Restoration of Geometry in Secondary School Mathematics (IV)

筆者らはさきの3つの報告において,「総合的」あるいは「統合的」と称されている学校幾何の課程について,いくつかの注目すべきプロジェクトを採り上げて,それらの分析と検討を試みてきた。本報においては,これまでに採り上げたプロジェクトを比較対照するとともに,それらに関連した主要課題についてのその他の論考にも触れることによって,幾何教育の復権の可能性もしくは蓋然性と,そのたどるべき方向を考察する。In their previous papers the authors have tried to give detailed analyses to some of the distinguished projects of geometry course in secondary schools which are now called to be "comprehensive" or "unified", i.e., the USSR program, W. Servais' textbooks "Mathématique" and SSMCIS' textbooks "Unified Modern Mathematics". In the present paper the authors try to make a confrontation of the projects previously analysed and to refer to the relevant problems. Every project we consider here suggests that the geometry course in secondary schools should be organized by the following leading ideas: 1) the use of geometric transformations (symmetries or pararell projections) 2) synthetic structuring of geometry based on the transformations 3) construction of two (and three) dimensional vector spaces with inner products. It should be pointed out that, although these leading ideas could not satisfactorily realised in those projects, quite plausively in near future pedagogical efforts, both in theory and in practise, will find the links between the leading ideas and the deficiencies now available