The Integration Study Of Variant Teaching And APOS Theory In The Study Of Mathematical Concepts

In the development process of the curriculum reform,more mathematics educators began teaching and learning about mathematical concepts,and advocates active and exploring ways of learning.Students can be independent,cooperative and inquiry,through activities,operating autonomously,active learning,is the basic requirement of new curriculum reform,and this change also focus on the development and arouse the potential of students,promote students' independent,comprehensive and distinctive development.The domestic and foreign research on APOS,the change of teaching in the aspects of theory and practice has been the emergence of a large number of results,but the domestic and foreign research on integration of APOS theory and teaching theory is still lacking.So far no in-depth research on integration of APOS theory and teaching theory.If we can in two mature theory based on the study of bold theoretical integration,so as to provide guidance for middle school mathematics concept teaching,will be a big breakthrough.This study will focus on from the concept of duality,if able to in-depth understanding of APOS theory and teaching theory,and explore the conformity,will be conducive to promoting the study of theoretical research and empirical teaching APOS variant teaching.From the theory research of APOS contact theory in the teaching.Based on the theory,to explore the integration of construction and integration of theoretical framework and specific content,and study the teaching forms and guiding significance-By the research of mathematical concepts of duality,teaching and learning of mathematics concept in the process of "object" and "operation and structural" are closely linked,especially in the process of change.In the first three stages of the APOS theory,namely activity process,process and object the loop demonstrates duality of mathematics concept learning in the importance of mathematics learning,which demonstrates the process of variant APOS theory and teaching of duality and mathematical concepts.Through the research on the relevance of the two theories,through the analysis of teaching cases of integration of the two theories,and construct the basic framework of integration theory.That is:change teaching theory in the lateral longitudinal APOS theory to get a variant of integrated teaching under the theory of APOS-V-APOS theory variant teaching;V,APOS represent the four stages of APOS theory.The author from the two major directions:process variation and conceptual variation,based on the specific teaching case and theory study,according to various stages of the APOS theory teaching form and guiding significance to do related research.The study shows that the integration of theoretical research will be conducive to the promotion of APOS and variable type the teaching of theoretical research and empirical teaching,make some contribution to the development of mathematics concept teaching in middle school.Finally,the author makes a summary and Reflection on the theoretical research,prospects,hope to be able to in the teaching practice,theory and practice,further study and perfect integration theory,fully integrated theory in middle school mathematics concept teaching,improve the ability that students of mathematics concept learning.