The Ninth Grade Students’ Understanding On The Concept Of Variance

With the era of big data coming,statistics is everywhere in our daily life.Improving the statistical literacy of the whole people has become the purpose of popularizing probability and statistics education in all countries.Emphasizing statistical content and carrying out statistical teaching has become an inevitable trend of current social development.Variance is a very important index of variation in descriptive statistics,and it is also widely used in inferential statistics.Therefore,it is necessary to conduct an in-depth research on students’ understanding of the concept of variance.The research focuses on three main questions.First,how well do ninth graders understand the concept of variance and can they calculate the variance? Second,without calculating the variance,how well do students compare the size of the variance and what strategies do they use ? Third,what is the cognitive obstacles of ninth graders in understanding the concept of variance? In order to solve the above three research questions,four sets of test papers were designed and tested on 704 ninth-grade students from four middle schools in Guangzhou.The test 1 includes the literal definition of variance,examples of variance,formula and calculation of variance and simple life application of variance.Test 2,3,and 4 focus on the conceptual knowledge of variance,that is,to judge the variance of numerical classes,graph classes,and life situation classes and give reasons without calculating the variance.After the test,three types of students were selected for interview according to the test results.They are students who have both strong procedural and conceptual understanding of variance,students who have strong procedural understanding of variance but weak conceptual understanding of variance and students who have weak procedural understanding of variance but strong conceptual understanding of variance.Furthermore,from the interview results of students,two teachers were interviewed.The results show that students perform well in the procedural understanding of variance,and most students can calculate variance;Students are weak in conceptual understanding of variance,that is,when variance is not calculated,students are weak in judging the size of variance correctly.Students’ performance varies with the presentation of data.In the process of judgment,students’ ability to judge the variance by comprehensive use of strategies is weak.As to the concept of variance,students mainly has the following cognitive obstacles :(1)In the aspect of the verbal information obstacle,it is manifested as poor reading ability of the topic,weak mathematical representation ability,poor understanding ability of the figure,unclear expression of the other side’s poor conceptual knowledge and non-standard writing.(2)In terms of intellectual skills obstacle,they are unable to deeply understand the concept of variance and the fundamental characteristics of variance formula,weak ability to comprehensively consider various factors of variance size,confusion between old and new knowledge,and negative thinking set.(3)In the cognitive strategy obstacle,it is manifested as the weak metacognitive ability and the cognitive strategy can not transfer correctly.Finally,based on the analysis results of this research,suggestions are put forward on course content setting,teaching methods and evaluation content.