条件概率的本质及其教学建议

Understanding the Meaning of the Conditional Probability and Its Teaching

概率是一个集合函数,是一种测度,用于度量随机事件发生的可能性的大小.概率采用公理化定义,条件概率也满足该定义,因此条件概率也是一种概率测度,条件概率是含参变量的集合函数,是概率的推广.采用质性研究方法,梳理近20年来高中一线教师撰写的概率教学文献,对存在的问题进行分类与归因,选择两篇代表性文献进行案例研究.研究发现,条件概率概念教学存在较多问题,问题出现的根本原因是一线教师对条件概率本质的理解存在欠缺.条件概率概念教学应当从概念的本质入手,借助正例反例与图形直观,讲清楚概念的内涵;解题教学应当从数学建模的理念入手,培养解题规范意识,掌握两种基本计算方法;高中数学要重视条件概率教学,展示概率理论的价值,激发学生学习概率知识的兴趣.

Probability is a set function;its essence is in measuring the chance of random events.The probability has been defined using axioms,so does conditional probability.Therefore,conditional probability is also a probability measure.Conditional probability is a set function with parameter variables.Using the qualitative research method,the literature on probability teaching written by inservice high school teachers in the past 20 years has been reviewed,the existing problems were classified and attributed,and two representative articles were selected for case study.Based on this research,it was found that there are many problems in the teaching of conditional probability.The rooted problems is that inservice teachers lack their understanding of the concept of conditional probability.Thus,teaching suggestions are as follows:The teaching of the concept should start from the essence of the concept,explaining clearly the connotation of the concept with the help of positive and negative examples and graphic intuition.The teaching of problem solving should start with the concept of mathematical modeling,cultivating the consciousness of problem-solving standardization,and mastery of two basic methods.High school mathematics should attach importance to the teaching of conditional probability,demonstrate the value of probability theory,and stimulate students’interest in learning probability knowledge.