The Research Of Application Of APOS Theory In The High School Mathematics Proposition Teaching

Mathematics originates from the abstraction of the real world.Based on the abstract structure,it understands and expresses the essence,relationship and law of things in the real world through symbolic operations,formal reasoning and model construction.Aiming to learn mathematical axiom,theorem,law,formula,property and so on,which we call mathematic proposition course,is an important fundamental course of mathematic.Only by learning mathematical proposition well can we seize the main idea of mathematic and enhance our cogitation to improve our mathematic accomplishment and the ability to solve the problem.Based on the study of the reflexive abstract theory of individual thinking,American mathematician Dubinsky discovered the characteristics of learners understanding mathematical concepts through continuous practice and put forward the relevant theory about mathematical concept learning.This theory holds that learners need to go through the following four stages in the learning process: the Action phase,the Process phase,the Object phase,and the Scheme phase,so it is called APOS theory.The good effect of APOS theory in guiding the teaching of high school mathematics concept class is widely recognized by scholars.So,can APOS theory guide the teaching of high school mathematical proposition?This is a groundbreaking question worth studying.This paper is divided into seven chapters.The first chapter is the introduction,mainly the purpose,significance and method of problem research.The second chapter is the teaching of high school mathematics proposition and its related theoretical basis.In this chapter,the author introduces the research on the teaching of high school mathematics proposition and the research status of APOS theory at home and abroad.In the following chapter 3,the author analyzes the feasibility of APOS theory for high school mathematics proposition teaching based on the connection and distinction between mathematical concepts and mathematical propositions.The fourth chapter is devoted to an investigation of the current situation of high school mathematics proposition teaching,combining with "feasibility analysis" and "teachingstatus analysis".In the fifth chapter,the author attempts to put forward the corresponding mathematics proposition teaching strategies,including: the mathematics proposition teaching activity stage strategy,the mathematical proposition teaching process stage strategy,the mathematical proposition teaching object stage strategy,the mathematical proposition teaching schema stage strategy,and combine the author's district-level open class to analyze specific cases.The sixth chapter is the application of theory to practice.Through a semester teaching experiment,the author verifies the validity of APOS theory for high school mathematics proposition teaching.In the last chapter,Chapter 7,the author summarizes the research and makes a reflection and a vision for the future.The author hopes this research can help teachers better carry out high school mathematics proposition teaching,help students master mathematical propositions,flexibly use definitions,axioms,theorems,inferences,formulas,etc.,deepen the understanding and application of mathematical thinking methods,and improve mathematics literacy and problem solving skills.