Cognitive Survey On Junior Middle School Students' Understanding Model Of Average

The statistical concept has become a universally applicable and quite powerful way of thinking in the information society,and statistical knowledge has become an essential quality of modern citizens.The "Mathematics Curriculum Standard for Compulsory Education(2011 Version)" states that in the study of "statistics and probability," it is very important to help students establish the concept of data analysis.The average is a basic concept in statistics.Understanding its meaning and role is an important part of data analysis and the basis for statistical inference.According to the Senior High School Entrance Examination of Hebei Province in the past ten years,the average has been examined almost every year.However,statistics has entered China for not a long time,teachers have not enough deep understanding of average,and there are few studies on average in China.So what is the perception of average among middle school students in China? What are the difficulties in studying average? These are issues that deserve attention and research.Based on literature reading(Jinfa Cai,2002),this thesis determines three models of understanding average: understanding of procedural algorithmic meaning,conceptual understanding of algorithmic meaning,and conceptual understanding of statistical meaning.These three models are integrated into problems of specific context.Through the test questionnaire and interview,223 third-year middle school students at three different levels in Shijiazhuang H Middle School were investigated and studied.The author mainly studies from the following four questions: first,the overall picture of the three understanding models of the average by these students;second,the types of cognitive errors of the three understanding models of the average by these students;third,the cause of the error;fourth,if there are different performances of students based on different levels and genders.The following conclusions are reached through research:(1)The middle school students' conceptual understanding of the statistical significance of the average is significantly lower than the procedural understanding of algorithmic meaning and the conceptual understanding of algorithmic meaning.(2)There are three types of cognition errors of middle school students on the three models of understanding of the average: conceptual understanding errors,question analysis errors,and calculation errors.(3)Causes of cognitive errors:(1)conceptual misunderstandings.On the one hand,students are limited by cognitive level and lack of understanding of the concept essence;on the other hand,students' understanding of the average only focuses on the meaning of the algorithm and ignores statistical significance;(2)question analysis is wrong,because the students' reading ability is weak and the ability to extract information from questions needs to be improved;(3)calculation is wrong,and reasons include lack of attention and students' fear of calculating too much data.(4)Research conclusions about differences.Both the total score and the average score of the girls in each model are slightly higher than boys,and the standard deviation is smaller,but there is no significant difference between students of different genders.There are significant differences among total scores of students at different levels,but under the procedural understanding model of the meaning of the average algorithm,there is no significant difference among students at different levels.Based on the research conclusions,the author puts forward the following suggestions on teaching average:(1)teachers should focus on the understanding of the statistical significance of average;(2)in the teaching of average,teachers should pay attention to the analysis of the key points in concepts,and guide students to grasp the connotation and extension of concepts;(3)set practical questions close to the life of students in teaching,and allow students to experience data collation and the process of analysis;(4)in the teaching of average,teachers should guide students to experience the difference between statistics and mathematics,and cultivate their statistical thinking.The article provides with an instructional design on conceptual understanding of the statistical significance of the average.