Research On Function Teaching In Junior Middle School Based On APOS Theory

Function as an important part of mathematics in junior high school,its definition,image,properties and application are the key and difficult points of mathematics learning.Under the Compulsory Stage Mathematics Curriculum Standards and the Opinions on further reducing the homework burden and off-campus training of students in the compulsory education stage,teachers need to think about how to improve the efficiency of students’ learning of functions in the limited time in the class,how to develop students’ functional thinking,and enable students to master the relevant knowledge of functions with high quality.APOS theory has a positive effect on the teaching of the definition of function.APOS theory divides the process of mastering concepts into four stages:action,process,object,and schema.If it is applied to the teaching of functions’ knowledge and can also have a positive impact,it will be extremely improve the quality of teaching to a great extent.Therefore,this article first collects relevant information about APOS theory and function teaching in middle school,especially in junior high school through literature research method,and then based on APOS theory,conducts an overall analysis on the content of quadratic function in junior high school.Combines the results of interviews with teachers and students to make sure the experimental content is the image and properties of the quadratic function,and use experiments to judge the impact of APOS theory on the teaching of properties of function.Through experiments,we get the following conclusions:（1）Function teaching based on APOS theory has a positive impact on students’ interest in learning,understanding of relevant knowledge and application ability.（2）Function teaching based on APOS theory can develop students’ core literacy and improve their academic performance.The author summarizes some problems in function teaching through experiments:（1）Students’ participation in class is generally not high.（2）Teachers don’t give students enough time.Aiming at the experimental results of quadratic function images and properties and the problems in teaching practice,the following teaching inspirations are summarized:（1）Action stage: This stage is mainly to awaken the perceptual cognition of students.（2）Process stage:At this stage,students should be given enough time to carry out multiple independent thinking operations to form a process.（3）Object stage: At this stage,it is necessary to combine algebraic expressions and images,sort out the connotation and extension of knowledge,and present its unique attributes in the mind.（4）Schema stage:At this stage,students should be guided to construct the overall structure of knowledge in the form of mind maps,tabulations and images.