A Cognitive Study Of High School Students' Understanding Of Correlation

In " Mathematics Curriculum standards for the General Senior High School (Experimental)", which is published in 2003, Chinese Ministry of Education changed statistics from the previous optional content to compulsory elective one. Statistics was classified as the basic knowledge of mathematics in senior high, and data processing a basic mathematical ability. To many high school teachers who teach statistics firstly, it is of great challenge.As teaching should be based on the students, this article aims at investigating high school students on their understanding of correlation. Researches are carried out based on such study specific issues: firstly, what are the different recognition situations between the students who have learned and those who have not learned the correlation when they are learning seeking various methods of linear regression? Secondly, for those who have learned the correlation, what's the different recognition situations upon association and regression equation? Is there any difficulties? Thirdly, does the real-life background of the students have any effect on their answers?This study is concerned with the understanding of the high school students upon correlation, based on the survey of 106 students in senior 1 who have not learned the correlation and 172 students in senior 2 and 3 who have learned it, following conclusions are drawn: (1) The historical parallelism does exist when high school students are making the linear regression equation, but the method that making the line according to a transparent ruler whose edge keeps moving among the spots until it can cover all or most of the spots is recognized best by the students that are tested ;(2) Senior high students need to improve the level of awareness on linear regression;(3) Students do better in Descriptive Titles than Analytical and digital ones.(4) High school students often misinterpreted correlation and extended it as a causal connection relationship, many students did not know that if it is a linear relationship we can use the correlation coefficient.(5) Students' undersanding of direction and strength are not satisfied, especially for median correlation and negative correlation.(6) A real-life background does good to students' understanding.Based on the conclusions of this study, the author provided thefollowing recommendations on the teaching of correlation:(1) Teach the method of least square based on the historical parallelism of students when they are making Linear regression equation;(2) The teaching of correlation should highlight the association between the direction and strength, emphasize the condition of the correlation coefficient ,and help students distinguish correlation and causation; (3) Teaching should be combined with the specific situations, and use information technology to help students understand.