An Investigation Of Elementary And Middle School Students’ Understanding Of The Concept Of Equal Sign

The transition from arithmetic to algebraic thinking is a critical period from elementary to middle school,and there are many factors that affect the development of students’ algebraic thinking.In this paper,the level of students’ understanding of the concept of the equal sign in the fifth and seventh grades is selected as the object of investigation,and the questions to be addressed are as follows:What are the characteristics and levels of understanding of the concept of the equal sign among fifth and seventh graders?Are there any differences in the characteristics and levels of students’ understanding of the concept of the equal sign across grade levels?If there are differences,what are the factors associated with the differences?Is there a correlation between students’ level of understanding of the concept of the equal sign and their level of algebraic thinking?In the study,a mixed research method was used to investigate students’understanding of the concept of the equal sign in two different grades:grade 5 and grade 7,and to analyze four dimensions:the type of understanding of the concept of the equal sign,the tendency to understand the concept of the equal sign,the type of understanding of the concept of the equal sign in different equation structures,and the relationship between the type of understanding of the concept of the equal sign and their strategies for solving equations.A questionnaire was used to test the algebraic thinking level of fifth and seventh graders and to analyze the correlation between it and the level of students’ understanding of the concept of the equal sign.The analysis revealed that:(1)students’ understanding of the concept of equal sign can be classified into four categories:"relational" definition,"operational"definition,double definition,and other non-relational definitions;(2)most students in both grades prefer "relational" definition,and the overall level of understanding of the concept of equal sign is higher in grade 7 than in grade 5;(3)students’ understanding of the concept of equal sign is influenced by the structure of equations and is related to their choice of strategies for solving equations;(4)students’ understanding of the concept of equal sign is positively related to their level of algebraic thinking.Based on the above findings,this paper makes the following suggestions for the teaching of fifth and seventh grade:(1)In the teaching process,students can strengthen their relational understanding of the concept of the equal sign,so that they can understand the meaning of the equal sign is that both sides of the equation are equal,regardless of the structure of the equation;(2)Starting from the understanding of the concept of the equal sign,focus on the development of students’ relational thinking;(3)Pay attention to whether the mistakes students make in algebraic problems are caused by a low level of understanding of the concept of the equal sign,and correct them,so as to improve students’ algebraic thinking and help them make the transition from arithmetic to algebraic thinking.It is hoped that this will provide insight for mathematics educators,teachers,and students.