Research On The Concept Teaching Of Exponential Function Based On APOS Theory

As the logical starting point of mathematics,mathematical concept is not only the basis of students’ cognition,but also the core of students’ mathematical thinking.Students’ mastery and understanding of mathematical concepts is the key for students to use mathematical knowledge to understand the mathematical world,the real world and solve problems.The exponential function is abstracted in a large number of realistic backgrounds,which accords with the educational idea that mathematics learning is close to real life.After the reform of the new curriculum,the exponential function is no longer the first elementary function to learn,but it still paves the way for the study of logarithmic function and so on.The study of power function provides the method and train of thought for the study of exponential function.However,due to individual differences,each student has different understanding of exponential function,and the level of thinking development of students who have just entered high school is also limited and hierarchical.Under this background,it is extremely necessary to divide the students’ understanding of exponential function concept and analyze the difficulties of students in each stage,and teach students in accordance with their aptitude.The final research questions are as follows :(1)what is the understanding and mastery of exponential function among senior high school students based on APOS theory?(2)What are the common errors in the comprehension of the high school students’ exponential function? What’s the reason?(3)What should teachers do when teaching the concept of exponential function to solve the problems of students? Any good advice?In order to solve the above research problems,the exponential function test paper was compiled,and some high school students were selected as the research object in two high schools.According to the APOS theory,the exponential function stage division standard was scored,and the data results were analyzed.The conclusion is as follows:(1)Under the APOS theory,the learning of the exponential function of the first-year senior students is unbalanced and continuous;(2)the problems existing in the study of the exponential function of senior high school students in APOS theory are as follows: action: the ability of representation is not strong and it is easy to omit information,solving practical problems do not care about the definition domain,and poor drawing habits;process: lack of essential understanding of the definition of exponential function,lack of awareness of categorization and discussion of the base to be determined;object:do not seek the definition range and value range of exponential function;the ability to examine questions and recognize graphs needs to be improved;Scheme: It is difficult to apply exponential function model to solve practical problems;The problem solving ideas are not clear and standardized,The ability of reflection and summary needs to be improved;(3)The reasons for the difficulties in learning exponential function in the above stages are as follows: exponential power and its operation understanding problems,lack of practical problem practice,writing drawing is not standard;exponential function definition memorization is too formal,exponential function image nature understanding is not in place;compound,piecewise function contact is less,mathematical thinking method needs to be improved;do not understand the practical significance of exponential function model,can not effectively build knowledge network.Based on the above research conclusions,the following teaching suggestions are put forward :(1)strengthening the relationship with the real model to understand the background of exponential function;(2)paying attention to the definition form of exponential function and training exponential function variant;(3)making proper use of information technology to perceive exponential function image change;(4)repeatedly infiltrating ideas and methods,focusing on number-form combination and classification discussion;(5)improving the ability of induction and summary,constructing exponential function knowledge network;(6)to "concretize" the research ideas of exponential function,standardize the problem-solving procedures;(7)to realize the hierarchical teaching of exponential function in each stage.