Cognizance Of The Function Conception Learning From The APOS Theory And The Teaching Suggestions

The function is an important mathematics model which describes the rules of the changes in the objective world, and it is one of the most important basic conceptions in mathematics of middle schools as well. Knowledge about function has always been regarded as the critical foundation of the further study of mathematics, however, it is also known as one of the most difficult conceptions for the middle school students in their studies. They can hardly get a thorough understanding of it. This thesis is based on constructivism, that is, APOS Theory, and makes an analysis on the construction process of the function studies. It then makes cognitive analysis on the typical problems which are easily found during the whole learning process. Finally some suggestions are raised about the function teaching.Chapter one is an introduction and it firstly claims the importance of the function conception to the mathematics teaching in middle schools together with the control conditions of the middle school students in their teaching practice. The main themes and topics of this thesis are also raised in this chapter.Chapter two makes a brief introduction to some respective viewpoints in cognitive theories and constructivism, and it also makes an overview of the two major means of study to the conception of mathematics and the theory of conception. Chapter three concentrates on the details of APOS theory, and it illustrates some cases of the function conception as well.Chapter five serves as the core of the thesis, and it makes a detailed analysis of construction layers in the teaching of the function conception in middle schools from the perspective of APOS theory. It raises the different aims of different construction layers, analyses the typical problems of the students in those previous layers, and also points out some suggestions for the teaching of the function conception in middle schools.In the following part, the thesis describes the developing stages of the function conception, and analyses the corresponding features, difficulties and problems it has confronted in different developing periods. It then suggests some key points which should be noted in the teaching of the function conception.