Advanced Study On The Concept Of Exponential Function In High School Based On APOS Theory

Mathematics Curriculum Standards for Senior High Schools(2017 Edition,2020revision)(New Curriculum Standards for short)clearly put forward the requirement of taking functions as the main line and running through the core literacy of the subject.The concept of exponential function,as one of the important basic elementary functions in the compulsory curriculum of high school mathematics,is a very important concept that high school students need to understand and master,and has a fundamental role for high school students to learn the content of function.However,the concept of function is abstract and complex,so it is difficult for students to understand the concept of exponential function.At the same time,teachers have some problems in teaching the concept of exponential function.Learning progression is mainly a study of the changing process of students’ thinking ability and cognitive ability over time.Meanwhile,the four stages of APOS theory,namely operation,process,object and schema,conform to the changing sequence of students’ thinking level and cognitive level from easy to difficult.Therefore,under the background of the importance of the concept of exponential function and the problems existing in teachers’ teaching,as well as the similarity between the four stages of APOS theory and the development of thinking and cognitive level of learning progression,a learning progression model of the concept of exponential function in senior high school is constructed based on APOS theory to reveal the law of cognitive development in the process of learning the concept of exponential function.It is very necessary to provide the basis for teaching the concept of exponential function.The research method mainly adopts the top-down structure sequence,and mainly adopts the confirmatory empirical research.Through the three stages of "hypothesis--test--revision",the learning progression model of the concept of high school exponential function is finally obtained.In the hypothesis stage,literature analysis is adopted to analyze the new Curriculum Standard.In combination with the 2019 HumanEducation A(unified referred to as Human-Education A),2019 Beijing Normal University(unified referred to as Beijing Normal University)and 2020 Shanghai(unified referred to as Shanghai),in the first compulsory textbook of the three editions,As for the knowledge content of the concept of exponential function,the four stages of learning progression and their respective progression levels are divided,and the corresponding achievement level and learning performance of the progression level are described.The hypothetical learning progression model of the concept of exponential function in high school is preliminarily constructed,and the predictive test tool is developed.In the verification stage,50 and 200 students from grade one to grade three of a high school in Q City,Heilongjiang Province were randomly selected twice by using the test paper survey and interview method to carry out the pre-test and formal test,so as to obtain the test data.SPSS software was used to analyze the test tool and adjust the test paper.In the revision stage,the data results of the formal test stage are adopted to analyze the scores of each item,and the hypothetical learning progression model of the concept of exponential function in senior high school is revised with the interview suggestions of front-line mathematics teachers,and the final learning progression model is obtained.On the basis of data analysis and interview content analysis,the learning progression module of the concept of high school exponential function is obtained(1)The advanced model consists of 4 stages and 8 levels;(2)Students’ learning performance is negatively correlated with their advanced level;(3)The advanced level of senior students is generally higher than that of junior students;(4)There is little difference in the level of advancement between students’ genders.Finally,according to the students’ learning disabilities in the process of learning exponential function concept,appropriate teaching suggestions and teaching design are given.