Variant Teaching Of Mathematics Concept Based On APOS Theory

With the promulgation of the curriculum standard of ordinary high school(2017),it is necessary to embody the teaching idea of taking students' development as the foundation and promoting the core accomplishment in mathematics teaching.The abstractness,logicality and wide application of mathematical concept determine its important position in middle school mathematics learning.The classical variant teaching theory of our country and the APOS theory of western authority are aimed at the concept teaching.By consulting a large number of relevant documents about APOS theory,variant teaching theory and mathematics concept teaching,we try to integrate these two theories.To provide a more effective model for the teaching of mathematical concepts,and to cultivate the students' core elements of mathematics.Raise.This article uses the literature review method,the case analysis method,the experiment research method,the investigation interview method and so on to carry on the research,the author through consult a large amount of related literature,It is found that both the APOS theory and the variable teaching theory are closely related to the duality of mathematical concepts,which provides a theoretical basis for integration.This paper analyzes the four stages of APOS theory,which are activity stage,process stage,object stage,schema stage and variant teaching,and forms four stages of mathematics concept teaching based on two theories.The variable teaching strategy is embedded in the teaching process,and the variable factors contained in the mathematics teaching material are deeply excavated,from various angles.By carefully designing the variation group,grasping the law of invariance in the process of change,applying modern information technology to optimize the concept variant classroom,finally a mathematical concept variant teaching model based on APOS theory is formed.In order to verify the practicability of this teaching model,the teaching cases and experiments which accord with the development of students' thinking are designed,and the results before and after the experiment are analyzed qualitatively and quantitatively.The research shows that this mathematical concept teaching model can promote students' meaningful learning,provide a certain reference for teachers to design teaching process and improve practical teaching efficiency.It can also enable students to form a multi-angle,multi-level,multi-dimensional understanding of the concept.Deeply grasp the essence of the concept,and improve the students' mathematical thinking ability at the same time.The research shows that the variable teaching model of mathematical concepts based on APOS theory is helpful to promote students' deep understanding of mathematical concepts,and information technology can also effectively assist variable teaching.However,the variable teaching model studied in this paper is still in its infancy.This model focuses on the variable strategies in the first two stages,and the strategy of how to form the conceptual schema needs to be perfected gradually in practice.