Teaching Design And Practice Of Exponential Function Concept Under APOS Theor

Mathematical concept is the logical starting point of mathematics.It is an important basis for students’ cognition and the core of students’ mathematical thinking.The concept of function and its mathematical thought and method have penetrated into all fields of mathematics,which are the basis of further learning mathematics.The concept of exponential function is abstracted from a large number of real backgrounds.It reflects the educational concept of mathematics learning close to real life.Moreover,exponential function plays a connecting role in senior high school.It not only further deepens and consolidates the method of exploring power function,but also lays a foundation for learning the next logarithmic function.It plays a vital role in the learning of the whole function part.Under this background,the purpose of this study is to improve the concept teaching of exponential function.Complete the teaching design of exponential function under the guidance of APOS theory,and carry out practical research.Therefore,the research questions of this paper are as follows:(1)What is the current situation of function concept teaching?(2)How to teach the concept of exponential function under the guidance of APOS theory? How to design teaching cases?(3)What is the implementation effect of the teaching design of exponential function concept under the guidance of APOS theory?In order to solve the above problems,this paper takes the teachers and students of a senior one in Qingdao as the research object,uses the methods of questionnaire and interview,understands the current situation of teaching and learning the concept of exponential function:students can use the concept of function to solve problems,but they do not have a deep understanding of the concept of function and do not form a network framework of corresponding knowledge;In order to improve classroom efficiency and teaching progress,teachers mostly use discrimination methods to make students understand the meaning of the concept,and explain its background and process briefly.According to the current situation,this paper puts forward the corresponding teaching strategies: Introduce life examples and gradually abstract the index model;Make rational use of information technology and break through teaching difficulties;Pay attention to the integrity of teaching and help students form a conceptual network.Then,according to the teaching strategy and APOS theory,the teaching design of exponential function is carried out under the guidance of theory and practice.A comparative experimental study is carried out on the designed teaching cases.The author selects two classes with the same initial level as the control class and the experimental class for concept teaching under the guidance of conventional concept teaching and APOS theory.Through the teaching process and test results,this paper analyzes the improvement of APOS Theory on teaching.Finally come to conclusions:(1)The current concept of exponential function needs the guidance of APOS theory;(2)The concept teaching of exponential function under APOS theory has a positive impact on students;(3)The teaching practice of the concept of exponential function under APOS theory has enlightenment.