Research On Collective Teaching Design Based On APOS Theory

APOS theory is a constructivist learning theory that attaches importance to the formation process of concepts,and encourages students to construct cognitive structure and acquire knowledge and abilities through mathematical activities,which conforms to the six core qualities,"four bases" and "four abilities" proposed by the new curriculum standards.As a language and tool,set is the basis for students to learn high school mathematics,but students have many difficulties in applying the collection knowledge to solve problems.This article attempts to integrate teaching design based on APOS theory and conducts empirical testing to explore the effect of APOS theory on high school mathematics concept teaching,and provide teaching design examples and teaching suggestions for concept teaching based on APOS theory.The first part of this article analyzes the new curriculum standards and asks questions.The second part uses the literature analysis method to sort out the relevant literature,and briefly describes the research status of APOS theory,theory of set,APOS theory and set teaching.The third part uses questionnaire survey and interview methods to investigate the mastery of the assembly part of a middle school in Chaoyang District of Shantou City,and get the following conclusions: Firstly,the completion of the activity stage of the concept of student assembly is poor and affects the overall picture Completion of the stage of formulating and schema transfer;secondly,the teacher did not provide enough examples or enough time to help students understand the concepts in the teaching of related concepts.The fourth part completed the teaching design of the definition of the set based on the APOS theory,the relationship between the sets,the calculation of the set,the overall scheme of the set and the transfer of the scheme,and then the first three teaching designs were designed in a middle school in Shantou City Chaoyang District 115 and 116 classes(experimental classes)are implemented in the teaching.The fifth part uses the questionnaire survey method to investigate the mastery level of the experimental class and the control class.The results show that the completion of the experimental class at each stage is basically better than that of the control class.Practical results show that teaching based on APOS theory can effectively help students master the concept of sets on the basis of accumulating sufficient experience in mathematical activities,so as to better use sets as languages and tools to solve other mathematical problems.The test results also suggest that it is necessary to strengthen the arrangement and feedback of after-class exercises to make up for the shortcomings of less training time in class based on APOS theory teaching.The sixth part puts forward the strategy of teaching based on APOS theoretical concepts: in-depth study of curriculum standards,timely update of teaching concepts;careful study of teaching materials and supplementary materials,and creative use of teaching materials;fully understand the level of students and pay attention to the recent development areas of students;ingeniously design problem situations,Guide students to improve their own cognitive structure.