Research On The Teaching Design Of High School Mathematics Concept Course Based On APOS Theory

The idea of “Student-centered,teacher-led” is more and more considered to be the most suitable educational idea for the development of students' cognition amid the development of the new curriculum reform in China.In today's subject teaching,teachers are more and more focuses on encouraging students to learn.In addition to the reform of one-sided knowledge education,the reform also has correcting the tendency to emphasize only knowledge transmission and training skills,and at the same time,strengthening inquiry teaching,cultivating students' sense of self-exploration and learning habit of active participation.Concept teaching is an indispensable part of mathematics teaching.As early as the 1990 s in the reform of American higher education,APOS theory has emerged and achieved initial results.APOS theory,which established on the basis of the characteristics of mathematics,is a kind of constructivist learning theory.APOS theory proposes that the learning of mathematical concepts goes through four stages: action,process,object and schema.It emphasizes that the concept of mathematics should be permeated in the practical background and have certain sociality.Its main content is to make students abstract the perceptual representation of concepts and the background of subjects in the process of learning mathematical activities.And it enables students to carry out exploratory thinking activities on the basis of the existing knowledge and experience,and realize the construction of mathematical concepts in the cognitive system.This construction process will enrich the connotation of mathematical concepts,including both reality prototype and abstract thinking schema.And it fits perfectly with the idea of student's initiative construction advocated by the New Curriculum Standard.As a basic and key content in modern mathematics,the concept of vector is a bridge connecting geometry and algebra,and also one of the tools used to express the real world.Teachers should have the awareness of training students' thinking ability in plane vector teaching and to make students understand mathematics better.Based on the comparison with the traditional teaching mode,this thesis takes plane vector as an example to study the application of APOS theory in concept class in senior high school.This thesis firstly summarizes the content of APOS theory and researches of mathematics concept teaching.Secondly,it compares the traditional teaching mode with the teaching mode under the guidance of APOS theory,and combines APOS theory with the teaching of mathematics concept course,and applies it to the teaching of plane vector concept course Finally,in the process of designing the case,it reflects continuously and forms the APOS theory teaching suggestion for the concept lesson teaching,and provides the guidance suggestion for the concept lesson teaching.