反例在中学数学教学中使用情况的调查研究

Investigation and Study of the Usage of Mathematical Counter Examples in Mathematics Teaching

反例在数学中占着较为特殊的地位,尤其在新课标中对反例做出了相关建议,在各种考试也考察了对反例的构造能力.然而,目前数学反例的使用中主要存在以下几个问题：教师自身对数学反例的了解不深刻,缺乏良好的数学反例的教学观;教师没有掌握构造反例的方法,不能系统地教给学生反例的思维;教师获取反例的途径很多,但最主要的途径是从教材及教材参考书和自己的经验所得,很少自己主动去从其它渠道获取;大部分的教师都是在平时教学过程中适当地穿插使用反例.

Mathematical counter examples occupy a special position in teaching; especially these are relevant recommendations about counter examples in the new curriculum standard. As well as in the various examinations it examines the capacity of structuring counter example. However, the current mathematics counter-example usage mainly has the following problems： Teachers know a little about mathematical counter examples and are lack of good mathematics counter-example teaching view; Teachers do not have the capacity of structuring counter example, and can not systematically teach students reverse thinking; Teachers get counter examples most from the teaching materials and their own experience, but rarely from other channels; most of the teachers use counter examples in teaching.