| APOS Theory is a Mathematical learning theory of constructivism.lt is proposed by American mathematics educator Ed Dubinsky in the practice of mathematics education research.This theory has obtained success when it was first used in American higher education reform in the1980s.Educators have brought APOS Theory into China’s secondary school education of funtion,curve and array.This thesis exploit APOS Theory to the teaching of the concept of the real numbers,then makes analysis on how to obtain good effect.Part one is an introduction about the importance of mathematical concepts,and pointed out the difficulties encountered by students learning the concept of real numbers and the importance of the concept of real numbers.On the basis of relevant research results,this thesis’s research and methods are proposed.Part two makes an introduction to this research’s theoretical basis,which include mathematical concepts and characteristics of the specific content of the four stages of APOS Theory,mathematical concept teaching model of APOS Theory,the teaching of mathematical concepts and the significance of APOS Theory in the teaching of mathematical concepts.Then pointed out that the APOS Theory reflects the mathematical concepts from concrete operations to abstract the process of psychological structure,in line with students’ cognitive development law.Part three analysis of the concept of real numbers in the textbook,the curriculum standards of the concept of real numbers and textbook content arrangement and the influence of learning this concept in students’ math ability.Then analysis the difficulties secondary school students will face during learning this concept,and the feasibility and necessity of APOS Theory applied to the teaching of this concept.Part four specify the arrangement of teaching process about the concept of the real numbers,then the content and notes when use APOS Theory to teach the concept of real numbers.Finally,there is a teaching case about the concept of real numbers based on APOS Theory.Postscript part of this thesis pointed out the innovation and inadequacies of this paper and the direction of my efforts in the future. |
