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A study of methods of teaching and learning that promote concept formation of geometric figures

Research Project

Project/Area Number 13680191
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Science education
Research InstitutionChiba University

Principal Investigator

MATSUO Nanae  Chiba University, Faculty of Education, Associate professor, 教育学部, 助教授 (70292654)

Project Period (FY) 2001 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2004: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2003: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2002: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2001: ¥600,000 (Direct Cost: ¥600,000)
Keywordsgeometric figure / concept formation / understanding / using / identifying / verbalization / definition / mathematics education / 包摂関係 / 小学校と中学校の連続性 / 図形教育 / 理解の促進 / 相違性 / 授業実践 / 自覚 / 面積
Research Abstract

The purpose of this study is to offer the efficient methods of teaching and learning that promote concept formation of geometric figures in mathematics.
Through the lessons with emphasizing the factors which were pointed out theoretically to promote the transitions of states of understanding of the relations between two geometric figures, the possibility of implementation of factors was verified. The methods of teaching and learning of geometric figures in second, fifth and eighth grade that proposed based on the results are as follows.
In the second grade, points of the method of teaching and learning are to notice that four angles of a rectangle are right angles by comparing parallelograms except for rhombi and rectangles to rectangles except for squares after defining of a rectangle and to understand that a rectangle has four right angles through the activities which are making rectangles by folding papers, drawing rectangles and confirming right angles of a rectangle by using triangles.
In the fifth grade, points of the method of teaching and learning are to measure area of geometric figures by considering their properties and to measure area of parallelograms, rhombi and squares by relating the ways of measuring area of each of them with ways of measuring areas of geometric figures that have already learned by using of the geometric figures and the relations between them and to confirm it.
In the eighth grade, points of the method of defining of geometric figures are to represent definitions of geometric figures without using of negative expression, i.e. the sides are different, the angles are not right angles, etc. and to discuss about the reason why definitions of geometric figures do not contain negative expression.

Report

(4 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • Research Products

    (26 results)

All 2004 2003 2002 2001 Other

All Journal Article (18 results) Book (1 results) Publications (7 results)

  • [Journal Article] 定義の捉え方が図形の概念形成に及ぼす影響-小学校6年生と中学校2年生の捉え方の分析を通して-2004

    • Author(s)
      松尾 七重
    • Journal Title

      第37回数学教育論文発表会論文集(日本数学教育学会)

      Pages: 307-312

    • NAID

      110007175371

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Influence of understanding of definitions of geometric figures for concept formation of them : Analysis of sixth-and eighth-grade students' understanding of definitions of geometric figures.2004

    • Author(s)
      Nanae Matsuo
    • Journal Title

      Proceedings of the Thirty-seventh Research-Oriented Annual Conference of Mathematics Education(JSME)

      Pages: 307-312

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] 定義の捉え方が図形の概念形成に及ぼす影響-小学校6年生と中学校2年生の捉え方の分析を通して-2004

    • Author(s)
      松尾七重
    • Journal Title

      第37回数学教育論文発表会論文集

      Pages: 307-312

    • NAID

      110007175371

    • Related Report
      2004 Annual Research Report
  • [Journal Article] 図形の概念の相違性を捉えるための要因の検証2003

    • Author(s)
      松尾 七重
    • Journal Title

      千葉大学教育学部研究紀要 第51巻

      Pages: 69-73

    • NAID

      110004628628

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] 図形間の関係についての指導2003

    • Author(s)
      松尾 七重
    • Journal Title

      第36回数学教育論文発表会「課題別分科会」(日本数学教育学会)

      Pages: 138-143

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Verifying factor that promotes understanding the difference between two concepts of geometric figures.2003

    • Author(s)
      Nanae Matsuo
    • Journal Title

      Bulletin of the Faculty of Education, Chiba University 51

      Pages: 69-73

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Teaching of the relations between geometric figures.2003

    • Author(s)
      Nanae Matsuo
    • Journal Title

      WG Proceedings of the Thirty-sixth Research-Oriented Annual Conference of Mathematics Education(JSME)

      Pages: 253-258

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Mathematics education for knowing of enjoyment and interest of thinking.2003

    • Author(s)
      Nanae Matsuo
    • Journal Title

      Mathematics Education for Promoting the Transition of Levels of Understanding by Jumping up the Actual Situation

      Pages: 134-141

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] 図形の概念理解を促進する概念活用の場面-小学校5年生の面積の授業において-2002

    • Author(s)
      松尾 七重
    • Journal Title

      千葉大学教育実践研究 第9号

      Pages: 101-110

    • NAID

      110000558521

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] 図形の概念間の関係についての理解を保持する指導-構成要素に基づく分類と総合的な作図-2002

    • Author(s)
      松尾 七重
    • Journal Title

      千葉大学数学教育研究 第2号

      Pages: 14-17

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] 図形の概念の弁別を促す要因の検証-直角を基にした長方形の捉え方を中心にして-2002

    • Author(s)
      松尾 七重
    • Journal Title

      第35回数学教育論文発表会論文集(日本数学教育学会)

      Pages: 253-258

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Situations of using concepts of geometric figures to promote understanding of the concepts : In the lessons of area measurement for fifth-grade students.2002

    • Author(s)
      Nanae Matsuo
    • Journal Title

      Research in Teaching Strategies and Learning Activities : A Bulletin of the Enter for Educational Research, Training and Guidance in Educational Practice(Faculty of Education, Chiba University) 9

      Pages: 101-110

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Teaching for maintaining of understanding relations among concepts of geometric figures : Classification based on components of geometric figures and construction of them.2002

    • Author(s)
      Nanae Matsuo
    • Journal Title

      Chiba Journal of Educational Study in Mathematics 2

      Pages: 14-17

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Verifying factors that promote identifying concepts of geometric figures : Focus on understanding of rectangles based on right angles.2002

    • Author(s)
      Nanae Matsuo
    • Journal Title

      Proceedings of the Thirty-fifth Research-Oriented Annual Conference of Mathematics Edxication(JSME)

      Pages: 253-258

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] 図形の概念の活用による理解の促進-小学校5年生の面積の授業を通して-2001

    • Author(s)
      松尾 七重
    • Journal Title

      第34回数学教育論文発表会論文集(日本数学教育学会)

      Pages: 463-468

    • NAID

      110007174986

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Promotion of understanding geometric figures by using of them : Through, fifth-grade lessons on area measurement.2001

    • Author(s)
      Nanae Matsuo
    • Journal Title

      Proceedings of the Thirty-fourth Research-Oriented Annual Conference of Mathematics Education(JSME)

      Pages: 463-468

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] 相違点及び類似点から図形の概念を分類する条件-平行四辺形と正方形,ひし形と長方形の関係を基に-

    • Author(s)
      松尾 七重
    • Journal Title

      算数・数学教育の新世紀 (発表予定)

      Pages: 19-26

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Factors to classify geometric figures based on the differences and similarities between them : Parallelograms and squares, rhombi and rectangles.

    • Author(s)
      Nanae Matsuo
    • Journal Title

      New Century of Mathematics Education (in press)

      Pages: 19-26

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Book] CD-ROM版 中学校数学科教育実践講座理論編 考えることの楽しさ、面白さが分かる数学教育 現実を乗り越え、‘知'の水準を高める数学教育(PP.134-141)2003

    • Author(s)
      松尾 七重(分担執筆)
    • Total Pages
      193
    • Publisher
      (株)ニチブン
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Publications] 松尾 七重: "図形の概念の弁別を促す要因の検証-直角を基にした長方形の捉え方を中心にして-"第35回数学教育論文発表会論文集. 253-258 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 松尾 七重: "図形の概念の相違性を捉えるための要因の検証"千葉大学教育学部研究紀要. 第51巻. 69-73 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] 松尾 七重(分担執筆): "中学校数学科教育実践講座理論編 考えることの楽しさ、面白さが分かる数学教育 現実を乗り越え、'知'の水準を高める数学教育(pp.134-141)"(株)ニチブン(CD-ROM版). 193 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] 松尾 七重: "相違点及び類似点から図形の概念を分類する条件-平行四辺形と正方形,ひし形と長方形の関係を基に-"算数・数学教育の新世紀. 19-26 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 松尾 七重: "図形の概念の活用による理解の促進-小学校5年生の面積の授業を通して-"第34回数学教育論文発表会論文集. 463-468 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 松尾 七重: "図形の概念理解を促進する概念活用の場面-小学校5年生の面積の授業において-"千葉大学教育実践研究. 第9号. 25-34 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] 松尾 七重: "図形の概念間の関係についての理解を保持する指導-構成要素に基づく分類と総合的な作図-"千葉大学数学教育研究. 第2号. 14-17 (2002)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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