The Investigation Of The High School Students' Understanding Of Mathematical Expectation

Mathematical expectation is one of the most important numerical characteristics.It is an indicator to depict the average level of the value of random variables.Its clear intuitive meaning and good mathematical properties make it always occupy an important position in probability theory.In this paper,three content dimensions are selected to explore high school students' understanding of discrete random variable mathematical expectations from the aspect of content,namely memory,explanatory understanding and exploratory understanding.According to the three dimensions,the following questions are mainly studied: 1.Discuss the basic status quo and level of high school students' understanding of mathematics expectation;2.Combined with students' specific answers,analyze the typical mistakes and difficulties in students' understanding of mathematical expectations statistically.3.Give specific Suggestions for the teaching of mathematics expectations.The main tool of this study is the test paper on mathematical expectation understanding.This study selects 4 senior high school students from science classes of different levels in Taiyuan No.5 Middle School as the research objects and conducts a test investigation on them.A total of 200 questionnaires were sent out and 168 valid questionnaires were collected,with an effective rate of 84%.After the test question was recovered,Excel and SPSS were mainly used for data analysis,descriptive statistics,Mann-Whitney U test,Spearman rank correlation test and cluster analysis.Based on the test results,the following conclusions can be drawn:1)The vast majority of students correctly memorized the calculation method and properties of expectation,but did not perform well in expressing(summarizing)the mathematical expectation concept itself.Students performed poorly in understanding the meaning of mathematical expectations and the relationship between mathematical expectations and sample mean values.The main performance is: do not know the meaning of mathematical expectation completely;The expected value is understood as the value with the highest probability of occurrence in the actual experiment;Think of the expected value as the value that the random variable tends to take after many trials.In practical open problems,students' awareness of using mathematics expectations is weak.2)There was no significant difference between male and female students in understanding the concept of mathematical expectations.3)There is no significant correlation between memory and interpretive understanding;There is a positive correlation between interpretive understanding and exploratory understanding.4)All students' understanding of mathematical expectations is divided into three levels.There is not much difference in the memory performance of the concept of mathematical expectations in each level,but there is significant difference in explanatory understanding and exploratory understanding.Based on the results of the research,targeted Suggestions are put forward for daily teaching to help students overcome difficulties in understanding and improve their understanding level,including: 1)To strengthen the explanation and analysis of concepts;2)Understand the meaning of concepts in practical situations;3)Exercise the ability to use concepts in complex classical problems;4)Correct errors through questions and counter examples.