中学数学部分概率内容的问题与建议

Teaching Discussion on Some Concepts in Probability Theory for Middle School

针对中学概率论中部分重要概念以及教学中常见的问题展开讨论,从历史发展的角度出发指出,教材最好先系统介绍概率论,在此基础上再介绍统计.应该明确基本事件与随机事件之间的关系,随机变量概念的定义适宜严格化,特别是不适合将随机变量与函数做类比,前者是随机现象的量化表示,是一个数学化过程,后者是不同确定性事件量化后的数量关系,两者不属于同一个范畴,随机变量的合适类比对象是确定性变量.同时指出,随机思想、随机方法是概率教学价值的两个重要方面.此外,对教材中出现的一些疏忽提出了一些建设性意见,并指出有必要将分布函数引入中学课堂.

This paper discussed some important concepts in the probability theory of middle school and the common problems in teaching. From the perspective of historical development, the article pointed out that the textbook should first systematically introduce the theory of probability, and on the basis of this, the statistics was introduced. The relationship between basic events and random events should be clarified, and the definition of the concept of the random variables should be strict. Especially, it was not suitable for the analogy between random variables and functions. The former was a quantitative representation of random phenomena, it was a mathematical process, the latter was the quantitative relationship after the quantification of different deterministic events. The two concepts were not in the same category, and the appropriate analogy of random variables was the deterministic variable. Meanwhile, it was pointed out that random thought and stochastic method were two important aspects of probability teaching value. In addition, some constructive suggestions for some carelessness in teaching materials were put forward, and it is pointed out that it was necessary to introduce distribution function into middle school classroom.