Error Analysis Of Quadratic Function Problem Solving For Junior Middle School Students And Teaching Strategies

In the process of solving mathematical problems,students will inevitably make mistakes,which is the temporary result of students' continuous attempts to learn knowledge in the process of mathematics learning.However,in the process of teaching,teachers hope that students can better understand mathematics knowledge,as far as possible,there will be no or fewer mistakes.On the other hand,students' problem-solving errors are also a good teaching resource,making full use of this resource is conducive to improving teaching efficiency.Quadratic function is one of the key and difficult points in junior high school mathematics,and also one of the key points in the examination of junior high school.Based on this,this paper studies the quadratic function problem-solving errors of junior high school students,mainly focusing on the following three issues:(1)what are the main types of errors in the quadratic function problem-solving of junior high school students,(2)what are the causes of these errors,(3)how to improve teaching to reduce the occurrence of students' quadratic function problem-solving errors.In view of the above research problems,this study selected some teachers and students of a middle school in Xuzhou City,Jiangsu Province,as the research object,using test paper analysis,questionnaire survey,interviews and other methods to collect data,through the collation and analysis of data,draw conclusions.Through the analysis of students' test papers and the classification theory of problem-solving errors made by Professors Dai Zaiping and Luo Zengru,it is found that the main types of errors in solving quadratic function problems of junior middle school students are knowledge errors and psychological errors.At the same time,logical errors and strategic errors will occur to varying degrees in the process of problem-solving,and each type of errors has its specific manifestation in the second time.The main types of errors in different knowledge modules of functions are also different.Through the analysis of test papers,students' questionnaires and interviews with teachers and students,the author summarizes the main reasons for the above errors into the following six aspects: 1.lack of solid basic knowledge,2.lack of examination and calculation ability,3.weak ability to read and draw,4.lack of experience in solving problems,5.inflexible use of mathematical thinking methods,6.influence of non-intellectual factors.According to the conclusion of the investigation and the corresponding educational and teaching theories,this study puts forward the corresponding teaching countermeasures: 1.consolidating the foundation and penetrating the ideas(attaching importance to the generating process of the concept of quadratic function,guiding students to experience the deduction process of formulas and rules,paying attention to the comparison of the three expressions of quadratic function,and realizing the penetration of mathematical thinking and methods);2.attaching importance to the cultivation of students' problem-solving ability(notes).Focus on cultivating students' ability of examination and calculation,focusing on training students' ability of understanding and drawing.3.Enriching students' experience in solving problems(encouraging multiple solutions to one problem to open up ideas for solving problems,inducting typical quadratic function questions through variant teaching,delicate exercises and timely feedback).4.Focus on the influence of non-intellectual factors on solving problems(attaching importance to cultivating students' habit of reflection,correcting students' learning functions).Attitude,stimulate students' interest in quadratic function learning and problem solving.