20CE 中学数学教育 (陈建功)

20世纪(1950s -1970s)的中国数学教育改革是迎合WW2 战后工业化, 影响我们中学数学 Secondary School Math (13-18 岁) 。

21世纪 (2000s – 2030s) 迎合的是 工业 4.0 (AI, Big Data, IoT, Fintech… ),中学数学改革 是什么呢?



陈建功 (1893-1971) 和 师弟 苏步青是二战前 留学日本派的数学教育家 (微分几何),建立浙江大学和复旦大学数学系 – 与 陈省身 的 留法/德/美 “南开”派,华罗庚的留英/俄 “清华” 派 三派鼎立,融合成特有的 中国数学派 。

https://m.toutiaocdn.com/group/6771961322671178247/?app=news_article_lite&timestamp=1576803223&req_id=201912200853420100140400930DC57A0B&group_id=6771961322671178247

这三本数学(中三/中四)书是我们 70s年代 新加坡华文中学的课本 (文言文) :

Note [*]: Henry Fine was the Founder of the Princeton Institute of Advanced Study (IAS) , who hired the first professor  – Albert Einstein.

]This 《葛氏平面三角》(Granville Trigonometry) text book was arcane and translated in ‘old’ Chinese (文言文).


德国 Gottingen 学派 Felix Klein 引入 Function (函数) 进 中学(Secondary 3)数学主题 (main theme) :


Jewish / French Math vs German Math

The French “Bourbaki” School of Abstract Math (based on Set Theory as Foundation of ALL Math) influenced the post-WW2 French University Math Syllabus and 1970s Baccalaureate (High School) Math, led by the French Jewish Mathematicians Andre Weil et al, and (last batch) Jewish mathematician Grothendieck (who once proposed – but rejected – Category Theory to replace Set Theory) .

The leaders of the German ‘Gottingen School’ of Mathematicians, although learned from the French school masters (French Charles Hermite’s German student Lindemann, French Camille Jordan’s German student  Felix Klein), were more inclined to concrete math, eg. Gauss, Riemann, Hilbert, Dedekind, Noether, etc.


….

中国的中学数学教育:为了删掉抽象 (Abstract)概念,却同时也丢掉 "近代数学" (Modern Math)。可惜!

改革提议]:应该学习 法国中学数学(16 -18岁) 一部分 Modern Math 教材:
  1. 基本代数结构 Basic Algebraic Structures: Group 群, Ring 环, Fields 域, Vector Space 向量空间.
  2. Analysis 分析: Epsilon-Delta Calculus.
  3. Affine Geometry 仿射几何
  4. 减少一些老旧的中国数学教材(立体几何,复杂的 Trigonometry, … ),减轻学生负担。

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