Research On The Understanding Level Of Limit Concept Of College Students Based On APOS Theory

This research is based on the APOS theory to evaluate the understanding level of the undergraduate normal students in the mathematics department of ordinary colleges and universities.Through empirical research,they analyze their specific performance in different stages of the APOS theory,and point out the existence of college students when constructing the concept of limit Typical problems and influencing factors,put forward teaching suggestions to improve the teaching of limit concept.In this study,data was collected in the form of a questionnaire.The subjects of the survey were students of mathematics majors in local colleges and universities.The subjects of the survey were all students who had taken the course of Mathematical Analysis.In this study,the data collected after the questionnaire test was quantitatively analyzed by SPSS21.0 software,followed by a qualitative analysis of the students' responses to the research methods such as classroom observation and interviews,and the following research conclusions and teaching suggestions were obtained:1.There is a hierarchical difference in the students' understanding of the limit concept,which is mainly manifested by the basic level structure that the APOS theory assumes.2.There is a big problem in the transition from the process stage to the object stage,which is mainly manifested as the difficulty to realize the "cohesion" process from the process to the object.3.Very few students can construct the schematic structure of the limit concept,which is mainly manifested as the difficulty of solving other related concepts and general principles from the limit perspective.4.Combining APOS theory and research conclusions to explore strategies for improving the teaching of limit concepts,specific suggestions are as follows:(1)Recognize limit relationships in "activities" with the help of intuitive mathematical objects;(2)Deep understanding of accurate limit process with strict limit language;(3)Dialectical understanding of biphasic infinity and comprehensive understanding of limit objects;(4)Understand the connection between concepts and construct the schema structure of the limit.