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Practical Research on Improving Primary School Mathematics Lessons Based on the Two-Axes Process Model of Understanding Mathematics

Research Project

Project/Area Number 16530591
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 InstitutionHiroshima University

Principal Investigator

KOYAMA Masataka  Hiroshima University, Graduate School of Education, Associate Professor, 大学院教育学研究科, 助教授 (30186837)

Project Period (FY) 2004 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2005: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2004: ¥1,000,000 (Direct Cost: ¥1,000,000)
KeywordsUnderstanding Mathematics / Two-Axes Process Model / School Mathematics Education / Lesson Improvement / Practical Research / In-Service Teacher Education / Pre-Service Teacher Training
Research Abstract

As a result of this research, the followings are found out. First, the "two axes process model" of understanding mathematics can be embodied and used for improving primary school mathematics lessons as the teaching and learning mathematics in a classroom by analyzing mathematics curriculum and teaching materials. Second, we can identify and refine the three principles and three methods for designing lessons based on the "two-axes process model" of understanding mathematics;
Principle 1 [Understanding mathematics as a complex and dynamic process], Principle 2 [Setting up hierarchical levels and learning stages], Principle 3 [Emphasizing both activities of individual and social construction], Method 1 [Clarifying hierarchical levels of understanding], Method 2 [Assessing students' level of understanding], and Method 3 [Embodying learning stages]. Third, these principles and methods are used as effective guidelines for a teacher when he/she improving mathematics lessons in order to deepen his/her students' understanding of mathematical concepts, properties and relations through the long-going and intensive "lessen study" with teachers in a school. Fourth, the "two axes process model" of understanding mathematics and its principles and methods can be applicable in pre-service teacher training and in-service teacher education at primary school level for improving their mathematics lessons.

Report

(4 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (13 results)

All 2006 2005 2004

All Journal Article (13 results)

  • [Journal Article] 数学理解の2軸過程モデルに基づく授業構成の原理と方法2006

    • Author(s)
      小山 正孝
    • Journal Title

      日本教科教育学会誌 第28巻・第4号

      Pages: 61-70

    • NAID

      110008094594

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary 2005 Annual Research Report
  • [Journal Article] 数学学習における理解過程に関する研究 (I)2006

    • Author(s)
      小山 正孝
    • Journal Title

      全国数学教育学会誌 数学教育学研究 第12巻

      Pages: 71-81

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Principles and Methods for Designing Mathematics Lessons Based on the Two-Axes Process Model of Understanding Mathematics2006

    • Author(s)
      Masataka KOYAMA
    • Journal Title

      The Bulletin of Japanese Curriculum Research and Development Vol.28, No.4

      Pages: 61-70

    • NAID

      110008094594

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Research on the Process of Understanding in Learning Mathematics (I)2006

    • Author(s)
      Masataka KOYAMA
    • Journal Title

      Journal of JASME : Research in Mathematics Education Vol.12

      Pages: 71-81

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] 数学学習における理解過程に関する研究(I)2006

    • Author(s)
      小山 正孝
    • Journal Title

      全国数学教育学会誌 数学教育学研究 第12巻

      Pages: 71-81

    • Related Report
      2006 Annual Research Report
  • [Journal Article] 教科教育学の研究動向と展望-日本の数学教育学における近年の研究動向と展望-2005

    • Author(s)
      小山 正孝
    • Journal Title

      日本教科教育学会誌 第27巻・第4号

      Pages: 91-100

    • NAID

      110008094557

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Research on the Process of Understanding Mathematics : Ways of Finding the Sum of the Measure of Interior Angles in a Convex Polygon2005

    • Author(s)
      Koyama, Masataka
    • Journal Title

      Proceedings of the 29th PME Conference Vo1.1

      Pages: 253-253

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Trends and Prospects in Curriculum Research and Development : Recent Trends and Prospects in the Research on Mathematics Education in Japan2005

    • Author(s)
      Masataka KOYAMA
    • Journal Title

      The Bulletin of Japanese Curriculum Research and Development Vol.27, No.4

      Pages: 91-100

    • NAID

      110008094557

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Research on the Process of Understanding Mathematics : Ways of Finding the Sum of the Measure of Interior Angles in a Convex Polygon2005

    • Author(s)
      Masataka KOYAMA
    • Journal Title

      Proceedings of the 29th PME Conference Vol.1

      Pages: 253-253

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Research on the Process of Understanding Mathematics : Ways of Finding the Sum of the Measure of Interior Angles in a Convex Polygon2005

    • Author(s)
      Koyama, Masataka
    • Journal Title

      Proceedings of the 29th PME Conference Vol.1

      Pages: 253-253

    • Related Report
      2005 Annual Research Report
  • [Journal Article] 教科教育学の研究動向と展望-日本の数学教育学における近年の研究動向と展望-2005

    • Author(s)
      小山 正孝
    • Journal Title

      日本教科教育学会誌 第27巻・4号

      Pages: 91-100

    • NAID

      110008094557

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Research on the Process of Understanding Mathematics : The Inclusion Relation among Fractions, Decimals and Whole Numbers2004

    • Author(s)
      Koyama, Masataka
    • Journal Title

      Proceedings of the 28th PME Conference Vol.1

      Pages: 315-315

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary 2004 Annual Research Report
  • [Journal Article] Research on the Process of Understanding Mathematics : The Inclusion Relation among Fractions, Decimals and Whole Numbers2004

    • Author(s)
      Masataka KOYAMA
    • Journal Title

      Proceedings of the 28th PME Conference Vol.1

      Pages: 315-315

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary

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Published: 2004-04-01   Modified: 2016-04-21  

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