Diagnosis Analysis Of Junior Middle School Students' Errors In Factorization

"Numbers and algebra" occupies an important position in mathematics education in compulsory education.It can help students to understand the world from the quantitative relationship and solve real-world problems.The factorization is one of the contents of the "numbers and algebra" module.Its ideas and methods always run through algebraic transformations,except for the use of algebra in constant deformation.It is also an extremely important problem solving tool in terms of partition and division,algebraic value,division problem,and solving equation.Learning the content of factorization plays a crucial role in further studying other mathematical problems.Through reference to the existing literature,this article adapted the exercises on factorization,compiled a test volume,and selected 111 students from Grade 9 as samples in a general middle school in Shijiazhuang City to conduct a survey.Through the results of the students 'tests,they were counted,collated,and analyzed.To explore the common error types and their causes in the process of learning factorization.According to the statistical results of the test volume,based on the research theory of Dai Zaiping,the types of mistakes that students have made are sorted out from the following three aspects:(1)Knowledge errors: The concept of factorization is unclear;Confusion with the deformation of the equation;The factorization is not an identity deformation;Go "back to the road",circular operations;After the common factor is raised,there is no complement;There is no operation property of power.Cross phase multiplication is not applied.(2)Strategic errors:the common factor has not been mentioned;Lack of overall consciousness in solving problems;Decomposition is not complete;When solving a quadratic equation,the root is lost;Unreasonable grouping leads to inability to decompose;The application of factorization meaning is lacking in the actual situation.(3)Neglect error: There is an error in the symbol during the operation;The form of factorization does not meet the requirements;The common factor is not lifted;An error occurred in the application of the formula.By analyzing the results of the test volume and referring to the theoretical knowledge in the relevant literature,the main reasons for summarizing the above mistakes are:(1)The concept is unclear;(2)Weak reverse thinking ability;(3)Lack of overall awareness;(4)Metacognition is weak.Based on the above research results,the author puts forward some suggestions for the teaching of factorization:(1)Do a good job in concept teaching and lay the foundation for students to obtain new knowledge;(2)Teachers should pay attention to the cultivation ofstudents 'ability to reverse thinking;(3)Strengthening the cultivation of students 'overall consciousness in mathematics teaching;(4)Strengthen students 'metacognitive ability.