1992 Fiscal Year Final Research Report Summary
The role of conjectures on teaching geometry with computer
| Project/Area Number |
03045015
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| Research Category |
Grant-in-Aid for international Scientific Research
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| Allocation Type | Single-year Grants |
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| Section | University-to-University Cooperative Research |
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| Research Institution | University of Tsukuba |
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Principal Investigator |
NOHDA Nobuhiko University of Tsukuba, Institute of Education, 教育学系, 教授 (80020121)
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| 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
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| Project Period (FY) |
1991 – 1992
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| Keywords | Computer / Cabri-Geomitry / conjecture / Inference / proof / Mathematics / Education |
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| 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) ;
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Research Products
(6 results)
