Teaching Design For Concept Of Conic Curve Based On APOS Theory

Mathematical concept is the cornerstone of the mathematics' building,the correct understanding and mastery of mathematical concepts is the prerequisite to learn mathematics.Conic section occupies a pivotal position in high school mathematics teaching,and its concept teaching is especially important,but there are many problems in students' study at present,such as the difficult to define the form of transformation and the application consciousness is not strong.Because the concept of conic section is used in the form of concept assimilation,these problems can not be solved effectively.In order to help students really understand and grasp the concept of conic,we must gradually reveal the essence of the concept reflected in the teaching,so that students can establish mental structure actively in the process of learning.APOS theory emphasizes that concept teaching should pay attention to the formation of concepts and the construction process of students' thinking,Meanwhile,it can individuals to establish appropriate mental structure in a phased teaching.Therefore,this study aims is to explore the teaching design of conic section concept based on APOS theory.Based on the present situation of teaching,this paper analyzes the concept teaching of conic section,and designs the concept teaching of conic section on the basis of APOS theory.First of all,this paper combs the current research situation of APOS Theory and conic section concept teaching through the literature research method,and lays the theoretical foundation for the research.Secondly,the present situation is investigated and analyzed by the way of interview and questionnaire among teachers and students respectively.The results show that: for the construction of conic section concept,most students can reach the two stages of operation and process,Nearly half of the students can reach the target stage,only a handful of students can reach the schematic stage.Thirdly,according to the problems existing in the present situation,the paper analyses the concept teaching of conic section from the operation,process,object and schematic stage of APOS theory respectively.Finally,based on the theory of APOS,the teaching design of the concept teaching of ellipse,hyperbola and parabola is carried out,and compared with the teaching design of conic section concept based on the theory of APOS.The results of comparison and analysis show that it can help students understand and grasp the concept of conic,there are several aspects to be affirmed: the design is based on the students' cognitive rules and psychological development sequence,and the spiral-ascending learning method enables the students to understand and master the concepts more deeply.Based on the present situation of teaching,this design can help teachers to recognize the problems existing in the teaching of conic section concept so as to better improve the teaching.The design divides the concept teaching into four stages with specific action behavior and goal,which provides teachers with specific operational model,and it is implemented easily by the first-line teachers in classroom teaching.This design uses the dynamic teaching software to assist the conic section concept teaching,to visualize the abstract concept and to meet the variable requirements of the action stage and object stage in the concept teaching.