A Study On The Cognitive Development Of Sixth Grade Students From Arithmetic To Algebraic "variable" Thinking

The author conducted a survey which investigated the variate thinking recognition condition of 181 sixth grade students in Jimo District,Qingdao City by in virtue of professor Stephens' questionnaire.Through SOLO classification theory,this paper analyses the solving strategies of the sixth grade students to the arithmetic problems,and studies a series of questions such as whether they form variable thinking and to what extent they form variable thinking.The purpose is to get a knowledge of the development of variate thinking.The conclusion is as follows.1.The variate thinking of the students has specific performance.There are mainly three types of variate thinking in sixth grade students.When comparing the three types of subjects,students are more likely to use variate thinking on type II and type III instead of type I.There are significant differences between male and female students' thinking level,and in general,boys are more likely to construct variate thinking.2.The variate thinking of the students has specific features.They are capable of regarding equality sign as a connector,and mainly apply methods like regrouping,counteracting and dissembling to solve problems.They also pay more attention on the structure of the equation,but there are obvious difference on their focuses.Then,based on the students' error cases in the test paper,the author uses APOS theory to analyze the difficulties in students' construction of variable thinking.It is found that different students will encounter different difficulties in four aspects: activity operation,process reasoning,object understanding and schema construction.At last,Aiming at the conclusion of this study and the practical difficulties of students,the author gave suggestions on how to stimulate the development of students' variate thinking from teacher quality,instructional design,teaching process and Classroom examination.