A Case Study Of Primary School Students' Arithmetic Thinking And Algebra Thinking Transformation

The basic object of arithmetic is a number,and the basic object of algebra has a more general symbol in addition to the number.The transition of students from arithmetic to algebra is not only the renewal of knowledge content as it seems on the surface,but also the transformation of internal cognitive structures.It is a leap from arithmetic thinking to algebraic thinking.The sixth grade happens to be a transition period from elementary school to junior high school,and the applied topic teaching in the sixth grade is not only the development of the applied topic in the senior grade of elementary school,but also the thinking pad for the student to study the algebraic relationship in the seventh grade.Therefore,the author studies the transformation of the sixth grade students from arithmetic thinking to algebraic thinking with the application topic teaching as the carrier.Combining the data,the author mainly analyzes the development of students from arithmetic thinking to algebraic thinking from the following three dimensions:(1)Analyze and classify all the mistakes of middle school students in the research data.Then,the paper combines the literature research to find out the cognitive errors and the causes of the mistakes.(2)Combining data to describe the transition from arithmetic thinking to algebraic thinking,it is hoped that educators will pay attention to this stage.(3)Analyze which strategies of teachers can help students transition from arithmetic thinking to algebraic thinking smoothly.There are 13 kinds of common cognitive errors in students during the stage of thinking transition,among which the influence of arithmetic thinking on the application of algebraic problems is:persistence in arithmetic methods;Only focus on the solution of the equation and ignore the final answer to the problem;There are difficulties in taking procedural operations as part of the answer;The understanding of equal signs is difficult;Use arithmetic to calculate the answer to assign the unknown;The influence of arithmetic reverse thinking on finding equal relationship;Misunderstanding of parallel symbols;List algebraic equations that contain unknowns instead of equations.In the process of thinking transition,the reasons why students rely on arithmetic thinking are as follows:the application of the problem structure is simple;Its own mathematical foundation is weak;The ability of arithmetic reverse thinking is strong.Students are often separated from arithmetic and algebra by mastering the form of algebraic method solutions without understanding the nature of algebraic thinking,such as the understanding of "1" in the "set 1 method." For certain specific types of topics,its mathematical relationship is a fixed formula or line segment diagram,and these formulas and line segment diagrams are often used by students as the"prototype" of the equation.Therefore,students 'transition from arithmetic thinking to algebraic thinking is mainly based on formulas and schemata.On the question of whether to choose "arithmetic method" or "algebra method",the more skilled the student's own arithmetic thinking is,the less willing he is to use algebra to solve problems;From the point of view of the type of problem,students are more willing to choose algebra to solve the problem of fixed equal relationship.Combined with literature analysis and data analysis,the author believes that the following strategies of teachers can help students to transition smoothly from arithmetic thinking to algebraic thinking in the application of topic learning.(1)We pay attention to cultivating students 'ability to analyze "equal relationship".(2)Pay more attention to the cultivation of students 'ability to express themselves.(3)In the teaching of applied questions,both arithmetic and algebraic methods are used to guide students to discover the differences between the two methods in order to better understand the superiority of algebraic thinking.