Investigation And Research On Problem Solving Errors Of Univariate Quadratic Equation Of Junior Middle School Students

The teaching requirement for equations in the mathematics curriculum standard for compulsory education(2017)is that students can clarify the quantitative relationship in specific problems,list the corresponding equations,understand and feel the important role of equations as a model describing the quantitative relationship in real life.This paper studies the following two questions:(1)what are the main manifestations and types of problem-solving errors of junior middle school students in the process of solving univariate quadratic equations?(2)From the perspectives of students and teachers,this paper analyzes the main reasons for students' errors in solving univariate quadratic equations?Using the methods of questionnaire,test paper,classroom observation and interview,this paper takes the students of two rural middle schools in artush as the research object,and investigates and studies the current situation of their problem-solving errors of univariate quadratic equation.Through the test paper,329 students from two rural schools were tested,and the main manifestations and types of junior middle school students' problem-solving errors in univariate quadratic equation were analyzed.Through questionnaire survey,classroom observation and interview with 329 students and some teachers in two schools,this paper analyzes the main causes of junior middle school students' errors in solving univariate quadratic equation.Through the analysis of the research results,it is concluded that there are four types of errors in the problem-solving of "univariate quadratic equation" by junior middle school students:first,knowledge errors: the concept of univariate quadratic equation is not mixed clearly,the basic properties are not mastered enough,the relationship between the discriminant of root and the root of univariate quadratic equation is not clear,the law is not understood thoroughly and can not be used correctly.The second is strategy error: it can not correctly identify the type of application problems of univariate quadratic equation,and the solution of univariate quadratic equation is not flexible enough to contact the context and correctly use the known conditions.The third is logic error: the logical relationship between the parameters in the univariate quadratic equation cannot be clarified,resulting in deviation or error in the understanding of the meaning of the question.Fourth,psychological errors: the implicit conditions of quadratic term coefficients are often ignored.In order to deeply understand the main causes and specific manifestations of students' problem-solving errors,this paper adopts the research paradigm of the combination of students' questionnaire survey and teacher-student interview.Through the analysis of the results of the survey and interview,it is found that the main subjective reasons for students' problem-solving errors are:(1)lack of interest in equation learning;(2)Insufficient knowledge reserve;(3)Improper problem representation;(3)Pattern recognition method error;(4)Lack of problem-solving monitoring ability;(5)Problem error handling.The main objective reasons are:(1)teachers' lack of subject teaching knowledge and ability;(2)Teachers' subject content knowledge reserve is insufficient.The specific manifestations of the causes of problem-solving errors: first,lack of interest in mathematics learning;Second,the knowledge reserve is insufficient and prone to mistakes;Third,the problem representation ability is weak;Fourth,they did not form the habit of self problem-solving monitoring;Fifth,there are errors in topic meaning analysis;Sixth,lack of awareness of post solution research.Based on the analysis of the current situation,this paper puts forward the following teaching suggestions: from the perspective of students,timely summarize and review,consolidate conceptual knowledge,be familiar with algorithm and strengthen operation practice and investigation,learn to use noun discrimination diagram method and diagram method to improve their problem representation ability,and summarize common problem-solving methods.From the perspective of teachers,teachers help students understand conceptual knowledge through systematic knowledge schema,summarize and focus on common operation errors,and use noun discrimination diagram and diagram to make students form the habit of summarizing and refining problems,so as to improve their representation ability of mathematical problems,so as to guide students to analyze the causes of errors and improve their self-monitoring awareness,Improve their own knowledge of equation subject content and subject teaching knowledge ability.