Lesson Study On High School Probability Based On Learning Difficulty Analysis

The result of "The study of difficult high school math concepts" which conducted by Ruan Xiaoming in Songjiang District,Shanghai,in 2012,shows that probability is one of the most difficult concepts in high school mathematics.Based on this result,this paper analyzed the difficulties in learning probability in high school.Then we developed a teaching design based on our analysis,and conducted a teaching-case study.This paper analyzed the difficulties of probability from three aspects:the logical structure,the historical development and the cognition process. The main difficulties in learning classical probability are:determining whether a stochastic event satisfy classic probability model,find out the number of elementary events in event A and all the number of elementary events included in the whole trial. When learning the frequency interpretation of probability the main difficulties are:the stability of the frequency,the consistency of the probability in classic probability model and the frenquency stability.In this study,for the above difficulties,we carry out two case classes:<17.1 Classic Probability Model> and<17.2 Frequency and Probability> in a senior high school in Shanghai.70 students in the experimental class take the posttest. This paper analyzed the effects of teaching activities and the mistakes students made in the test. It has been found that:1. The error rate of representativeness decreased after learning classical probability,that is to say teaching can help students to overcome this misconception.There are still two fifth students did not accurately understand the classical probability, most of the students can solve simple geometry probability problem,and be aware of the eaui-probability of the elementary event when using classic probability model. After learning the frequency interpretation of probability,more than half of the students undetstand the connotation of probability. The common mistake is "frequency is equal to probability","probability is the limiting value of frequency" and neglect the influence of the sample size".