幾何教育の復権(第3報)

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前報にひきつづき本報では,アメリカのH.F.Fehrを代表者とするSSMCISによる「Unified Modern Mathematics」1～6の幾何について分析と検討を試みる.以下においては,次の諸点について考察を加える.(1) Unified Modern Mathematicsにおける"unified"(2)どのような幾何学像を期待するか(3)実数系と数直線の構成What to teach in the geometry course has been, and is now, one of the most crucial and frequently controversial issues in the teaching of secondary school mathematics. There have been, however, developed several noticeable projects, in which it would be expected to get over the existing obstacles of school geometry and to improve the present situation, resulting in the "comprehensive" teaching of geometry. In their previous papers the authors have tried to analize and evaluate some of those projects in detail along with our geometry program authorized by the Ministry of Education. One of them is the USSR geometry program implemented in 1970 and the other is the project in Belgium devised by W.Servais and his collaborators, being materiarized in their text-books "Mathématique 1, 2 et 3". In the present paper here is under close consideration the treatment of geomentry revealed in the text books "Unified Modern Mathematics 1-6" written by SSMCIS team. The SSMCIS text-books as well as the W.Servais' aims at uniflying all the school mathematics, via the basic concepts of sets, relations, mappings, and operations, on which are built up such fundamental structures as groups, rings, fields and vector spaces. We can, however, single out an essentially different feature between their treatment of geomentry. While W.Servais chooses the unique approach, begining from the structure of affine plane, via the metric plane, arriving at the structure of 2-3 dimensional Euclidean vector space, H.F.Fehr chooses various approaches which he calls 'eclectic'. He intends to include, not a unique geometry, but various geometries, and thereafter he expects that the geometries would be integrated into a unified body of secondary school mathematics. When we consider about the present situation of school geometry in USA, these text-books aim at an overall and radical revision of the traditional course, especially by abandoning substantially the usual treatment of the deductive synthetic geometry. In the present paper the authors try to give a detailed analysis, in comparison with the USSR program and the text-books by W.Servais and his collaborators, on the treatment of geomerty in the SSMCIS text-books, i.e., 1) Which geometric approaches are used and how are they developed eclecticly informal or/and formal levels? 2) By these eclectic approaches what conception of the geometrical space do we expect pupils to formulate and where can we find the pedagogical significance of it? 3) How successfully would be rearised their claim that various geometries would be integrated into the unified body of secondary school mathematics? Especially in this view point the treatment of geometric transformations, the construction of vector spaces, and the construction of the real number system and the number line should be examined carefully.
大阪教育大学の論文

幾何教育の復権(第3報)

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