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A study on students' own representation and their refinement processes in arithmetic and mathematics classes

Research Project

Project/Area Number 25381208
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 InstitutionFukuoka University of Education

Principal Investigator

Norihiro Shimizu  福岡教育大学, 教育学部, 教授 (50284451)

Co-Investigator(Kenkyū-buntansha) 岩崎 浩  上越教育大学, 大学院学校教育研究科, 教授 (80251867)
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)
Project Period (FY) 2013-04-01 – 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: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords数学教育 / 表現
Outline of Final Research Achievements

The purpose of this study is to identify informal representation by students and teachers in arithmetic and mathematics lessons and to clarify their roles in mathematics learning.
As a result of the study, we constructed a theoretical framework to capture informal representation and clarified the roles played by informal representation in classes for constructing figure concepts and discovering the numerical relations in multiplicative table, using the framework. We pointed out the importance that teachers have a positive stance to take the students' informal representation as the subject of classroom discussion and they examine and analyze the teaching materials to realize such classes.

Report

(5 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (8 results)

All 2017 2016 2015 2014

All Journal Article (6 results) (of which Acknowledgement Compliant: 5 results,  Open Access: 1 results,  Peer Reviewed: 1 results) Presentation (2 results)

  • [Journal Article] 数学教育における反省的思考力の育成2017

    • Author(s)
      清水紀宏
    • Journal Title

      日本数学教育学会春期研究大会論文集

      Volume: 5

    • NAID

      40022278405

    • Related Report
      2016 Annual Research Report
    • Acknowledgement Compliant
  • [Journal Article] 数学教育における汎用的能力の育成:問題解決という観点から2016

    • Author(s)
      清水紀宏
    • Journal Title

      日本数学教育学会春期研究大会論文集

      Volume: 4 Pages: 293-300

    • NAID

      40022277934

    • Related Report
      2016 Annual Research Report
    • 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

      愛知教育大学数学教育学会誌イプシロン

      Volume: 58 Pages: 21-34

    • NAID

      120006460697

    • Related Report
      2016 Annual Research Report
    • Acknowledgement Compliant
  • [Journal Article] 算数授業の振り返り活動を通じた説明表現の構成と修正の指導に関する一考察2015

    • Author(s)
      山田篤史・片野慶子
    • Journal Title

      愛知教育大学数学教育学会誌『イプシロン』

      Volume: 57 Pages: 29-38

    • NAID

      120005723131

    • Related Report
      2015 Research-status Report
    • Open Access / Acknowledgement Compliant
  • [Journal Article] 算数・数学の授業におけるインフォーマルな表現を捉える枠組み2015

    • Author(s)
      清水紀宏・山田篤史
    • Journal Title

      数学教育学研究

      Volume: 21(2)

    • NAID

      130007580516

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [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

      愛知教育大学数学教育学会誌『イプシロン』

      Volume: 56 Pages: 37-44

    • NAID

      120005723101

    • Related Report
      2014 Research-status Report
  • [Presentation] 「九九のひょうときまり」の授業に見られるインフォーマルな表現2017

    • Author(s)
      清水紀宏・山田篤史
    • Organizer
      全国数学教育学会第45回研発表会
    • Place of Presentation
      広島大学教育学研究科(広島県東広島市)
    • Year and Date
      2017-01-28
    • Related Report
      2016 Annual Research Report
  • [Presentation] 算数・数学の授業におけるインフォーマルな表現を捉える枠組みについて2015

    • Author(s)
      清水紀宏・山田篤史
    • Organizer
      全国数学教育学会
    • Place of Presentation
      広島大学
    • Year and Date
      2015-01-31 – 2015-02-01
    • Related Report
      2014 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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