Research On Variable Teaching Of High School Mathematical Concepts Based On APOS Theory

Mathematical concepts are the basis of mathematical learning,The foundation,abstractness and universality of high school mathematical concepts determine the important position of mathematical concepts teaching in high school mathematical teaching.Because of the many characteristics of mathematical concepts,scholars at home and abroad have carried out in-depth research on "mathematical concepts" in the early stage.From the experience of Chinese teachers,It is clear that variable teaching is a traditional teaching theory related to concept,Foreign scholars have found that APOS theory is the most authoritative theory for mathematical concepts.Teachers would use appropriate teaching models and theories when teaching mathematical concepts,but although each theory has its own merits and differences,research has shown that using a single teaching theory is not very effective for students and has limitations.Based on the promulgation of general high school curriculum standards in2017 and the implementation of new high school mathematics textbooks in 2019,Mathematical teaching should be built on student development and the main goal is to cultivate students' mathematics core accomplishment.Therefore the author attempts to combine China's traditional variable teaching theory with foreign APOS theory for concept teaching,taking the advantages of both and filling their shortcomings to provide a more effective model and carry on the practice,in order to deepen students' understanding of mathematical concepts,improve their overall quality and develop their core literacy.Therefore,it can provide some references for front-line teachers in concept class.This thesis adopts literature research method,investigation method and experimental method for research and analysis.Through consulting and reading a large number of literature,the author sorted out the sources,history and research status,related concepts,theoretical elements and the relationship between various theoretical stages of variable teaching and APOS theory.This thesis summarizes the close relationship between them and their effects on concept teaching,thus providing a theoretical basis for the construction of variable teaching model of high school mathematical concepts based on APOS theory.In the early stage,the process of variable teaching and the four stages of APOS theory,including action stage,process stage,object stage and schema stage,are analyzed to form the variable teaching process of APOS theory.In the process of vertical deepening,the strategy of variable teaching is horizontally integrated,the nature of variable teaching is analyzed and explored with the help of teaching materials,and variable topics such as situation variable,problem variable and condition variable are set.Finally,the variable teaching model of high school mathematical concept based on APOS theory is formed.In order to verify the validity of the model,teaching cases and experiments were designed in accordance with the development of students' thinking,so as to conduct qualitative and quantitative analysis of students' scores before and after the experiment.The analysis results has shown that: for students,the function monotonicity based on APOS theory and the variable teaching model of power function have a positive impact on these two classes,which is helpful to deepen students' understanding of mathematical concepts from different angles and levels,and then can cultivate students' relevant mathematical core literacy.It can provide some references for teachers at the front line.The research shows that the variable teaching model of high school mathematical concepts based on APOS theory can promote students' deep understanding of mathematical concepts,construct the schema structure of corresponding knowledge,stimulate students' interest in learning,improve their comprehensive quality,and expect to provide concrete practical experience for high school mathematical concept class.However,the teaching model constructed in this thesis is still in the initial stage,the experimental time and the scope of the reasearch participants are limited,and the setting of variable questions in the teaching process is still at a relatively shallow stage,so the teaching model designed needs to be further improved and perfected.