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Study on the opportunity to improve proportional reasoning from the perspective of articulation between primary and lower secondary school curriculum

Research Project

Project/Area Number 22530952
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  宇都宮大学, 教育学部, 教授 (70272143)

Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords比例的推論 / 小中の接続 / 数学教育 / 数学的表記
Research Abstract

Purpose: To understand 7th graders' proportional reasoning and to trace their learning trajectories of different representations for proportional relationship over one year, and to design a series of lessons on the basis of the results.
Method: To conduct written assessment to 171 students in two public schools. From the results of the assessment, to select 14 students who are in different levels on the conceptualization of rate, and to conduct task-based interviews over one year (2-5 times per student).
Results: From the written assessment conducted at the beginning of the school year, large differences on proportional reasoning were found. During the interviews as well, the students expressed quantitative relationship given in the tasks in a variety of representations. Their variations were explored by distinguishing four types of their ways of grasping the relationship. By using these results, a series of lessons in the areas of "Number and Expression" and "Function" were designed.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (19 results)

All 2014 2013 2012 2011 2010

All Journal Article (12 results) (of which Peer Reviewed: 7 results) Presentation (7 results)

  • [Journal Article] 小中移行期の生徒による比例の問題場面の表現の特徴:個別インタビューにおける共通問題への応答の比較2014

    • Author(s)
      日野圭子
    • Journal Title

      宇都宮大学教育学部紀要

      Volume: 64号, 第1部 Pages: 95-110

    • NAID

      110009771588

    • Related Report
      2013 Final Research Report
  • [Journal Article] 小中移行期の生徒による比例の問題場面の表現の特徴:個別インタビューにおける共通問題への応答の比較2014

    • Author(s)
      日野圭子
    • Journal Title

      宇都宮大学教育学部紀要

      Volume: 64 Pages: 95-110

    • NAID

      110009771588

    • Related Report
      2013 Annual Research Report
  • [Journal Article] 中学校入学初期における生徒の比例的推論の多様性:筆記調査の結果と示唆2013

    • Author(s)
      日野圭子
    • Journal Title

      宇都宮大学教育学部紀要

      Volume: 63号, 第1部 Pages: 117-129

    • NAID

      110009560262

    • Related Report
      2013 Final Research Report
  • [Journal Article] 中1生徒による比例の問題場面の表現に関する考察2013

    • Author(s)
      日野圭子
    • Journal Title

      日本数学教育学会第46回秋期研究大会発表集録

      Volume: 46 Pages: 299-302

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 中学校入学初期における生徒の比例的推論の多様性:筆記調査の結果と示唆2013

    • Author(s)
      日野圭子
    • Journal Title

      宇都宮大学教育学部紀要

      Volume: 63 (1) Pages: 117-129

    • NAID

      110009560262

    • Related Report
      2012 Annual Research Report
  • [Journal Article] Students creating ways to represent proportional situations: In relation to conceptualization of rate2012

    • Author(s)
      Keiko Hino
    • Journal Title

      Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education

      Volume: Vo. 2 Pages: 283-290

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 中1生徒による式の生成における比例的推論の影響:個別インタビューの結果の考察から2012

    • Author(s)
      日野圭子
    • Journal Title

      第45回数学教育論文発表会論文集

      Volume: 第1巻 Pages: 653-658

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 異なる問題場面における生徒の比例の式の扱い:「比例」学習前の中1生徒への筆記調査から2011

    • 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

      Volume: 34 Pages: 39-48

    • NAID

      110009424209

    • Related Report
      2013 Final Research Report
  • [Journal Article] Students' uses of tables in learning equations of proportion : A case study of a seventh grade class2011

    • Author(s)
      Hino, Keiko
    • Journal Title

      Proceedings of the 35^<th> Conference of the International Group for the Psychology of Mathematics Education

      Volume: Vol.3 Pages: 25-32

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 生徒が作り出した数量の関係を表すグラフ2011

    • Author(s)
      日野圭子
    • Journal Title

      第44回数学教育論文発表会論文集

      Volume: 第2巻 Pages: 681-686

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 数学学習における記号論的視点の近年の動向と課題2011

    • Author(s)
      日野圭子
    • Journal Title

      第44回数学教育論文発表会論文集

      Volume: 第1巻 Pages: 11-20

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [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:グラフに焦点をあてて2010

    • Author(s)
      日野圭子
    • Journal Title

      第43回数学教育論文発表会論文集

      Volume: 1 Pages: 211-216

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] 中1生徒による比例の問題場面の表現に関する考察2013

    • Author(s)
      日野圭子
    • Organizer
      第46回秋期研究大会発表集録
    • Related Report
      2013 Final Research Report
  • [Presentation] 中1生徒による比例の問題場面の表現に関する考察2013

    • Author(s)
      日野圭子
    • Organizer
      日本数学教育学会第46回秋期研究大会
    • Place of Presentation
      宇都宮大学峰キャンパス
    • Related Report
      2013 Annual Research Report
  • [Presentation] 中1生徒による式の生成における比例的推論の影響:個別インタビューの結果の考察から2012

    • Author(s)
      日野圭子
    • Organizer
      第45回数学教育論文発表会論文集第2巻
    • Related Report
      2013 Final Research Report
  • [Presentation] Students creating ways to represent proportional situations : In relation to conceptualization of rate2012

    • Author(s)
      Hino Keiko
    • Organizer
      Proceedings of the 36th Annual Conference of the International Group for the Psychology of Mathematics Education
    • Place of Presentation
      Taipei (Taiwan)(Vol.2, pp. 283-290)
    • Related Report
      2013 Final Research Report
  • [Presentation] 生徒が作り出した数量の関係を表すグラフ2011

    • Author(s)
      日野圭子
    • Organizer
      日本数学教育学会第44回数学教育論文発表会論文集第2巻
    • Related Report
      2013 Final Research Report
  • [Presentation] 数学学習における記号論的視点の近年の動向と課題2011

    • Author(s)
      日野圭子
    • Organizer
      日本数学教育学会第44回数学教育論文発表会論文集第1巻
    • Related Report
      2013 Final Research Report
  • [Presentation] Students'uses of tables in learning equations of proportion : A case study of a seventh grade class2011

    • Author(s)
      Hino Keiko
    • Organizer
      Proceedings of the 35th Annual Conference of the International Group for the Psychology of Mathematics Education
    • Place of Presentation
      Ankara (Turkey)(Vol.3, pp.25-32)
    • Related Report
      2013 Final Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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