Conic Curve Concept Teaching Empirical Study Based On APOS Theory

Mathematical concept is the logical beginning of maths, the basis for students'cognition. It has an important position in mathematics study and the teaching. Since long ago, mathematics concepts teaching have usually been suggested in the way of Concept Form and Concept Assimilation. Most teachers adopt Concept Assimilation. This kind of teaching process is relatively simple and enable students to learn concepts more directly, and it is called " themost essential way for students to obtain mathematical concepts ". However, this teaching method emphases on teaching the logical structure of concepts. A quite universal tendency is not to take the process of teaching and knowledge seriously.Then various types of exercises are introduced by teachers and students have to do a large number of imitation and practice. Students are unable to utilize the concepts which they obtain through the classroom instruction actually isunable to perform to utilize, thus causing many average students and students who have difficulty in learning to make mistakes when solving problems because of misunderstanding the concepts. The traditional teaching method of the mathematical concept has led to a series of negative consequences. It runs counter to " to the development of students" , the basic idea of elementary education put forward by our country . It's advocated in the current curriculum standard that mathematical concepts teaching must be reverted to simplicity, reveals the formation of mathematical concepts, thus enabling students to multidimensionally understand the concepts from the prototype to abstract process, the guiding role of mathematical thinking, the use of symbols and forms of expression, which, conforms to the education principle of constructing the construction on their own initiative. Therefore, in order to promote the development of students, we must shift the concept teaching from the traditional model.American education experts Grosso (Ed Dubinsky) and so on, proposed APOS Theory in mathematics education research practice, which is very enlightening to concept teaching. The theory focuses on the specific contents, that is the learning process of the mathematical concept and proposes four stages to learn mathematics concepts, that is"activity", "process", "object", and "scheme". After the students learn mathematical concepts to "activities" and "process" and "targets", "plans" four stages. APOS theory stressed that the concept resides in real social backgrounds. Students experience its links with reality through activities, experience the integrity of the study process, and use methodology to establish the concept. Concepts based on this method contains a rich connotation, which contains the concept's prototype, abstract process, thinking method and formalization and so on. The goal of constrcting the mathematical concepts is achieved. It is consistent with"students taking the initiative"advocated in the New Curriculum Standard complies with the current mathematics education reform.Based on discussing and analyzing the APOS theory, the research applies the APOS theory to the conic curve concept teaching and further examines the implementation effects of the APOS theory concept educational mode being applied to tomathematics concept teaching. The research consists of the fundamental research and teaching empirical study. The fundamental research lays the foundation for teaching empirical study, and the latter also makes a better interpretation for the former. They support each other, which is our basic idea. On the basis of the related literatures, and based on the schema theory of constructivism theory, we analyse the four-phases of APOS theory, and explore the APOS theory concept teaching design and the implementation process, so as to provide theoretical support and teaching strategies for the development of the mathematics concept teaching research and the practical research. Empirical research covers 131 Senior 2 students in two classes in Liuzhou No 1 Middle School. In six months of research, from the preparation to the entire process, through questionnaire surveys, interviews, classroom observation, test analysis, analyze the data by using statistical analysis as a tool, combine with the actual classroom teaching, analyse feasibility and effectiveness or difficulty in implementing APOS theoretical concepts in the regular teaching. The key point is to compare students'mathematics results, mathematics interest, mathematical awareness of exploration between key class and the tested classes, as well as compare and analyse the teaching processes on the same teaching content between the two teaching modes, the APOS theory concepteducational mode and the traditional concept educational mode.Empirical research findings better fits the theoretical study. The results show that math concept teaching based on inspires students to participate in teaching and learning, stimulate students'interest in mathematics, enhance their understanding of the concept of conic curve, and do better in math. The APOS theory concept educational mode provides some room for students to research by themselves, find the problems and solve them. It's helpful to strengthen students'awareness of exploration and it demonstrates feasibility and effectiveness of the APOS theoretical mode.According to research and analysis of implementing the APOS theory concept educational mode in practical teaching, this article finally puts forward several suggestions in implementing the APOS theory concept teaching process. First, the four phases of APOS theory is a relatively continuous process. Each phase is indispensable during the establishment of a concept in the brain. Second, Creating situations is not the ultimate goal of the concept teaching. Concept teaching shouldn't stay on activities (operational) level, and take other stages hastily. Third, the establishment of mathematical concepts from the "process" to "targeted" needs to be repeated, step by step. Fourth, The object and thescheme stages should be stressed, and they can be recycled up. At last, the four stages are not necessarily reflected in a math class, nor every lesson must traverse the four stages. It applies to the establishment of a mathematical concept in the minds of students for a period of time, not limited to a certain class.