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本文主要是討論幾何教本教材編排上的幾個問題。根據個人的感覺、和數學教師們交談的結果,對格拉哥列夫教授改變吉西略夫第二部教本的教材,一致認為在教學法的觀點上,是不够正確的。第一章(空間的直線和平面)的教材內容有些改變,吉西略夫的舊版本以及達維多夫,格伯爾,拉舍夫斯基等的教本,都把第一章分為四節命名如下: 1) 平面位置的確定, 2) 平面的垂線和斜線, 3) 平行的直線和平面, 4) 二面角和多面角, 教材这樣的編排,是完全合乎由易到難的原则,學習“平面的垂線和斜組”的定理此學習“平行直線與平面”的定理困難要少些,平行直線与平面的定理,常用反證法證明,大家知道這是一種較直接證法難以使學生接受的證法。
This article mainly discusses several problems in the layout of textbooks for geometry textbooks. According to personal feelings and the results of conversations with mathematics teachers, Professor Glagorev has changed teaching materials for the second textbook of Gysyllove, and he is unanimously of the view that the teaching method is not correct enough. The contents of the first chapter (straight lines and planes of space) are somewhat changed. The old version of Ghiglilfoy and the textbooks of Davydov, Geber, Lashevski, etc. all divide chapter one into four. Sections are named as follows: 1) Determination of plane position, 2) Plane’s vertical and oblique lines, 3) Parallel lines and planes, 4) Dihedral angles and polyhedral angles. The layout of textbooks is completely in conformity with difficulty. Principles, learning the theorem of the “perpendicular and oblique groups of planes” The study of the theories of “parallel lines and planes” is less difficult. The theorem of parallel lines and planes is often proved by counter-evidence methods. Everyone knows that this is a more direct proof that it is difficult to make Student acceptance of the proof.