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Analysis of mathematical thinking in terms of interactions with a diagram in mathematics education: from the cognitive and cultural perspective

Research Project

Project/Area Number 26381211
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Education on school subjects and activities
Research InstitutionHiroshima University

Principal Investigator

Kageyama Kazuya  広島大学, 教育学研究科, 准教授 (60432283)

Co-Investigator(Kenkyū-buntansha) 山田 篤史  愛知教育大学, 教育学部, 教授 (20273823)
岡崎 正和  岡山大学, 教育学研究科, 教授 (40303193)
和田 信哉  鹿児島大学, 法文教育学域教育学系, 准教授 (60372471)
岩田 耕司  福岡教育大学, 教育学部, 准教授 (90437541)
Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords図式 / 数学的思考 / 身体化理論 / 記号論 / ネットワーキング / 身体的認知 / 文化歴史理論 / 図式的推論
Outline of Final Research Achievements

The purpose of this research is to understand students' mathematical thinking by supposing that it is related to constructing and using diagrams, which are inscriptions on a paper, such as figures, tables and signs, with certain rules.
Diagrams are constructed originally through bodily actions or experiences, while these include some useful ideas and are handed on to the next. This research implied that students thought mathematically by reading a pattern or law to make a hypothesis and verifying the range in which they could deal with it as a theory.

Report

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

    (14 results)

All 2016 2015 2014

All Journal Article (9 results) (of which Peer Reviewed: 6 results,  Acknowledgement Compliant: 5 results) Presentation (4 results) (of which Int'l Joint Research: 1 results) Book (1 results)

  • [Journal Article] 数学教育における図式との相互作用による数学的思考の分析2016

    • Author(s)
      影山和也・和田信哉・岩田耕司・山田篤史・岡崎正和
    • Journal Title

      数学教育学研究

      Volume: 22 Pages: 163-174

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] 現成主義の視座からみた行為の様相と数学的知り方の特質2016

    • Author(s)
      影山和也
    • Journal Title

      数学教育学論究臨時増刊

      Volume: 98 Pages: 9-16

    • NAID

      130007938176

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] 数学教育における表現研究の立場からみた割合指導の困難性と方向性2016

    • Author(s)
      山田篤史
    • Journal Title

      イプシロン

      Volume: 58 Pages: 21-34

    • NAID

      120006460697

    • Related Report
      2016 Annual Research Report
    • Acknowledgement Compliant
  • [Journal Article] 数学教育における図式との相互作用による数学的思考の分析―記号論と身体化理論のネットワーク化を通した図式の意味について―2016

    • Author(s)
      影山和也,和田信哉,岩田耕司,山田篤史,岡崎正和
    • Journal Title

      全国数学教育学会誌

      Volume: 22

    • NAID

      130007580639

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] 小学校における式の意味論的認識に関する研究─代数的推論の観点から─2016

    • Author(s)
      和田信哉
    • Journal Title

      鹿児島大学教育学部研究紀要 教育科学編

      Volume: 67 Pages: 1-11

    • NAID

      40020873883

    • Related Report
      2015 Research-status Report
  • [Journal Article] 為すこととしての数学的認知論の基礎的考察2015

    • Author(s)
      影山和也
    • Journal Title

      数学教育学論究 臨時増刊

      Volume: 97 Pages: 65-72

    • NAID

      110010007004

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] 算数教育における数学的思考に関わる数学的気づきの調査研究2015

    • Author(s)
      影山和也
    • Journal Title

      数学教育学研究

      Volume: 21(2)

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] 問題解決的な授業における数学的表現の使用とその修正:考え方の説明における図の場合2014

    • Author(s)
      山田篤史
    • Journal Title

      イプシロン

      Volume: 56 Pages: 37-44

    • NAID

      120005723101

    • Related Report
      2014 Research-status Report
  • [Journal Article] 加法と減法の相互関係に関する研究─代数的推論の観点から─2014

    • Author(s)
      和田信哉
    • Journal Title

      数学教育学研究

      Volume: 20(2) Pages: 77-91

    • NAID

      130007580539

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Presentation] The nature of embodied mathematical objects2016

    • Author(s)
      Kazuya Kageyama
    • Organizer
      the 40th Conference of the International Group for the Psychology of Mathematics Education
    • Place of Presentation
      Szeged, Hungary
    • Year and Date
      2016-08-03
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 身体化理論の視座からの数学的対象論の展開2016

    • Author(s)
      影山和也
    • Organizer
      第4回日本数学教育学会春期研究大会
    • Place of Presentation
      埼玉大学
    • Year and Date
      2016-06-12
    • Related Report
      2016 Annual Research Report
  • [Presentation] 数学教育における図式との相互作用による数学的思考の分析―図式に関わる諸理論の比較検討―2016

    • Author(s)
      影山和也,和田信哉,岩田耕司,山田篤史,岡崎正和
    • Organizer
      第43回全国数学教育学会
    • Place of Presentation
      広島大学
    • Year and Date
      2016-01-30
    • Related Report
      2015 Research-status Report
  • [Presentation] Toward theorizing the embodiment of mathematical cognition2014

    • Author(s)
      影山和也
    • Organizer
      the 38th Conference of the International Group for the Psychology of Mathematics Education
    • Place of Presentation
      Vancouver(Canada)
    • Year and Date
      2014-07-15 – 2014-07-20
    • Related Report
      2014 Research-status Report
  • [Book] Selected Regular Lectures from the 12th International Congress on Mathematical Education2015

    • Author(s)
      岡崎正和
    • Total Pages
      932
    • Publisher
      Springer International Publishing Switzerland
    • Related Report
      2015 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2018-03-22  

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