Apos Research On Application Of Theory In Mathematics Teaching

Mathematical concept studying, solving problems, cognitive problems and so on are the great concern issue of mathematical study. High school curriculum standards emphasize that teaching should appear the mathematical occurrence, development process in order to help students understand the mathematical knowledge. This is actually let the students construct knowledge actively. Based on the APOS theory, this article introduces the theory from different perspective of the cognitive psychology. The passage introduces the application in mathematical teaching, problem solving, and learning.First, combining with other learning theories explains and analysis the APOS theory. This article analysis the college students'learning process of the infinite concept study.Combining with the understanding,puts forward three stages of the teaching design. Through the design can help students understand the comprehensive and holistic of the concept, and provides a good reference for the teachers. The article does a comparative about the traditional classroom teaching and the APOS theory teaching.Second integrated with the middle school students'mental development and the cognitive law, through the investigation and detection and talking of the individuals to know the problems in mathematical study. Using the four stages of APOS theory analysis the students'thought process in the study, and put some proposals for teachers and students. For more effective to explain the theory, investigate the first year,the second year,the third year students in middle school and the high school students, have made varying degrees, different aspects of the investigation and inquiry mechanically, and detailed the research data, and analysis the data from different aspects.At last summary and reflect the finished paper, and has below conclusions:APOS theory can significantly improve teaching performances; APOS theory may help teachers to understand the students'thought disturbances; APOS theory can improve the students'problem solving abilities, enhance the student to summarize and the reflection abilities; Unifying the APOS theory to the teaching may be helpful in enhancing the students'study interesting, raise the students'mathematical study emotion; and it takes an important role in students'comprehensive development.