Research On Inverse Proportional Function Teaching Based On APOS Theory

Mathematical understanding is one of the focuses in the research and practice of mathematics education.Understanding mathematics concept is the key of mathematics classroom teaching.Function is an important part of algebra in junior high school,and it is an important model to describe and study the law of change in the real world.Inversely proportional function is one of the most basic elementary function,and it is an important carrier for junior high school students to understand the function.However,for the students of grade eight,there is difficulty in the formation and understanding of the concept of inversely proportional function.Based on the above background,this paper attempts to study the following problems:1.The difficulty of understanding the concept of inversely proportional function2.How to use the APOS theory to optimize the teaching design of inversely proportional function to break through the difficulties of students' understanding3.The problems that should be paid attention to in the application of APOS theory in concept teachingIn order to solve these problems,this paper compares the teaching content and arrangement of the inversely proportional function between two versions of textbooks,and puts forward the question based on analyzing students difficulty in learning inversely proportional function.This paper also elaborates the feasibility and necessity in applying APOS theory in the inversely proportional function in teaching and design and tries to put forward the teaching design of learning inversely proportional function based on APOS theory.With the adaptation of different teaching designs of inversely proportional function for two classes of grade eight students in the same school,(the control class and the experimental class),then it analyzes students' understanding of inversely proportional function in the four stages,i.e.operation,process,object and schema.Finally,after analyzing classroom dialogue,classroom activities,teaching design,and students' cognitive evaluation,it comes to the conclusion that students' understanding level of inversely proportiongal function can be improved based on the APOS theory.The students have a good mastery of the knowledge of the anti scaling function,and the formal definition of the inversely proportional function is not comprehensive enough.The majority of students understand the anti scaling function in the process of operation,the process of a small number of students rose to the object,the stage of the schema,the ability of comprehensive application is weak.As for teaching concepts,teachers should pay attention on how to help students understand the concepts and guide them to watch how concepts form through the steps of operation,process,object schema.This paper summarizes the teaching of inversely proportional function:(1)Focuse on the intrinsic link of different classes,(2)Focus on the formation process of the concept of the inversely proportional function,(3)Guide students to learn with questions,(4)How to break through the difficulties,and understand the nature of concept.The concept teaching enlightenment:(1)Do do a good job in the concept teaching,(2)Improve the students' understanding of the concept through a variety of forms,(3)Focus on the guidance of reflection,and induction refining.Implications for mathematics teaching:(1)Pay attention to the process,so as to promote the understanding of mathematics,(2)improve the effectiveness of teaching design.