A Study On The Causes And Countermeasures Of Quadratic Function Problem Solving Errors For Grade 9 Students

Quadratic function is an important mathematical model to describe the law of movement change in the objective world,and is a powerful tool to solve practical problems in production practice.It is widely used in mathematics,physics and chemistry.As the main content of the connection between junior and senior high school,the combination of quadratic function with equations,inequalities and other knowledge contains a variety of mathematical thoughts and methods,which is the key and difficult point for students to learn mathematics,and also an effective carrier for cultivating students’ core literacy of mathematics.However,due to the influence of many factors,the ninth grade students are easy to make many mistakes when learning quadratic functions,which directly affects the quality and effect of learning quadratic functions.In order to fully understand the current situation of students’ learning of quadratic function,this study carries out research from three aspects: the performance of students’ error types of quadratic function solving,the analysis of the causes of quadratic function solving errors and the countermeasures to reduce students’ error of quadratic function solving.The following three main questions are proposed in this study:(1)What are the types and manifestations of errors made by ninth grade students in solving quadratic function problems?(2)What are the main causes of quadratic function problem solving errors of ninth grade students?(3)What are the teaching strategies to reduce the quadratic function solving errors of ninth grade students?In this study,285 grade 9 students and 5 mathematics teachers from two middle schools in Kangxian County,Longnan City,Gansu Province were selected as research objects.Literature analysis,testing,questionnaire,interview and case analysis methods were used to collect data and materials,and SPSS23.0 and Excel software were used to process and analyze the data of test papers and questionnaires.According to this study,there are four main types of errors in solving quadratic function problems for grade 9 students.One is knowledge error: it is manifested as unclear understanding of the concept,image and nature of quadratic function.Second,logical errors: improper classification,unequal transformation;Third,strategic error: the performance is improper method,thinking set,problem solving direction wrong;Fourth,psychological errors: errors in examining questions,calculating and writing caused by carelessness.Through the analysis of students’ questionnaires and interviews with teachers and students,it is found that basic knowledge,mathematical ability,learning interest,learning habits,learning motivation,students’ error handling and problemsolving habits are the main factors that affect students’ mathematical problem-solving,and the two objective factors of teachers’ teaching and learning environment have relatively little influence on students’ mathematical problem-solving.Based on the above research conclusions,six teaching strategies are proposed to deal with students’ error in solving problems of quadratic function: The first is to strengthen the essence of mathematics concept teaching to promote students’ understanding of basic knowledge;The second is to pay attention to the application of the combination of number and form to enhance students’ mathematical thinking ability;The third is to guide students to construct mathematical models,highlighting the important value of function thought;The fourth is to advocate the effectiveness of variable teaching and broaden students’ thinking of mathematical problem solving;Fifth,pay attention to the cultivation of the consciousness of examining the problem and improve the ability of solving mathematical problems;Sixth,make reasonable use of wrong resources to improve students’ ability to solve problems and reflect.