香港与上海数学课堂中的论证比较——验证还是证明

Justification in Mathematics Classroom in Hong Kong and Shanghai——Verification or Proof

由于教育技术的广泛使用,对证明的处理重新成为课程关注的热点.中国香港地区和上海地区教师对证明的处理有许多不同之处.香港课堂中,处理定理的主要方式是通过直观或具体的活动来确认定理的真实性,而上海教师至少介绍一种数学证明,而且四分之三多的教师介绍2种以上数学证明方法.上海教师比香港教师更加紧扣教材,而香港教师使用的教材可以是不同的.香港教师总是将探索问题的过程或证明的步骤程序化,不利于学生探索能力的培养,在这一点上上海教师的做法值得借鉴.

Through fine-grained analysis of eight Hong Kong lessons and eleven Shanghai lessons, in which Pythagoras?theorem was dealt with, it was found that the approach to justification of the theorem in Hong Kong is diverse while that in Shanghai is quite unified. In Hong Kong, the theorem was basically verified by visual and concrete manipulation and in Shanghai, the theorem was unanimously mathematical proved. Finally, the implication of the findings to the implementation of the new curriculum was discussed.