: なし Pages: 221-238

    • DOI

      10.1007/978-3-319-10121-7_11

    • ISBN
      9783319101200, 9783319101217
    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Mathematical Modelling in Japan2015

    • Author(s)
      Toshikazu Ikeda
    • Journal Title

      Mathematical Modelling from Theory to Practice

      Volume: なし Pages: 83-96

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] 学習指導要領算数・数学科改訂に向けての検討課題2014

    • Author(s)
      金本良通・大久保和義・池田敏和・青山和裕・松嵜昭雄
    • Journal Title

      日本数学教育学会誌

      Volume: 96 Pages: 10-21

    • NAID

      130008018966

    • Related Report
      2014 Research-status Report
  • [Presentation] 数学的モデリングと統計的問題解決2018

    • Author(s)
      池田敏和
    • Organizer
      日本数学教育学会春期大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Constructing mathematical knowledge through modelling: From the shortest route between two points to a fundamental theorem of limit2017

    • Author(s)
      Ikeda,Toshikazu and Max Stephens
    • Organizer
      ICTMA18
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] 数学的モデリングの算数・数学科カリキュラムへの位置づけ2016

    • Author(s)
      池田敏和
    • Organizer
      科学教育学会
    • Place of Presentation
      ホルトホール大分
    • Related Report
      2016 Research-status Report
  • [Presentation] ORGANIZING MATHEMATICAL MODELLING IN JAPANESE MATHEMATICS CURRICULUM2016

    • Author(s)
      Toshikazu Ikeda
    • Organizer
      ICME13
    • Place of Presentation
      ハンブルグ(ドイツ)
    • Related Report
      2016 Research-status Report
  • [Presentation] 数学的モデリング・応用を算数・数学科にいかに位置づけるか2015

    • Author(s)
      池田敏和
    • Organizer
      科学教育学会
    • Place of Presentation
      山形大学
    • Year and Date
      2015-08-22
    • Related Report
      2015 Research-status Report
  • [Presentation] 複数の世界を行き来する活動に焦点を当てた教材開発2015

    • Author(s)
      池田敏和
    • Organizer
      日本数学教育学会
    • Place of Presentation
      札幌南高等学校
    • Year and Date
      2015-08-04
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Modelling as Interactive Translations among Plural Worlds2015

    • Author(s)
      Toshikazu Ikeda and Max Stephens
    • Organizer
      ICTMA17
    • Place of Presentation
      ノッティンガム大学(イギリス)
    • Year and Date
      2015-07-19
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] モデルを志向した数学教育の展開2015

    • Author(s)
      池田敏和
    • Organizer
      数学教育学会
    • Place of Presentation
      明治大学
    • Year and Date
      2015-03-22
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] スパイラルによる教育課程の一層の推進に向けて2014

    • Author(s)
      池田敏和
    • Organizer
      日本数学教育学会
    • Place of Presentation
      筑波大学
    • Year and Date
      2014-06-29
    • Related Report
      2014 Research-status Report
  • [Book] 小学校教育課程実践講座 算数2018

    • Author(s)
      齊藤一弥編著(分担執筆:池田敏和)
    • Total Pages
      242
    • Publisher
      ぎょうせい
    • ISBN
      9784324103050
    • Related Report
      2017 Research-status Report
  • [Book] 小学校学習指導要領ポイント総整理 算数2017

    • Author(s)
      清水美憲・齊藤一弥編著(分担執筆:池田敏和)
    • Total Pages
      213
    • Publisher
      東洋館出版社
    • ISBN
      9784491033990
    • Related Report
      2017 Research-status Report
  • [Book] 数学的活動の再考2016

    • Author(s)
      池田敏和・藤原大樹
    • Total Pages
      144
    • Publisher
      学校図書
    • Related Report
      2015 Research-status Report
  • [Book] 算数と数学の一貫した指導が学力を向上させる2015

    • Author(s)
      片桐重男・向山宣義・廣田敬一・山崎憲・上野和彦・茂呂美恵子・青木裕子・高山保子・鎌須賀幹子・池田敏和・鈴木誠・羽住邦男・藤原大樹・傍士輝彦・矢嶋昭雄・山崎浩二
    • Total Pages
      132
    • Publisher
      学事出版
    • Related Report
      2014 Research-status Report
  • [Book] 数学的思考に基づく教材開発のストラテジー242014

    • Author(s)
      池田敏和
    • Total Pages
      140
    • Publisher
      明治図書
    • Related Report
      2014 Research-status Report

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Published: 2014-04-04   Modified: 2023-03-16  

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