Research On Teaching Design Of "Solving Triangle" Based On CPFS Structure Theory

With the implementation of the new curriculum reform in 2013,the content and structure of senior high school mathematics curriculum have changed."Solving triangle" in the new PEP mathematics textbook,located in the first chapter of compulsory 5,plays an important role in connecting the preceding and the following.It is not only the hot spot of college entrance examination,but also an important tool to solve measurement problems in real life."Solving triangles" includes the exploration,proof and application of sine and cosine theorems,as well as the application examples in real life.In college entrance examination,it often combines the properties of triangles,trigonometric functions,sequence,plane(solid)geometry and other knowledge.The more knowledge points involved in the problem,the more difficult it is for students to understand it.They need a correct,clear and complete mathematical cognitive structure.Good mathematical cognitive structure can help students absorb new knowledge faster and more firmly.CPFS structure is a kind of cognitive structure that can help students understand,remember and use mathematical concepts and propositions.Among them,C stands for concept,P stands for proposition,F stands for field,S stands for system.CPFS structure is composed of concept field,concept system,proposition field and proposition system.It is a kind of mathematical knowledge network internalized in the mind of learners,which is helpful to mathematics learning.On the one hand,CPFS structure can help learners to organize and memorize knowledge and strengthen their understanding of knowledge;on the other hand,CPFS structure contains knowledge and methods,which is the basis of problem solving and can improve the effect of problem solving.Based on this,this paper studies the teaching design of "solution triangle" with the help of CPFS structure theory,and further carries out educational experiments.This paper selects two classes in grade two of X Middle School in G province and G city as the test objects,and some teachers in the mathematics teaching and research group of grade two as the interview objects to conduct educational research.First of all,through the pretest,understand the CPFS structure of the two classes and the corresponding knowledge of problem-solving situation,and interview the teachers to know the teaching situation.Then,combined with CPFS structure theory,the teaching design of "sine theorem","cosine theorem" and "application examples" is carried out,and experiments are carried out.The experimental class was taught according to the teaching design of CPFS structure theory,while the control class was taught normally.Finally,the test results of the two classes are obtained through the experiment,and the conclusions are drawn after the analysis with the help of SPSS0.24 :(1)the teaching design of "solving triangle" based on CPFS structure theory can deepen students' understanding,proof and application of sine and cosine theorems.(2)The teaching design of "triangle solution" based on CPFS structure theory can help students to construct a good "triangle solution" CPFS structure and solve related problems.(3)In the problem of solving triangles,the average score gap between CPFS teaching and traditional teaching is related to the complexity of the problem.The more complex the topic is,the larger the average score gap is,and vice versa.After interviews with teachers,it is found that most of the teachers affirm the teaching design based on CPFS structure theory,and are willing to try it in the future.