中学数学变式教学探究

论文总字数：10572字

摘 要

自上海青浦实验以来，顾泠沅先生将传统的概念性变式推广到动态的教学之中，进而提出了过程性变式的概念，使得中国的数学变式教学得以立足于更高的理论台阶．本文以概念性变式与过程性变式在课堂教学中的应用为例，阐述了变式教学在数学教学改革中的重要地位．

关键词：变式教学，概念性变式，过程性变式，问题变式

Abstract：Since Shanghai qingpu experiment, Mr Gu lingyuan will expand the traditional conceptual variant to the dynamic teaching, and then puts forward the concept of process variations, variations of mathematics teaching to base on the theory of higher level. Based on conceptual change type and procedural type application in classroom teaching as an example, this paper expounds the variable type teaching in the important position in the mathematics teaching reform.

Keywords：variant teaching， conceptual variant， procedural variant， problematic variant

目 录

1 引言··················································································4

2 变式教学的形成···································································4

2.1 变式教学形成的原因·························································4

2.2 变式教学的本土特征·························································5

3 变式教学的相关理论····························································5

3.1 变式教学的心理学依据······················································6

3.2 概念性变式与过程性变式···················································6

4 变式教学的课堂呈现···························································7

4.1 基本概念的变式······························································7

4.2 数学命题的变式······························································8

4.3 数学语义的变式······························································9

4.4 图形图像的变式······························································10

5 数学解题教学中的变式························································11

5.1 一题多变·······································································11

5.2 一题多解·······································································11

5.3 一法多用·······································································13

6 变式教学的反思·································································14

6.1 变式教学的意义······························································14

6.2 变式教学中应注意的问题··················································15

结论·····················································································16

参考文献···············································································17

致谢·····················································································18

1 引言

近几十年来，中国学生在国际数学奥林匹克中屡屡取得优异成绩；在国际数学教育成就调查中，中国中小学生的数学成绩也明显优于西方学生．但是，也有西方研究者的调查与研究认为：“中国学习者”的数学学习环境存在着许多缺陷，尤其在教学方式上，属于典型的“被动灌输”和“机械训练”．例如，金斯伯格（Ginsberg）对中国教学的调查研究认为，中国教学是教师主导的被动灌输式教学，教学是“一个受尊敬的长者传输知识给处于服从地位的年少者”，进而认为中国的数学教学不具有先进性^[1]．

这两种矛盾的现象构成了所谓的“中国学习者悖论”，并一度成为国际比较教育研究的热点．什么是“悖论”的合理解释呢？许多西方学者开始重新审视中国的数学教学，致力于从深层次去揭示中国数学教学的一些有价值的成分，他们发现中国的数学教师经常使用一种特殊的教学方式——变式教学．

2 变式教学的形成

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