Analysis Of Errors In Solving Problems Of Quadratic Equations In One Variable For Junior Three Students And Research On Teaching Strategies

Equation is the process of refining specific relationships in real life into mathematical problems through mathematical symbols.The knowledge of equations can lay the foundation for the subsequent learning of inequalities and functions.The quadratic equation of one variable is one of the important components in the equation model,and the learning of its content has a link between the past and the next in the junior middle school mathematics curriculum.In order to understand the errors in solving the problems of quadratic equations in one variable for junior high school students,this article conducts research from three aspects: error types,causes of errors,and teaching strategies.This paper draws up the following research question: What are the main types of errors that students in junior high school solve in the solution of quadratic equations in one variable? What are the reasons for the problem-solving errors?Based on the above error types and cause analysis,what are the strategies that can be implemented in teaching to reduce problem-solving errors?This article is based on 404 ninth grade students and some mathematics teachers from municipal demonstration middle schools in Lanzhou City,Gansu Province.It adopts various methods such as literature method,case analysis method,testing method,questionnaire method,interview method to collect information and data.On this basis,with the help of SPSS and Excel software for sorting and analysis.Based on the data obtained from the test paper,referring to students’ usual practice homework answers,and with the help of Dai Zaiping’s error classification theory,the paper concludes that there are four main types of errors in solving quadratic equations in one variable for junior high school students:1.intellectual errors:errors in the examination of the questions and the unclear concept of the quadratic equation in one variable.2.logical errors:inappropriate classification of questions involving parameters in solving quadratic equations in one variable and can’t perform equivalent transformation correctly.3.strategic error:the coefficients and degrees of terms in a quadratic equation of one variable cannot be regarded as a whole and the wrong conversion of the roots of the quadratic equation in one variable.4.negligent errors:ignoring the special conditions implied in the problem of quadratic equation in one variable,there is a transient misunderstanding when analyzing the problem,and writing calculation errors.By analyzing the content of student questionnaires and teacher-student interviews,it is found that the main reasons for the errors in solving quadratic equations in the third grade of junior high school students are internal causes and external causes.The main internal factors are: non-intellectual factors,knowledge factors,problem-solving habits.External factors mainly include:learning environment.Aiming at the typical types of errors that students appear in solving problems of quadratic equations in one variable,combined with the analysis of the causes of errors,the author proposes the following teaching strategies:1.attach importance to the teaching of examination questions and improve students’ examination ability;2.attach importance to the teaching of concepts and formulas to consolidate students’ basic knowledge;3.attach importance to the teaching of classified discussion ideas,and enhance students’ awareness of classified discussion;4.attach importance to enlightenment and guidance to cultivate students’ logical thinking ability;5.attach importance to the training of overall thinking,and enhance students’ overall substitution awareness;6.pay attention to the teaching of problem-solving strategies to improve students’ problem-solving efficiency;7.attach importance to the implementation of individual tutoring to improve students’ problem-solving ability;8.pay attention to the teaching of problem-solving review,and enhance students’ awareness of problem-solving reflection;9.pay attention to the teaching of standard writing and cultivate students’ good writing habits.