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Development and evaluation of mathematics lessons by exploring mathematical notations that foster proportional reasoning

Research Project

Project/Area Number 19530782
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Education on school subjects and activities
Research InstitutionUtsunomiya University

Principal Investigator

HINO Keiko  Utsunomiya University, 教育学部, 准教授 (70272143)

Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords比例的推論 / 数学的表記 / 比と比例 / 授業分析 / 算数・数学科教育 / 記号的活動
Research Abstract

In this study, I analyzed student's construction of meaning to mathematical notations with respect to proportion and explored the situations that foster their proportional reasoning. Results showed students' difficulties in developing appropriate meanings to tables, formulas and graphs for proportion. On the other hand, students were more familiar with tables compared with formulas and graphs and their use of tables functioned as scaffolding to construct meanings to other expressions. Results also showed the significance of situations in which students communicate each other through self-developed notations as medium. Based on the results, I made implications for lessons in which students interact positively with their mathematical notations.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (21 results)

All 2009 2008 2007

All Journal Article (17 results) (of which Peer Reviewed: 12 results) Presentation (4 results)

  • [Journal Article] 中学校比例の授業での生徒の表・式・グラフの内化の様相 : 表に焦点をあてて2009

    • Author(s)
      日野圭子
    • Journal Title

      第42回数学教育論文発表会論文集

      Pages: 505-510

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 子どもの授業中の問題解決における他者の影響2009

    • Author(s)
      日野圭子
    • Journal Title

      宇都宮大学教育学部教育実践総合センター紀要 32

      Pages: 61-70

    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Journal Article] コミュニケーション手段の創造と修正 : 数学的コミュニケーションにおける学習の側面を考える2009

    • Author(s)
      日野圭子
    • Journal Title

      第42回数学教育論文発表会論文集, 課題別分科会

      Pages: 82-87

    • Related Report
      2009 Final Research Report
  • [Journal Article] 中学校比例の授業での生徒の表・式・グラフの内化の様相:表に焦点をあてて2009

    • Author(s)
      日野圭子
    • Journal Title

      第42回数学教育論文発表会論文集

      Pages: 505-510

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] コミュニケーション手段の創造と修正:数学的コミュニケーションにおける学習の側面を考える2009

    • Author(s)
      日野圭子
    • Journal Title

      第42回数学教育論文発表会論文集,課題別分科会

      Pages: 82-87

    • Related Report
      2009 Annual Research Report
  • [Journal Article] 指導を介しての比例的推論の発達に関する一考察 : 1年を通しての比例の問題に対する児童のアプローチの変化2008

    • Author(s)
      日野圭子
    • Journal Title

      筑波数学教育研究 27

      Pages: 1-10

    • NAID

      40016322429

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 数学的表記の内化を促す文脈についての一考察2008

    • Author(s)
      日野圭子
    • Journal Title

      日本数学教育学会誌 90(4)

      Pages: 33-44

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 一次関数の授業でみられた「操作的な考え」について : The Learner's Perspective Study 日本データの分析から2008

    • Author(s)
      日野圭子
    • Journal Title

      第41回数学教育論文発表会論文集

      Pages: 447-452

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] 発達の途上にある生徒の関数的見方・考え方を大切に2008

    • Author(s)
      日野圭子
    • Journal Title

      日本数学教育学会誌 90(9)

      Pages: 39-45

    • NAID

      110006937265

    • Related Report
      2009 Final Research Report
  • [Journal Article] 発達の途上にある生徒の関数的見方・考え方を大切に2008

    • Author(s)
      日野圭子
    • Journal Title

      日本数学教育学会誌・数学教育 62-5

      Pages: 39-45

    • NAID

      110006937265

    • Related Report
      2008 Annual Research Report
  • [Journal Article] 一次関数の授業でみられた「操作的な考え」について:The Learner's Perspective Study日本データの分析から2008

    • Author(s)
      日野圭子
    • Journal Title

      第41回数学教育論文発表会論文集

      Pages: 447-452

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 指導を介しての比例的推論の発達に関する-考察:1年を通しての比例の問題に対する児童のアプローチの変化2008

    • Author(s)
      日野圭子
    • Journal Title

      筑波数学教育研究 27

      Pages: 1-10

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 数学的表記の内化を促す文脈についての一考察2008

    • Author(s)
      日野圭子
    • Journal Title

      日本数学教育学会誌・算数教育 57(2)

      Pages: 33-44

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Studying lesson structure from the perspective of meaning construction : The case of two Japanese mathematics classrooms2007

    • Author(s)
      Hino Keiko
    • Journal Title

      Proceedings of the 29th PME Conference vol. 3

      Pages: 25-32

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Toward the problem-centered classroom : Trends in mathematical problem solving in Japan2007

    • Author(s)
      Hino Keiko
    • Journal Title

      ZDM Mathematics Education 39

      Pages: 503-514

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Toward the problem-centered classroom: Trends in mathematical problem solving in Japan2007

    • Author(s)
      Hino Keiko
    • Journal Title

      ZDM Mathematics Education 39

      Pages: 503-514

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Studying lesson structure from the perspective of students' meaning construction: The case of two Japanese mathematics classrooms2007

    • Author(s)
      Hino Keiko
    • Journal Title

      Proceedings of the 31th Conference of the International Group for the Psychology of Mathematics Education 31(3)

      Pages: 25-32

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Coherence in student's construction of mathematical meanings : Glimpses from three Japanese classrooms2009

    • Author(s)
      Hino Keiko
    • Organizer
      The 3^<rd> Redesigning Pedagogy International Conference
    • Place of Presentation
      National Institute of Education, Singapore
    • Year and Date
      2009-06-03
    • Related Report
      2009 Annual Research Report
  • [Presentation] Coherence in student's construction of mathematical meanings : Glimpses from three Japanese classrooms2009

    • Author(s)
      Hino Keiko
    • Organizer
      On-Line Proceedings of 3rd Redesigning Pedagogy International Conference
    • Place of Presentation
      National Institute of Education, Singapore
    • Related Report
      2009 Final Research Report
  • [Presentation] 異なる表現様式における生徒の比例の式の扱い :「比例」指導前の中1生徒への筆記調査から2008

    • Author(s)
      日野圭子
    • Organizer
      全国数学教育学会第28回研究発表会資料
    • Place of Presentation
      広島大学
    • Related Report
      2009 Final Research Report
  • [Presentation] 異なる表現様式における生徒の比例の式の扱い:「比例」指導前の中1生徒への筆記調査から2008

    • Author(s)
      日野圭子
    • Organizer
      全国数学教育学会第28回研究発表会
    • Place of Presentation
      広島大学
    • Related Report
      2008 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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