A Study On The Understanding Types And Errors Performance Of Equal Sign Concept Among Fifth Grade Students In Primary School

The equal sign is a bridge between arithmetic and algebraic thinking,and is not only an important vehicle for developing early algebraic thinking and algebraic reasoning,but also an important knowledge vehicle for developing students’ core mathematical literacies such as number sense,symbolic awareness,reasoning awareness,and arithmetic skills.The study shows that students at all learning stages,even adults and teachers,have some degree of lack of understanding of the concept of equal sign,so it is of great value and significance to study the understanding of the concept of equal sign among primary school students.This study used a combination of qualitative and quantitative research methods to investigate the characteristics of primary school fifth graders’ comprehension types of the concept of equal sign using questionnaires and interviews,to investigate the characteristics and causes of primary school fifth graders’ errors under different comprehension types,and to analyze teaching strategies to promote primary school fifth graders’ comprehension of the concept of equal sign through the interview method,classroom observation method,and text analysis method.The main research results are as follows:The types of equals concept comprehension for fifth grade students are differentiated and transformed.Elementary fifth graders’ understanding of the concept of equal sign was classified as operational,relational-computational,and relational-structural.The number or proportion of the three types of understanding of the equal sign concept,in descending order,were relational-computational,relational-structural,and operational,and were mainly concentrated in the relational-computational and relational-structural types of understanding.Students of the operational type view the equal sign as an operation symbol to perform certain operations or a connecting symbol to connect equations and results,and are able to use the"operation = answer" strategy to successfully solve some equation problems.Students of the relational-structural type view the equal sign as a symbol indicating the equivalence or equivalence of the equation or the number obtained on both sides of the equation,and have the flexibility to use arithmetic,algorithms,laws of operations,"and invariant","equation properties" and "reasoning" to solve equation problems."and "reasoning",operator’s law,etc.to successfully solve equation problems.The three types of equation concepts are understood to be interchangeable between types.The error performance and causes of different types of understanding of the concept of equal sign among primary school fifth graders show diversity and variability.The largest number of error performance of operational students include the equal sign is an operation symbol,the equal sign is a connecting symbol,inaccurate criteria for judging the equation,unclear understanding of the equation relationship,and inaccurate methods for decomposing the equation,which arise mainly because of insufficient attention to the meaning or significance of the equal sign and insufficient knowledge of the equation.The number of relational-computational students’ errors performance is relatively less,including the understanding that the equal sign is the symbol of operation considered unique,the ambiguity of the numbers on both sides of the equal sign,the confusion of the operation of the equivalence relation,and the inaccurate judgment criteria of the equation,which are mainly caused by the insufficient integration of the meaning or significance of the equal sign in different contexts,the unfamiliarity with a typical equations,and the misconception of algebraic equations.The number of relational-structural students’ errors performance is relatively less,including failure to master the operation of the equal sign,imprecise application of the properties of equations,unclear understanding of quantitative relationships,and confusion over the order of algebraic operations.The main reasons are the wrong use or mechanical transfer of “equality properties” “sum invariance” “difference invariance” and other properties.Teaching strategies to promote fifth grade students’ understanding of the concept of the equal sign should focus on understanding and application in three main ways: first,teachers should improve students’ understanding of the nature of the content of the equal sign,create problem situations that integrate non-operational and operational aspects,use multiple representations such as scales and line graphs to understand the nature of the content of the equal sign,and focus on emphasizing the meaning of the equal sign or the meaning of the equal sign in operational situations;second,focus on students’ knowledge and understanding of the equation;third,to improve students’ ability to use equals to solve problems,to understand equivalence by designing task activities,to focus on equivalence to understand equations,to encourage diversity of problem solving strategies,and to promote students’ understanding of the concept of equals.