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Characterization of learning processes of students reflection on their processes of planning a proof based on S. E. Toulmin s concept of argumentation

Research Project

Project/Area Number 26780504
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Education on school subjects and activities
Research InstitutionChiba University (2016)
Keiai University (2014-2015)

Principal Investigator

Tsujiyama Yosuke  千葉大学, 教育学部, 准教授 (10637440)

Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords数学教育 / 証明の構想 / 証明 / 振り返り / argumentation / 議論 / トゥールミン / 学習過程 / 教科教育学 / 科学教育
Outline of Final Research Achievements

Proving is an essential component in mathematical activities, but a difficult one for many students. We assume that one reason for this might be that unsuccessful arguments made during the process of planning a proof do not appear in the completed proof, and therefore students cannot see how those arguments influenced the proof. If students could reflect on such arguments, they would be able to learn about proving.
This study focused on Toulmin’s studies on argumentation, characterized processes of proving concerning its plausibility and probability, and examined students’ learning processes by designing, implementing, and analyzing eighth-grade geometry lessons. It constructed a learning process that consists of conjecturing statements, planning and constructing proofs of the statements, reflecting on the processes of planning proofs based on constructed proofs, finding new statements and considering the relationship between the initial and new statements based on the plans.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (15 results)

All 2016 2015 2014 Other

All Int'l Joint Research (1 results) Journal Article (4 results) (of which Peer Reviewed: 3 results,  Open Access: 1 results,  Acknowledgement Compliant: 3 results) Presentation (9 results) (of which Int'l Joint Research: 2 results) Remarks (1 results)

  • [Int'l Joint Research] エクセター大学(英国)

    • Related Report
      2015 Research-status Report
  • [Journal Article] S. E. トゥールミンにみるargumentationの意味とその数学教育上の意義:証明の構想の過程に焦点を当てて2016

    • Author(s)
      辻山洋介
    • Journal Title

      敬愛大学国際研究

      Volume: 29 Pages: 1-28

    • NAID

      120006016376

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] 演繹的な説明の過程における不確実な考えに焦点を当てる2016

    • Author(s)
      辻山洋介
    • Journal Title

      新しい算数研究

      Volume: 542 Pages: 36-37

    • Related Report
      2015 Research-status Report
  • [Journal Article] 「平行四辺形の性質」において課題探究として証明することの授業化2014

    • Author(s)
      辻山洋介・油井幸樹
    • Journal Title

      日本数学教育学会誌『数学教育』

      Volume: 96(9) Pages: 22-25

    • NAID

      110009857082

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Rethinking the discovery function of proof within the context of proofs and refutations2014

    • Author(s)
      Komatsu, K., Tsujiyama, Y., & Sakamaki, A.
    • Journal Title

      International Journal of Mathematical Education in Science and Technology

      Volume: 45(7) Issue: 7 Pages: 1053-1067

    • DOI

      10.1080/0020739x.2014.902135

    • NAID

      120007100998

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] 数学学習における問題の焦点化に関する実践的考察:連立方程式の解の追究を事例として2016

    • Author(s)
      杉田有一・小林隆義・安藤和弥・浜田滋樹・辻山洋介
    • Organizer
      日本数学教育学会 第49回秋期研究大会
    • Place of Presentation
      弘前大学
    • Year and Date
      2016-10-29
    • 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
    • Year and Date
      2016-08-20
    • 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
    • Year and Date
      2016-08-20
    • Related Report
      2016 Annual Research Report
  • [Presentation] Use of examples of unsuccessful arguments to facilitate students’ reflection on their proving processes2016

    • Author(s)
      Tsujiyama, Y., & Yui, K.
    • Organizer
      The 13th International Congress on Mathematical Education
    • Place of Presentation
      University of Hamburg (Hamburg, Germany)
    • Year and Date
      2016-07-29
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Use of examples of unsuccessful arguments to facilitate students’ reflection on their proving processes2016

    • Author(s)
      Yosuke Tsujiyama, Koki Yui
    • Organizer
      13th International Congress on Mathematical Education
    • Place of Presentation
      ハンブルク(ドイツ)
    • Year and Date
      2016-07-24
    • Related Report
      2015 Research-status 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「活動-内容対応表」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(東京)
    • Year and Date
      2015-06-28
    • Related Report
      2015 Research-status Report
  • [Presentation] 学校数学における証明と論駁の活動を促すデザイン実験の構想2014

    • Author(s)
      小松孝太郎・辻山洋介
    • Organizer
      日本数学教育学会 第47回秋期研究大会
    • Place of Presentation
      熊本大学
    • Year and Date
      2014-11-08
    • Related Report
      2014 Research-status Report
  • [Presentation] 中学校図形領域における課題探究として証明することの授業化:第2学年の内容「平行四辺形の性質」2014

    • Author(s)
      辻山洋介・油井幸樹
    • Organizer
      日本数学教育学会 第2回春期研究大会
    • Place of Presentation
      東京学芸大学
    • Year and Date
      2014-06-29
    • Related Report
      2014 Research-status Report
  • [Remarks] 三角形や平行四辺形の性質

    • URL

      http://mathematics-edu.net/cms/htdocs/?page_id=98

    • Related Report
      2016 Annual Research Report

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Published: 2014-04-04   Modified: 2022-02-03  

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