An Action Research On The Teaching Of Function Concept Based On HPM

Function is an important part of number and algebra in compulsory education,and the concept of function is one of the difficult concepts for students to grasp.The development of the concept of function has gone through several centuries,so it is necessary to combine the relevant materials of the development history of mathematics in teaching.In recent years,the development of HPM has been in full swing,providing a prerequisite for the use of mathematical history in teaching.Based on the research of the current status of function concept teaching,the researcher carried out action research from the perspective of integrating the history of mathematics into the function concept teaching in junior high school.The action research of functional concept teaching from the perspective of HPM in compulsory education stage is a less researched field of HPM teaching practice,so it is necessary to conduct in-depth research.It is an important purpose of this research to fill this gap through teaching examples and teaching practice.One of the purposes of this study is to improve teachers' understanding of students and their attention to concept teaching through the research on the cognitive development of students' functional concept learning in compulsory education.This research selects a middle school 3 classes all the students as the research object.During the whole process of action research,researchers conducted 3 interviews and 4 questionnaires respectively.The study was carried out in three stages: preparation,action implementation and data analysis.In the first stage,the researchers conducted questionnaire 1 among 44 students in Grade 9 of 2017 and interviews 1 with 9 teachers in junior high school.In the second stage,two teachers carried out the HPM teaching in three times: the first time,the teaching of function preliminary understanding,and conducted questionnaire 2 to 91 students before the teaching;Second,the teaching of function image;For the third time,function and its representation were taught.After the teaching,91 students from Grade 9 of Grade 2018 were asked a questionnaire 1,45 of them were asked a questionnaire 3,6 students were interviewed 2,and 2 practice teachers were interviewed 3.The above three teaching experiences are "planning,action,observation,reflection" four links.In the third stage,quantitative and qualitative research is conducted on the results of questionnaires and interviews to draw research conclusions.The purpose of this study is to explore the cognitive and affective problems of students.The main issues of this action study are:(1)What impact does the teaching of function concept from the perspective of HPM have on students' cognition?(2)What slight changes have taken place in the emotional attitude of teachers and students in the teaching of function concept from the perspective of HPM?Based on the history of the development of function concept and the contents of the textbook,this study designed and practiced HPM lesson examples.In the study of students' cognitive development,quantitative and qualitative methods are used.In quantitative research,students' understanding of function concept is divided into three levels: Functions and formulas,images and tables,corresponding relations.In the qualitative research,the cognitive level of students is divided into five levels,and the cognitive development of 6 students is investigated specifically.Through interviews before and after class,teachers' emotion and attitude changes are investigated,and teaching suggestions are put forward accordingly.Through the analysis of the data,the following conclusions are drawn:(1)The survey results show that the vast majority of students think that the class incorporating the history of mathematics is interesting and novel,and helpful to understand what they have learned.They hope that teachers can use this method more in future teaching.(2)Integrating the history of mathematics into the teaching of function concept helps students to understand the concept of function.Quantitative and qualitative studies show that there are significant differences in the level of students' understanding of functional concepts(participants and non-participants).By exploring the reasons for the cognitive development of students,it is found that the integration of mathematical history into function concept teaching is an important reason for promoting the cognitive development of students.According to the conclusion of the study,there are some suggestions for function teaching in junior middle school :(1)Design teaching examples to help students overcome the difficulties in understanding;(2)The concept of function should be emphasized in teaching;(3)Taking students' cognitive starting points into full consideration when setting teaching objectives;(4)Integrate historical data according to teaching objectives.