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Semiotic and cognitive research on social interaction in the process of mathematical generalization

Research Project

Project/Area Number 16530602
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 InstitutionFukuoka University of Education

Principal Investigator

YAMAGUCHI Takeshi  Fukuoka University of Education, Faculty of Education, Associate Professor, 教育学部, 助教授 (60239895)

Co-Investigator(Kenkyū-buntansha) YAMASHITA Akira  Fukuoka University of Education, Faculty of Education, Professor, 教育学部, 教授 (60036910)
IIDA Shinji  Fukuoka University of Education, Faculty of Education, Professor, 教育学部, 教授 (20184351)
SHIMIZU Norihiro  Fukuoka University of Education, Faculty of Education, Associate Professor, 教育学部, 助教授 (50284451)
IWASAKI Hideki  Hiroshima University, Graduate School of Education, Professor, 大学院教育学研究科, 教授 (50116539)
BABA Takuya  Hiroshima University, Graduate School for International Development and Cooperation, Associate Professor, 大学院国際協力研究科, 助教授 (00335720)
Project Period (FY) 2004 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2005: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2004: ¥1,500,000 (Direct Cost: ¥1,500,000)
Keywordsmathematical generalization / social interaction / intentional generalization / extensional generalization / separation model / division with fractions / teaching units / subtraction with negative numbers / 分数のわり算 / スター・パターン
Research Abstract

Regarding to the first research, we introduced "synectics" by Gordon, W. to clarify the substantial difference between extensional and intensional generalization from the angle of cognition although DOrfler distinguished them logically. The definition of those terms has the following predicates. The former is to make the familiar strange in addition to its logical sense of enlargement of the extent of a set. It gives us the new point for integration of various pieces of old knowledge by making the familiar strange as a consequence. On the other hand, the latter is to make the strange familiar in addition to its logical sense of elaboration of the properties of objects. We proposed "separation model" which has both extensional generalization and intensional generalization as the alternative of two cognitive processes just after "symbols as object" in Dorfler's generalization model.
Regarding to the second research, we focused on difficulties of division with fractions. The cause of this difference could be explained as qualitative difference of generalization after "symbols as objects" in terms of separation model. We designed an alternative teaching of division with fractions for extensional generalization, which could induce the transition from arithmetic to mathematics. The teaching experiment based on it was practiced for the sixth graders in this research. It showed us not only the effectiveness of an alternative teaching but also the cognitive process in the separation model.
The third research was to elaborate a theory of Wittmann's "Teaching Units (TU)" in terms of our separation model. We complemented TU diachronically by incorporating his theory into separation model. The fourth research was to consider current teaching way of "subtraction with negative numbers" critically in terms of our separation model to develop a teaching material for transition from arithmetic to algebra.

Report

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

    (7 results)

All 2006 2005

All Journal Article (7 results)

  • [Journal Article] 学としての数学教育研究の展開2006

    • Author(s)
      岩崎秀樹
    • Journal Title

      数学教育学論究 85

      Pages: 3-21

    • NAID

      110004718650

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] The development of mathematics education as a scientific discipline2006

    • Author(s)
      Hideki Iwasaki, Toshiyuki Nakano
    • Journal Title

      Journal of Japan Society of Mathematical Education : Research Journal of Mathematical Education 85

      Pages: 3-21

    • NAID

      110004718650

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] 学としての数学教育研究の展開2006

    • Author(s)
      岩崎 秀樹
    • Journal Title

      数学教育学論究 85

      Pages: 3-21

    • NAID

      110004718650

    • Related Report
      2006 Annual Research Report
  • [Journal Article] 一般化分岐モデルに基づく分数除の教授・学習に関する研究2005

    • Author(s)
      山口武志
    • Journal Title

      数学教育学論究 84

      Pages: 3-25

    • NAID

      10016160902

    • 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] 一般化分岐モデルに基づく教授単元の計画・実施・評価に関する研究2005

    • Author(s)
      岩崎秀樹
    • Journal Title

      科学教育研究 29・2

      Pages: 133-145

    • 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] Research on teaching and learning of division with fractions based on the separation model of generalization2005

    • Author(s)
      Takeshi Yamaguchi, Hideki Iwasaki
    • Journal Title

      Journal of Japan Society of Mathematical Education : Research Journal of Mathematical Education 84

      Pages: 3-25

    • NAID

      10016160902

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Design and practice and evaluation of teaching units : Research based on the separation model of generalization2005

    • Author(s)
      Hideki Iwasaki, Takeshi Yamaguchi
    • Journal Title

      Journal of Science Education in Japan 29(2)

      Pages: 133-145

    • NAID

      110002705995

    • 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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