Error Analysis Of Factorization Of Seventh Grade Students

Factorization is an important part of ‘Number and Algebra' in middle school.When all other conditions are equal,the person who is best at factorization is the best algebras.It can be seen that factorization plays an important role in middle school algebra.As a very important learning tool,factorization is the basis for learning fractions,quadratic radicals,quadratic equations,quadratic inequalities,quadratic functions,fractional equations and even geometry.Studying the learning situation of factorization of seventh grade students is helpful to improve teaching.Based on task about factorization and the analysis of the factorization questions in the high school entrance examination of Wuxi in the past ten years,a test paper is compiled,and the test paper was also modified by experienced teachers.100 seventh graders from Y middle school in Wuxi were tested.In order to explore the relationship between Mathematical Metacognition and students' factorization performance,the author also designed a questionnaire of factorization Mathematical Metacognition,which contains 12 questions,of which 5 questions are related to specific factorization questions,and the remaining 7 questions are combined with the error rate of students' whole factorization test paper.This study leads to the conclusions as follows:1.The author summarizes 13 kinds of students' main errors about factorization,including incomplete decomposition;The whole part can't see;the error in the application of the two formulas.2.In the relationship between Mathematical Metacognition and factorization,the stronger the students' awareness of one aspect of Mathematical Metacognition,the lower the error rate of factorization,and consciously enhance the students' Mathematical Metacognition in specific aspects,which can help some students reduce the errors of factorization.3.Reasons behind are: students lack the habit of testing,students do not grasp the two formulas well,students' overall thought is weak,and some factors in Teachers' teaching,including in order to avoid confusion between integral multiplication and factorization,teachers pay too much attention to separate teaching and the demonstration of teachers' explanation of exercises is weak.Teachers may help students in these ways: pay attention to guiding students to learn to summarize and reflect,strengthen the penetration of mathematical ideas and methods such as the overall thought,enhance the standardization and demonstration of exercise explanation,and strengthen students' understanding and memory of mathematical formulas.