The Study On Teaching Of Function In High School Based On APOS Theory

The fundamental goal in modern teaching is to promote the comprehensive development for each people . Today competition for survival in schools is increasingly fierce,it is necessary to find a teaching mode which can enhance teaching efficiency and can promote the student's diverse develpoment. In the 1980s the United States, the education reform had been carried out and proposed the slogan as "comprehensively improve the quality of education, education excellence, training for the 21st century work and life ".In 90's, from the government, the enterprise to the public school in America measures were taken to the reform ,They hoped the elementary and high middle schools education could enter the new century in the posture which was inceasingly enhanced by the quality. The APOS theory was produced and developed under this kind of background ,and had obtained the success in the American university educational reform ."Wise men learn by other men,s mistakes".We can benefit from it, and fusing it with our country educational reform, We may find the mode which suits for our country middle school educational reform .There were some educators in our country who introduced the APOS theory to the middle school educational reform, and obtained the certain effect in enhancing the teaching achievement. How this theory influences students'full scale development? Whether it suits for educational reform of all-around development in our country?This article draws up from the real diagnosis viewpoint, Through designing concrete teaching cases, carrying out teaching experiments for three months, we prove it is efficient to instruct the teaching for student's full scale development with the APOS theory .The function content is center in the entire algebra in high school. From the function concept development history, the function concept's developing process corresponds with the APOS theory four stages unconsciouly. The function concept's developing process ,the duality of function concept and the arrangement order of function content in high school--all above explain the feasibility of applying this theory .The function has important status in the high school knowledge system,and has the vital role in forming the student thought, these two views above explain the necessity in using the APOS theory. This research includes two parts: The theory mainly partially introduces the APOS theory's connotation, the epistemology essence, theoretical basis and the operation pattern;we choose two best classes, two ordinary classes, two artistic classes in the first middle school of Shandong Yiyuan city to carry out the measure, and the contrast experiment. This research had in the reference in the research foundation .the method used was the literature analysis, questionnaire, the experimental education law, and the combination of teaching cases. Mainly from the view that using the APOS theory to instruct teaching can enhance the teaching efficiency, it has proved the validity for student's full scale development, the tests include following several aspects:(1)Using students'performance before and after the test, we demonstrate the validity of improving students'learning achievement when the teaching was guided by APOS theory.(2) Using the teaching case, we explained the influence of enhancing the teaching efficiency in classroom instructed by the APOS theory. This highlights the following characteristics of the teaching mode : (i)The process of teaching is blended with cooperative and democratic thoughts.(ii) It is the reflexivity abstraction in forming the concept.(iii) The correlation in the knowledge is integrity.(3) Using interviews, we explain the influence to the students in solving the question when the teaching is guilded by APOS theory.(4) Using the experiment, we prove the influence to student's non- cognition factor when the teaching is instructed by APOS theory.(5) Using the experiment, we prove the influence to the correlation in function knowledge when the teaching is instructed by APOS theory.In this study, we have received the following conclusions : firstly, it can significantly improve teaching performance when teaching is instructed by APOS theory and it is suitable for the needs of the community; secondly ,it can fully mobilize the enthusiasm for study and improve teaching efficiency; thirdly, it can enhance student's ability to solve problems; fourthly, it make student's non-cognitive factors improve; fiftly, it is easier to construct the relevance between knowledge, and is easier to help student establish a more solid knowledge system.The APOS theory is effective for students'comprehensive development, so we make the following recommendations : firstly, we should pay attention to the double effects when the teaching is guided by APOS theory; secondly, the student can achieve full scale development; thirdly ,we should use the thinking mode of APOS theory to arrange teaching material.Finally,we propose our own understandings about the following problems: how to select sample in the study, how to choose teachers , how to select reliable examination papers, how to get supports in the reform, how to overcome limitations of APOS theory, and other limitatins of their own; and we have raised our future effort's direction of our research: how to use APOS theory dialectically, how to use APOS theory when we teach other theoretical knowledge, how to use APOS theory in"active teaching"?...