Research On Function Definition Teaching In Senior High School

Function is a main line running through high school mathematics.Function definition is one of the core concepts of high school mathematics.The teaching of high school function definition is a recognized difficult problem in teaching.It is of great significance to study the teaching of high school function definition.This paper reviews the relevant domestic and foreign literatures on the definition of high school functions from the perspectives of "four understandings",namely "understanding mathematics","understanding textbooks","understanding teaching" and "understanding students".Research literature found that there are "three difficulties" in the teaching of function definition in senior high school,namely,the difficulty of function definition itself,the difficulty of function definition teaching and the difficulty of function definition learning.Some teachers have studied the teaching design of high school function definition.These documents are instructive and instructive to further study the teaching design of high school function definition,but there are still some deficiencies.First,the mathematization process of function definition in teaching design is relatively simple.Second,the connection between the definition of junior high school function and the definition of senior high school function is not close enough.The third is the phenomenon of "wholesale" in the teaching process.From the two perspectives of non-cognitive factors and cognitive level,the author compiled the “Questionnaire on Non-cognitive Factors in High School Mathematics Learning” and “The High School Function Definition Test Paper”.The author also conducted a questionnaire survey and a test paper survey on the first-year high school students in three classes of Ziyang,Neijiang and Nanchong in Sichuan Province.The collected data were analyzed by SPSS 22.0 software.The results of the questionnaire survey show that the five dimensions of non-cognitive factors,namely motivation,emotional emotion,attitude,will and character,have certain influence on the learning achievement defined by the high school function,and the relevant factors of the five dimensions,such as external motivation,emotional stability,learning responsibility,persistence and competitive heart,have the greatest influence.The survey results of thetest paper show that: the definition of function of senior one students is not well understood;Different knowledge bases of students will lead to different understanding of function definition.There are differences between students’ gender in the operation stage,process stage,object stage and schema stage of function definition understanding.Interviews were conducted with several teachers and students.The results show that these teachers think that the essence of function definition and the understanding of abstract symbols are the most important and difficult points in teaching.The students’ understanding of high school function definition is not deep enough.They seldom combine function definition with the history of mathematics in teaching,and the connection between high school function definition and junior high school function definition is not close enough.According to the conclusions of literature research and investigation,based on the theory of problem driving,HPM theory,mathematics core literacy theory and mathematics three worlds theory,four teaching design cases are given,namely,high school function definition teaching design based on problem driving theory,high school function definition teaching design from HPM perspective,high school function definition teaching design from mathematics core literacy perspective,and high school function definition teaching design based on David Tall’s "The three worlds of mathematics".