Joint Research on Space Recognition and Teaching Geometry in France and Japan.

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Our research program is concerned with joint research on space recognition and teaching geometry in France and Japan. Its goal is to bring to light the influences of schooling and culture on the learning of geometry.The themes discussed were the following :Theme I : The role of conjectures in problemーsolving in geometryTheme II : Aspects of the language used in the teaching of geometryTheme III : Mastery of macroーspaceTheme IV : The role of graphic representations in the modeling of physical spaceFrenchーJapanese cooperative research program on the didactics of mathematics was begun in 1988. And the first meeting was held to discuss the above themes in the autumn 1989 in both Tukuba and Tokyo, Japan.The second meeting was held March 25th to 29th, 1991 at University of Grenoble 1 in France. There were nine Japanese participants and approximately twenty French participants.The group working on individual themes have reached various levels of progress. Theme 2 is ready for the final publication of its results.The French side of the cooperative research program intends to prepare a book on "Mastering space and learning geometry" until end of 1991.