Secondary School Mathematics Concept Map Teaching Action Research

The study on Schema Theory gradually turns to specific subject fields as the theory becomes perfect and develops day by day. With the joint efforts made by numbers of scholars, great developments has been achieved in the schema study of the mathematics field. More and more proofs show that mathematical schema plays a very important role in the mathematical study activities.The study process and teaching method differ with respect to different types of mathematical schema. It reveals that the study process of different types of mathematical schema helps to develop effective teaching method, which helps to promote students' study. On the basis of predecessors' study and with reference to Study Result Classify Theory of Gagne, R.M., the article divides high school mathematical schema into different types and selects the mathematical Conceptual Schema as its study object. After careful sort-out and comprehensive analysis on the related studies of Schema Theory, the writer specifically analyzes the study process of high school mathematical Conceptual Schema and sets up the study and teaching process model of mathematical Conceptual Schema with reference to the APOS (Action,Process,Object,Schema) theory of Dubinsky, E. and integration of practical teaching experiences.In the process of further action study, we carry out teaching design, turn over to think teaching behavior, and summarize teaching experiences on the basis of process model. Thus, the teaching method has been formed finally, which can effectively promote students' study on Conceptual Schema. These teaching methods are: (1) to select proper examples; (2) to be visual and intuitive; (3) to use analogies; (4) to design operational action; (5) to draw Concept Map.Appraisal study of "Concept Map" further explains the differences of good students and bad students on creating mathematical Conceptual Schema, the most distinct differences is that the "Concept Map" made by bad students lacks of concrete examples related to the concept. As an appraisal tool, "Concept Map" can help teachers to diagnose the existing problems in the study of the students and adopt relevant remedies. For example, when students draw "Concept Map" every time, we put forward "listing concrete examples related to concept issues" as a specific requirement in order to promote students to actively review study process and form complete Conceptual Schema.