| The new curriculum reform is based on the theory of multiple intelligence psychology and constructivism theory, the three-dimensional goal of new curriculum is knowledge and skill, process and method, emotion attitude and values. APOS theory was proposed by American scholar E. Dubinsky, which is based on Constructivism mathematics learning theory, its core is to guide the students in social cues in the learning of mathematical knowledge, mathematical problem situation, in order to construct their own mathematical thought. APOS theory focused on mathematics concept learning process research, it points out that the learning of mathematical concept is the process of construction, and shows that the construction has the order. In order to achieve the aim of constructing mathematics concept, in mathematics concept learning, the first processing mathematical problem should have social realistic background, and require students to experience a variety of mathematical activity, in the existing knowledge on the basis of experience in which the students thinking through operation and reflecting abstraction, the mathematical concept has the realistic background and form definition the necessary comprehensive, forming internal knowledge system. APOS pointed out the mathematical concept and way theory in abstract mathematics activity indirectly on the basis of Piaget’s theory.In this study the concept of function as the breakthrough point, to" high school function concept learning" research, mainly on the following three questions:(1) students’ awareness of the importance of the concept of function;(2) effects of high school freshmen function learning factor analysis, the students understanding of the concept of function level;(3) a preliminary formulation of the corresponding function concept teaching design. This paper tries to combine the APOS theory to high school function concept learning is analyzed, explored the function concept learning on different levels of students some typical errors and their causes, in order to function concept teaching enlightenment. On this basis, this paper formulates the function concept teaching design, in this case, the teaching process in accordance with the " cognitive conflict, creating teaching situation and experience variables to try to abstract summary and reflection learning process to improve application ability" this procedure step by step to deepen stage by stage, thinking, problem step by step for masterstroke perforative from beginning to end. This teaching process the initial manifestation of APOS theory in the four stage and the teaching activity process corresponding relations.This paper studies the concept of function in high school curriculum importance, through investigation analysis of the students, according to the education of practical teaching experience and teaching cases, analysis of the traditional teaching method of function concept teaching and in the APOS theory under the guidance of the concept of function teaching relation and difference. According to the function of the concept itself, combined with the condition of students’ learning and the students think which is the proper teaching methods, we believe that:APOS theory to the teaching of function concept is of guiding significance in the teaching practice, aiming at how to make good use of APOS theory, this paper puts forward the following five suggestions:(1) teachers to the rational use of materials, according to the students’ thinking process design learning activities;(2) teachers should learn some philosophy of education, to inspire and guide teaching;(3) teachers through feedback information about learning, teaching reflection;(4) teachers should be teaching influence character by environment to the students mathematical thinking, to show the mathematical thought and method;(5) teachers in teaching to enhance students’ applications of mathematics to solve practical problems and cultivate their consciousness, practical ability. |
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