Study On The Importance Of Trigonometric Functions From The Perspective Of CPFS Structure

Trigonometric function is a key content in high school mathematics learning,but many students can not understand and apply it well.Based on the usual teaching experience,the author finds that if we understand the trigonometric function based on the concept of trigonometric function,we can fully understand the knowledge structure of trigonometric function.Professor Yu Ping of Nanjing Normal University proposed the CPFS structure of mathematics learning psychology.He believed that the CPFS structure was composed of concept field,concept system,proposition field and proposition system.Its meaning is that in the network of mathematical knowledge internalized in the ind:ividual mind,each knowledge point(concept,proposition)is in a certain position,and the connection between knowledge points represents a logical relationship.Thus,when a proposition is stimulated,it is activated at the node of the proposition,and then it is activated along the four links of the node.It spreads,searches and extracts relevant information,and finally forms a solution method.Based on the guidance of CPFS's cognitive theory,the author draws a knowledge structure diagram of trigonometric functions.The structure chart shows that the knowledge structure of trigonometric function is just centered on the concept of trigonometric function,so it is very important for students to form a perfect cognitive structure of CPFS.In order to further verify this idea,the author interviews teachers and students,compiles questionnaires,investigates and analyses students,calculates statistical tests with SPSS software,and draws a conclusion from a statistical point of view:whether to grasp the concept of trigonometric function is closely related to whether to solve trigonometric function type of comprehensive questions.The relationship.Finally,the author puts forward effective suggestions on the teaching and learning of trigonometric function concept based on CPFS theory:1.Emphasizing on revealing the essential characteristics and internal relations of mathematical concept,making knowledge holistic and systematic;2.Guiding students to experience the generation process of concept personally,giving full play to students'subjective initiative in constructing cognitive structure.3.Multi-angle,multi-level reveal the process of knowledge generation,help students form a complete concept domain,concept system.