Study On The Analysis Of Errors And Teaching Strategies Of Solving Equation And Inequality Problems For Junior Middle School Students

Equation and inequality are the core of the algebraic content of mathematics in junior middle school.They are effective models for describing equality and inequality in the real world and are also important tools to realize the transformation of “practical problems-mathematical problems-practical problems”.In order to understand the learning status of equation and inequality of junior high school students,this paper will take the errors in problem-solving as the carrier,starting from three aspects: error type,cause analysis and teaching countermeasure.The following research questions are proposed: What are the types of students' mistakes in solving equation and inequality problems? What are the main causes of these problems? Based on the above error types and cause analysis,what countermeasures can be taken in the process of “teaching” and “learning” from the perspectives of teachers and students?In this study,374 grade 9 students and some math teachers from two middle schools in Qingcheng County,Qingyang City,Gansu Province,were selected as the research objects.Data were collected through the methods of literature analysis,test paper,case analysis,questionnaire and interview,and the results are obtained by sorting and analyzing the data.According to the statistical results of the test paper,based on the theory of error classification of Dai Zaiping and other scholars,it is concluded that there are five main types of errors in solving equation and inequality problems for grade 9 students: 1.errors in concept and property: insufficient grasp of basic properties;confusion of the concept of equation;when the solution set of inequality is represented on the number axis,the meaning of hollow circle and solid point is confused;the relation between the root of quadratic equation of one variable and the discriminant of the root is fuzzy.2.arithmetic errors: confusion of the algorithms and improper application;the “root check” step is missing;the elimination method is not clear;weak symbol awareness;the expression of the final result is not standard.3.errors in strategy and method: be poor in reverse thinking;unable to identify the type of application questions correctly;the solution of equation isn't flexible enough.4.logic errors: the logical relationship between the coefficients of parametric equations is not clear;determining quantity relation is blocked;deviation in understanding the meaning of the question.5.psychology errors: thinking inertia caused by stereotype;ignore the implicit condition that the coefficient of the quadratic term is not 0.Through the analysis of students' questionnaires and interviews with teachers and students,it is found that subjective factors such as knowledge structure,learning interest,mathematical ability,thinking habit and error handling are the main causes of students' problem-solving errors,while objective factors such as family background and teachers' teaching are also the causes,but the impact is small.The causes of the errors are as follows: 1.lack of interest in mathematics;2.the knowledge reserve needed to solve the problem is insufficient;3.weak mathematics ability;4.the habit of solving problems has not been developed;5.weak awareness of error analysis and utilization;6.poor psychological quality.According to the types of students' errors and based on the analysis of the causes,the author puts forward the following corresponding teaching countermeasures: 1.improve the interest in math;2.strengthen knowledge teaching;3.improve mathematics ability;4.cultivate good habits of problem solving;5.pay attention to the treatment and utilization of wrong questions;6.strengthen the psychological quality of problem solving.