A Study On Teaching Strategies Of Integrating APOS Theory And Variation Teaching

The learning of mathematical concepts is the key to students’ good mathematical knowledge.In this regard,educators continue to pay attention to research on teaching mathematical concepts,thinking about how to guide students to understand mathematical concepts at a deeper level and thus help them grasp the essence of mathematical content.Researchers at home and abroad have made many pedagogical suggestions on how to learn mathematical concepts well,but many front-line teachers have difficulties in choosing a concept teaching method.It is worth studying how to choose a suitable teaching theory to guide the teaching of mathematical concepts more effectively.Variational teaching is one of the common teaching methods used by teachers in China,and APOS theory is proposed by foreign researchers specifically for the study of concept teaching,both theories are beneficial to the inquiry of mathematics concept teaching.In this regard,based on the integration of APOS theory and variable teaching,this paper takes plane geometry as an entry point to explore whether teaching strategies based on the integration of the two theories are effective in improving teaching effectiveness.Translated with www.Deep L.com/Translator(free version)This paper firstly adopts the literature method,through reading a lot of domestic and foreign research literature about APOS theory and variable teaching,to clarify the purpose and significance of the research as well as the current situation of research at home and abroad,so as to lay a theoretical foundation for the smooth development of the paper.Secondly,a questionnaire survey was administered to 327 students in the second year of the internship school in order to understand the difficulties and obstacles in learning plane geometry,and then to explore the teaching strategy of integrating APOS theory and variation teaching mode.Based on this teaching strategy,the experimental class was taught with plane geometry as the carrier;again,the teaching aspects of the experimental class and the control class were analyzed through comparative case analysis,and the effect of the experiment was analyzed to see whether there were significant differences in students’ performance and understanding level based on this teaching mode;finally,interviews were conducted with teachers and students to understand the recognition of this teaching strategy to obtain relevant research Finally,interviews were conducted with teachers and students to find out the acceptance of the teaching strategy and to obtain relevant research conclusions and teaching suggestions.In this study,we proposed a teaching strategy of plane geometry based on the integration of APOS theory and variation teaching,and applied the teaching strategy to the experimental class to verify the effectiveness of the teaching strategy.The research conclusions obtained are as follows.(1)According to the analysis of the questionnaire,students are not interested in learning plane geometry,and there are certain difficulties in knowledge and cognitive barriers.(2)To understand students’ knowledge difficulties and cognitive barriers in learning plane geometry,and to explore teaching strategies of plane geometry based on the integration of APOS theory and variation teaching: variation in the activity stage;variation in the process stage;variation in the object stage;variation in the diagramming stage.(3)The teaching strategies based on the integration of APOS theory and variation teaching were developed and the classroom teaching was effective.(4)Compared with the control class,the experimental class had better dimensional levels in the object and illustration stages.(5)Based on the teaching strategy of integrating APOS theory and variable teaching,there was a significant difference between the experimental class and the control class,especially for the middle and upper level students.(6)The teachers and students had positive attitudes toward the teaching strategy based on the integration of APOS theory and variable teaching,and it could stimulate learners’ enthusiasm.