Research On Errors And Teaching Strategies For Eighth-grade Students Solving Linear Function Problems

Functions contain rich mathematical ideas and are important materials for cultivating students’ mathematical abilities.However,for middle school students who are exposed to functions for the first time,some errors often occur in the process of solving linear function problems.This article focuses on the following three issues:(1)What types of errors do eighth grade students have in solving linear function problems and their specific manifestations?(2)What are the reasons why eighth grade students make mistakes in solving a linear function problem?(3)How to improve teaching in order to minimize errors made by eighth grade students in solving linear function problems?This article selects 203 students from Class 18,19,22,and 23,Grade 8,from a middle school in Shijiazhuang City,Hebei Province,as the research objects,and four frontline math teachers as the interview objects.It uses literature research,questionnaire survey,and interview methods to collect rich raw data and textual materials.The research was conducted using SPSS 24.0 and Excel software to analyze the data.Firstly,based on Piaget’s theory of cognitive development,the error classification theory of Dai Zai Ping et al.and original data,this paper analyzes the types and specific manifestations of errors encountered by eighth grade students in the process of solving primary function problems:(1)intellectual errors,which are manifested as: There is no real understanding of the premise of the definition;Students are not clear about the relationship between a linear function and a binary linear equation;Students are not proficient in using images of linear functions;Students do not understand the incremental and subtractive properties,the values of k,b,and the positional relationship of the image of the function.(2)Logical errors,which are manifested as follows: Insufficient mining of implicit information;An error occurred in the nonequivalent transformation of the equation;Lack of awareness of classified discussions.(3)Strategic errors,which are manifested as follows: The method of solving problems is single;The relationship between linear functions and inequalities is not close.(4)Psychological errors,which are manifested as follows: Insufficient careful examination of questions,arithmetic errors,transcription errors,and nonstandard drawing.Secondly,the reasons for the above four types of problem are analyzed:(1)The reasons for the occurrence of intellectual errors include: Not accurately mastering the basic knowledge related to primary functions;Students fail to reasonably establish a knowledge system for functional learning.(2)The reasons for logical errors include: Lack of mathematical logical thinking;Weak awareness of modeling.(3)The reasons for strategic errors include: Insufficient reading and analysis skills;Improper selection of solving methods.(4)The reasons for psychological errors include: students’ learning attitudes are not proactive enough,students lack reflective thought,and students’ computational abilities need to be improved.Finally,based on the above analysis,the following teaching countermeasures are proposed to reduce students’ errors in solving linear function problems:(1)Countermeasures to reduce intellectual errors: Providing counter example teaching to deepen the formation of concepts and properties;Flexible use of teaching language,emphasizing the formation process of concepts and properties.(2)Countermeasures to reduce logical errors: Training students in mathematical logical thinking;Strengthen the cultivation of students’ modeling awareness.(3)Countermeasures to reduce strategic errors: Improving students’ reading and analytical abilities;Pay attention to the training of problem solving methods.(4)The countermeasures to reduce psychological errors include: Mobilizing students’ learning enthusiasm;Guide students to reflect on their own mistakes;Improve computing power.This article aims to provide reference for front-line teachers to improve the teaching of linear functions by collecting,classifying,attributing,and proposing countermeasures for errors in solving linear functions.