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The role of conjectures on teaching geometry with computer

Research Project

Project/Area Number 03045015
Research Category

Grant-in-Aid for international Scientific Research

Allocation TypeSingle-year Grants
SectionUniversity-to-University Cooperative Research
Research InstitutionUniversity of Tsukuba

Principal Investigator

NOHDA Nobuhiko  University of Tsukuba, Institute of Education, 教育学系, 教授 (80020121)

Co-Investigator(Kenkyū-buntansha) C. Laborde  グルノーブル大学, LSD, 助教授
J. Laborde  グルノーブル大学, LSD, センター長
N. Balacheff  グルノーブル大学, INP, 教授
HIGASIBARA Yoshinori  University of Tsukuba, Information Science and Electronics, 電情学系, 助手 (90143172)
SHIMIZU Shizumi  University of Tsukuba, Institute of Education, 教育学系, 助教授 (20115661)
NAKAYAMA Kazuhiko  University of Tsukuba, Information Science and Electronics, 電情学系, 教授 (50091913)
BALACHEFF Nicolas  University of Grenoble 1, INP
LABORDE Collette  University of Grenoble 1, LSD
LABORDE Marie  University of Grenoble 1, LSD
LABORDE C.  Crenoble大学, 数理学部, 助教授
LABORDE J.  Grenoble大学, 数理科学, 教育センター長
BALACHEFF N.  Grenoble大学, 数理学部, 教授
Project Period (FY) 1991 – 1992
Project Status Completed (Fiscal Year 1992)
Budget Amount *help
¥3,800,000 (Direct Cost: ¥3,800,000)
Fiscal Year 1992: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1991: ¥2,000,000 (Direct Cost: ¥2,000,000)
KeywordsComputer / Cabri-Geomitry / conjecture / Inference / proof / Mathematics / Education / カブリ・ジオメトリ-
Research Abstract

The group met during three two hours time-slots in addition to the time-slots scheduled in the program.
The common aim of the group is to discover the conditions which lead to conjectural activity for pupils, to study the relationship between the types of conjectures and mathematical contents and environments(with or without a computer), and finally to analyze the possible production of proofs. One of the main targets of the work is a point analysis of the production of conjectures and of problem solving strategies of both French and Japanese pupils.
The cultural benefit of this research lies in the fact that it is likely to demonstrate fundamental differences in the way mathematics is approached in both countries. Indeed, phenomena related to problems of validations are significant indicators of the ways scientific activity and mathematics as a discipline are considered in both countries whether as didactical objects or as cultural objects. In particular. the notion of contradiction does not have a priori the same status for a French subject as for a Japanese subject, In particular as it appears in social interaction.
The starting point consists of three experimental research activities already carried out in Japan and in France. These research activities are briefly described here :
(i) an analysis of the processes of proofs and refutations on the part of French pupils and Japanese pupils, repeating in its main features the study already done in Grenoble (Balacheff's work on polygones). We propose to analyze and to compare, in particular, the ways pupils treat counter-examples ;
(ii) an analysis of the effect of a computerized environment on the problem-solving strategies of French and Japanese pupils. This comparison of the effects of a paper and pencil environment with the effects of a computer environment is performed in the case of situations in Which Thales theorem plays a crucial role (Gallou's work) ;

Report

(2 results)
  • 1992 Final Research Report Summary
  • 1991 Annual Research Report
  • Research Products

    (8 results)

All Other

All Publications (8 results)

  • [Publications] NOHDA N.: "Study of problem-solving with CABRI-geometre in secondary shool" Tsukuba:Institute of Education.1-13 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Balacheff N.: "Une etude des processus de preuve en mathematiques chez des eleves de College.These de doctorat detat." Grenoble Univ.1-18 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] K.NAKAYAMA: "Procedure Definition and Higher-Order Programming in HyperLOGO." Computers and Education. 17. 1-4 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Nohda N.: "Study of problem-solving with CABRI-geometre in secondary shool" Tsukuba : Institute of Education.1-13 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] Balacheff N.: "Une etude des processus de preuve en mathematiques chez des eleves de College. These de doctorat d'etat." Grenoble Univ.1-18 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] K, Nakayama: "Procedure Definition and Higher-Order Programming in Hyper LOGO.Computers and" Education. 17. 1-4 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1992 Final Research Report Summary
  • [Publications] 垣花 京子: "新しい幾何学習環境としての‘GeoーWorld'" 筑波数学教育研究. 11. 63-72 (1992)

    • Related Report
      1991 Annual Research Report
  • [Publications] 山本 泰嗣: "コンピュ-タによる図形環境における中学生の数学学習活動に関する研究" 筑波数学教育研究. 11. 82-91 (1992)

    • Related Report
      1991 Annual Research Report

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Published: 1991-04-01   Modified: 2016-04-21  

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