The Common Mistakes Of Factorization In Junior High Schools And The Study Of Teaching Countermeasures

Factorization is the basis of algebraic operations and plays an important role in the junior high school mathematics system.Therefore,it is very important for students to learn the factorization.This study explores the types of errors in the factorization process of junior high school students and analyzes the causes of students' errors by the method of literature,test volume testing and interviews.Previous studies have paid more attention to understanding some errors of factorization in students' learning,and neglected the overall classification of the errors and the reasons for the theoretical analysis of the errors.Therefore,this paper uses Dai Zai ping's misclassification theory and Piaget's cognitive theory study above issues.In this study,an experimental class and two regular classes in the seventh grade of a Middle School in Shanghai were firstly tracked and the student's errors in the process of factorization were collected.Then,the students are subjected to take part in the factorization test,and the test results were analyzed on a case-by-case basis,and the common errors were classified.Finally,the results of the test analysis,the results of the student interviews and other data were unified.On the other hand,it analyzed the causes of students' errors and proposed targeted teaching strategies.It is expected that junior high school students will reduce the errors when learning factorization.The conclusions of the study are as follows:There are four types of errors in the learning process of factorization for junior high school students: the first type is knowledge error,it is expressed as,unclear concept,the confusion of publicity and the incomplete decomposition;the second type is logic error,it is expressed as,improper grouping and unequal transformation;the third type is strategic error,it is expressed as,the lack of overall thinking and improper factorization methods;the fourth type is psychological error,it is expressed as,computational errors and untested.The reasons why students make mistakes are students' lack of cognitive structure knowledge,students' unclear understanding of mathematics,students' weak metacognition,the improper selection of factorization methods,the lack of motivation for mathematics,the lack of willingness to learn mathematics and lack reflection.This study proposes the following teaching strategies: teachers should strengthen students' understanding of formula characteristics,strengthen students' understanding of the nature of factorization concepts,promote students' metacognitive strategies,strengthen teaching strategies of factorization methods,stimulate students' motivation for mathematics learning,develop students' willingness to learn mathematics and guide students to reflect on their own wrong questions.