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Design of task sequences for collaborative mathematical inquiry with dynamic geometry environment

Research Project

Project/Area Number 15H05402
Research Category

Grant-in-Aid for Young Scientists (A)

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

Principal Investigator

KOMATSU Kotaro  信州大学, 学術研究院教育学系, 准教授 (40578267)

Project Period (FY) 2015-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥9,230,000 (Direct Cost: ¥7,100,000、Indirect Cost: ¥2,130,000)
Fiscal Year 2018: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2017: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2015: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Keywords数学教育 / 数学的探究 / 教材系列 / 動的幾何ソフトウェア / 動的幾何ソフト
Outline of Final Research Achievements

This research project explored ways to engage students in collaborative mathematical inquiry with dynamic geometry environments. To this end, this project formulated task design principles for supporting students in this activity, and developed tasks and task sequences following the proposed principles. The project also examined the advantages of the designed tasks and task sequences by implementing task-based interviews and classroom-based interventions in lower secondary schools.

Academic Significance and Societal Importance of the Research Achievements

これまで証明と論駁の活動に関する研究は行われてきたが,その活動を授業の場で実現する方法は十分には明らかにされてこなかった。本研究はこの方法を教材系列の開発に焦点を当てて明らかにしたものであり,この点に学術的意義がある。また,学習指導要領や教育振興基本計画では,ICTの活用による協働型学習の推進が強く求められており,その推進に資する教材系列を開発したことに本研究の社会的意義がある。

Report

(5 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Annual Research Report
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • Research Products

    (36 results)

All 2019 2018 2017 2016 2015 Other

All Int'l Joint Research (3 results) Journal Article (12 results) (of which Int'l Joint Research: 7 results,  Peer Reviewed: 11 results,  Open Access: 8 results,  Acknowledgement Compliant: 2 results) Presentation (16 results) (of which Int'l Joint Research: 6 results) Book (5 results)

  • [Int'l Joint Research] University of Southampton(英国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] University of Southampton(United Kingdom)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] University of Southampton(United Kingdom)

    • Related Report
      2016 Annual Research Report
  • [Journal Article] Task design principles for heuristic refutation in dynamic geometry environments2019

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

      International Journal of Science and Mathematics Education

      Volume: 17(4) Issue: 4 Pages: 801-824

    • DOI

      10.1007/s10763-018-9892-0

    • Related Report
      2018 Annual Research Report 2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Curriculum development for explorative proving in lower secondary school geometry: Focusing on the levels of planning and constructing a proof2019

    • Author(s)
      Miyazaki, M., Nagata, J., Chino, K., Sasa, H., Fujita, T., Komatsu, K., & Shimizu, S.
    • Journal Title

      Frontiers in Education

      Volume: 4(31)

    • DOI

      10.3389/feduc.2019.00031

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Task design for developing students’ recognition of the roles of assumptions in mathematical activity2019

    • Author(s)
      Komatsu, K., Stylianides, G. J, & Stylianides, A. J.
    • Journal Title

      Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education

      Volume: 印刷中

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Secondary school students’ appraisal of mathematical proofs2018

    • Author(s)
      Komatsu, K., Yamazaki, M., Fujita, T., Jones, K., & Sue, N.
    • Journal Title

      Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education

      Volume: 3 Pages: 227-234

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Domain-specific frameworks for curriculum development of explorative proving in junior high school mathematics2018

    • Author(s)
      Miyazaki, M., Nakagawa, H., Chino, K., Iwata, K., Komatsu K., & Fujita, T.
    • Journal Title

      School mathematics curriculum reforms: Challenges, changes and opportunities (ICMI Study 24 conference proceedings)

      Volume: - Pages: 269-276

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Explanatory unification by proofs in school mathematics2018

    • Author(s)
      Komatsu, K., Fujita, T., Jones, K., & Sue, N.
    • Journal Title

      For the Learning of Mathematics

      Volume: 38(1) Pages: 31-37

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Proof validation and modification in secondary school geometry2017

    • Author(s)
      Komatsu, K., Jones, K., Ikeda, T., & Narazaki, A.
    • Journal Title

      Journal of Mathematical Behavior

      Volume: 47 Pages: 1-15

    • DOI

      10.1016/j.jmathb.2017.05.002

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Fostering empirical examination after proof construction in secondary school geometry2017

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

      Educational Studies in Mathematics

      Volume: 96(2) Issue: 2 Pages: 129-144

    • DOI

      10.1007/s10649-016-9731-6

    • Related Report
      2017 Annual Research Report 2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] 課題探究として証明することのカリキュラム開発と実践:領域「資料の活用」における取り組み2017

    • Author(s)
      青山和裕・永田潤一郎・辻山洋介・小松孝太郎
    • Journal Title

      愛知教育大学数学教育学会誌イプシロン

      Volume: 59 Pages: 27-36

    • NAID

      120006460718

    • Related Report
      2017 Annual Research Report
  • [Journal Article] Proofs and refutations in school mathematics: A task design in dynamic geometry environments2017

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

      Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education

      Volume: 印刷中

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A framework for proofs and refutations in school mathematics: Increasing content by deductive guessing2016

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

      Educational Studies in Mathematics

      Volume: 未定 Issue: 2 Pages: 147-162

    • DOI

      10.1007/s10649-015-9677-0

    • Related Report
      2016 Annual Research Report 2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Proof validation and modification by example generation: A classroom-based intervention in secondary school geometry2016

    • Author(s)
      Komatsu, K., Ishikawa, T., & Narazaki, A.
    • Journal Title

      Proceedings of the 13th International Congress on Mathematical Education

      Volume: -

    • NAID

      120007100761

    • Related Report
      2016 Annual Research Report 2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Task design with DGEs: The case of students’ counterexamples2019

    • Author(s)
      Jones, K., & Komatsu, K.
    • Organizer
      The Eleventh Congress of the European Society for Research in Mathematics Education
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] The role of ‘opportunity to learn’ in the geometry curriculum: A multilevel comparison of six countries2019

    • Author(s)
      Bokhove, C., Miyazaki, M., Leung, A., Mok, I., Komatsu, K., & Chino, K.
    • Organizer
      2019 American Educational Research Association Annual Meeting
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 課題探究として証明することを実現する指導法の開発:領域「データの活用」に焦点をあてて2018

    • Author(s)
      小松孝太郎・永田潤一郎・辻山洋介
    • Organizer
      日本数学教育学会第6回春期研究大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 科学教育の内容・活動に固有な非認知的スキルの評価法の開発:領域「データの活用」における調査内容について2018

    • Author(s)
      永田潤一郎・青山和裕・小松孝太郎・辻山洋介
    • Organizer
      日本科学教育学会第42回年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Unification by proofs: The case of star polygon2017

    • Author(s)
      Komatsu, K., Fujita, T., Jones, K., & Sue, N.
    • Organizer
      British Society for Research into Learning Mathematics
    • Place of Presentation
      University of London, UK
    • Year and Date
      2017-03-04
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Diagrams in students’ proving activity in secondary school geometry2017

    • Author(s)
      Jones, K., & Komatsu, K.
    • Organizer
      The Tenth Congress of the European Society for Research in Mathematics Education
    • Place of Presentation
      Croke Park, Ireland
    • Year and Date
      2017-02-01
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Interpretation of diagrams in dynamic geometry environments2017

    • Author(s)
      Komatsu, K., & Jones, K.
    • Organizer
      The 41st Conference of the International Group for the Psychology of Mathematics Education
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 課題探究として証明することのカリキュラム開発:領域「資料の活用」における指導法の開発に向けて2017

    • Author(s)
      永田潤一郎・青山和裕・辻山洋介・小松孝太郎・廣瀬俊哉
    • Organizer
      日本科学教育学会第41回年会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 領域固有な方法知を生成しようとする態度を養うタスクデザイン:オープンな場面で証明することを例として2017

    • Author(s)
      宮﨑樹夫・茅野公穂・小松孝太郎・松永泰幸・Christian Bokhove・Allen Leung Y. L.・Mok Ida A. C.
    • Organizer
      日本科学教育学会第41回年会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 証明と論駁を通じての数学的知識の生成2017

    • Author(s)
      小松孝太郎・Keith Jones
    • Organizer
      日本数学教育学会第50回秋期研究大会
    • Related Report
      2017 Annual Research Report
  • [Presentation] Interpretation and production of diagrams when tackling proof problems in a dynamic geometry environment2016

    • Author(s)
      Komatsu, K. & Jones, K.
    • Organizer
      British Society for Research into Learning Mathematics
    • Place of Presentation
      University of Brighton, UK
    • Year and Date
      2016-11-12
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 課題探究として証明することのカリキュラム開発:領域「資料の活用」における授業化に向けて2016

    • Author(s)
      青山和裕・辻山洋介・永田潤一郎・小松孝太郎
    • Organizer
      日本科学教育学会第40回年会
    • Place of Presentation
      ホルトホール大分(大分県大分市)
    • Year and Date
      2016-08-19
    • Related Report
      2016 Annual Research Report
  • [Presentation] 課題探究として証明することのカリキュラム開発:領域「資料の活用」における授業化の試み2016

    • Author(s)
      髙橋伸茂・青山和裕・辻山洋介・永田潤一郎・小松孝太郎
    • Organizer
      日本科学教育学会第40回年会
    • Place of Presentation
      ホルトホール大分(大分県大分市)
    • Year and Date
      2016-08-19
    • Related Report
      2016 Annual Research Report
  • [Presentation] 課題探究として証明することのカリキュラム開発:領域「資料の活用」における「内容-活動対応表」の作成2016

    • Author(s)
      辻山洋介・永田潤一郎・青山和裕・小松孝太郎
    • Organizer
      日本数学教育学会第4回春期研究大会
    • Place of Presentation
      埼玉大学
    • Year and Date
      2016-06-12
    • Related Report
      2016 Annual Research Report
  • [Presentation] 課題探究として証明することの授業化と評価の試み:中学校第三学年における証明の評価・改善に焦点を当てて2015

    • Author(s)
      小松孝太郎・石川智之
    • Organizer
      日本数学教育学会第48回秋期研究大会
    • Place of Presentation
      信州大学
    • Year and Date
      2015-11-07
    • Related Report
      2015 Annual Research Report
  • [Presentation] 課題探究として証明することのカリキュラム開発:領域‘資料の活用’の開発枠組みの構築2015

    • Author(s)
      永田潤一郎・青山和裕・辻山洋介・小松孝太郎
    • Organizer
      日本数学教育学会第3回春期研究大会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2015-06-28
    • Related Report
      2015 Annual Research Report
  • [Book] 初等算数科教育(第5章執筆)2019

    • Author(s)
      吉田武男(監修)清水美憲(編著)
    • Total Pages
      200
    • Publisher
      ミネルヴァ書房
    • ISBN
      9784623086023
    • Related Report
      2018 Annual Research Report
  • [Book] 新版算数科教育研究(第2章第5節執筆)2019

    • Author(s)
      算数科教育学研究会(編)
    • Total Pages
      218
    • Publisher
      東洋館出版社
    • ISBN
      9784491036816
    • Related Report
      2018 Annual Research Report
  • [Book] Proof technology in mathematics research and teaching(Part IVの1節を執筆)2019

    • Author(s)
      G. Hanna, D. Reid, & M. de Villiers (Eds.)
    • Publisher
      Springer
    • Related Report
      2018 Annual Research Report
  • [Book] Advances in mathematics education research on proof and proving: An international perspective(第9章を分担執筆)2018

    • Author(s)
      A. J. Stylianides, & G. Harel (Eds.)
    • Total Pages
      301
    • Publisher
      Springer
    • ISBN
      9783319709963
    • Related Report
      2017 Annual Research Report
  • [Book] 算数・数学科教育2015

    • Author(s)
      藤井斉亮・小松孝太郎・他29名
    • Total Pages
      256
    • Publisher
      一藝社
    • Related Report
      2015 Annual Research Report

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Published: 2015-04-16   Modified: 2020-03-30  

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