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Study of the Representational System in Mathematics Education

Research Project

Project/Area Number 07680279
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 教科教育
Research InstitutionHIROSHIMA UNIVERSITY

Principal Investigator

NAKAHARA Tadao  Hiroshiama Univ.Education Professor, 教育学部, 教授 (90034818)

Co-Investigator(Kenkyū-buntansha) KOYAMA Masataka  Hiroshiama Univ.Education Associate Prof., 教育学部, 助教授 (30186837)
IMAOKA Mitsunori  Hiroshiama Univ.Education Associate Prof., 教育学部, 助教授 (20031817)
Project Period (FY) 1995 – 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 1996: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1995: ¥1,200,000 (Direct Cost: ¥1,200,000)
KeywordsRepresentation / Mathematical Symbols / Interation / Understanding / 理解 / コミュニケーション
Research Abstract

In this study, we classified the modes of representaion used in mathematics teaching into five modes as follows.
E1.Realistic rep. : Representations using natural objects in the real world
E2.Manipulative rep. : Representations using artificial manipulative objects
1.Illustrative rep. : Representations using pictures, diagrams, and/or figures
S1.Linguistic rep. : Representations using written everyday language
S2.Symbolic rep. : Representations using mathematical symbols
Morevoer, we separated each mode of representation into children' internal representation and external representation. Based on the representational system, we examined characteristics and functional roles of each representational mode in mathematical lessons. Main findings can be summarized as :
(1) E1, E2 and I are strong iconizing. S1 and S2 are week iconizing.
(2) Following scheme will be suggested in the teaching-leraning process of mathematics ; E1 * E2 * I * S1 * S2
(3) Manipultive rep.and Illustrative rep.play important role in problem solving and understanding processes.
(4) The interactions in mathematical lessons are calssified into four types : 1.Decreased oppsition 2.Agreement 3.Integral enhancement 4.extensive enhancement.

Report

(3 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • 1995 Annual Research Report
  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] 今岡 光範: "空間認識に関する発展的教材の内容学的考察" 全国数学教育学会誌 数学教育学研究. 第2巻. 115-120 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Tadao Nakahara: "Study of the Constructive Approach in Mathematics Education" Hiroshima Journal of Mathematics Education. Vol.5. 1-10 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Masataka Koyama: "Research on the Complementarity of Intuition and Logical Thinking in the Process of Understanding Mathematics" Hiroshima Journal of Mathematics Education. Vol.5. 21-33 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 宮本泰司: "数学的概念の認識過程についての基礎研究(XVIII) -構成的アプローチに基づく算数科授業の検討(2)-" 広島大学教育学部・関係附属学校園共同研究体制 研究紀要. 第25号. 85-93 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 中原 忠男: "小学校算数実践指導全集9 表現力を育てる式の指導" 日本教育図書センター, 255 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Imaoka: "Study of Developmental Teaching Materials for Special Cognition : From a Viewpoint of Instructional Contents in Mathematics Education" Journal of JASME,Research in Mathematice Education. Vol.2. 115-120 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Nakahara: "Study of the Constructive Approach in Mathematics Education" Hiroshima Journal of Mathematics Education. Vol.5. 1-10 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] M.Koyama: "Research of the Complementarity of Intuition and Logical Thinking in the Process of Understanding Mathematics" Hiroshima Journal of Mathematics Education. Vol.5 Vol.42. 21-33 73-82 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Y.Miyamoto, M.Koyama, T.Nakahara et al.: "A Basic Study on Cognitive Processes of Mathematical Concepts (18)" The Annals of Educational Research, Joint Research System of Faculty of Education and Attached School of Hiroshima Univ.Vol.25. 85-93 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 今岡光範: "空間認識に関する発展的教材の内容学的考察" 全国数学教育学会誌 数学教育学研究. 第2巻. 115-120 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Tadao Nakahara: "Study of the Constructive Approach in Mathematics Education" Hiroshima Journal of Mathematics Education. Vol. 5. 1-10 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] Masataka Koyama: "Research on the Complementarity of Intuition and Logical Thinking in the Process of Understanding Mathematics" Hiroshima Journal of Mathematics Education. Vol. 5. 21-33 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 中原忠男: "数学的概念の認識過程についての基礎研究(XVIII)-構成的アプローチに基づく算数科授業の検討(2)-" 広島大学教育学部・関係附属学校園共同研究体制研究紀要. 第25号. 85-93 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 中原忠男: "小学校算数実践指導全集9 表現力を育てる式の指導" 日本教育図書センター, 255 (1995)

    • Related Report
      1996 Annual Research Report

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Published: 1995-04-01   Modified: 2016-04-21  

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