Research On Ability Of Solving Trigonometric Function Problem Based On CPFS Structure In Senior Middle School

In essence,the process of mathematics learning is the formation,development and perfection of mathematics cognitive structure in the individual mind.Whether the cognitive structure is perfect or not directly affects the effect of mathematics learning,and then affects the ability of solving problems.Problem solving ability is the key to mathematics learning,and the mastery of concepts and propositions is the basis of mathematics learning.Trigonometric function is one of the important contents of senior high school mathematics curriculum,is the basic tool to study periodic phenomenon,and has a close relationship with other disciplines.However,due to the features of abstract trigonometric function,various formulas and wide range,students need to build a good knowledge structure to flexibly use these knowledge to solve problems.The CPFS structure proposed by Professor Yu Ping is a unique cognitive structure in mathematics learning.It is a knowledge structure that internalizes concepts and propositions in an individual's mind and conforms to the characteristics of mathematical logic.Therefore,this paper takes the problem-solving ability of high school students' trigonometric function as the starting point to explore the influence of individual CPFS structure on their problem-solving ability,which has practical significance for improving the learning of trigonometric function of high school students.Based on the theory of CPFS structure,this study selects two students from two parallel classes of senior one in a middle school in Changchun City to investigate the structure and problem-solving ability of the trigonometric function CPFS:This paper investigates the current CPFS structure of trigonometric function and the ability of solving problems,and arranges the results of the investigation,andanalyzes the special cases of the papers.Conclusion: most of the students' CPFS structure and problem-solving ability are in the middle and upper level,but there are great differences among the students;some of the students' learning methods are not conducive to the construction of CPFS structure;with the help of SPSS to analyze the survey results,we can find that good CPFS structure and problem-solving ability have a significant positive correlation.Based on the investigation and analysis of trigonometric function and teaching design of CPFS structure,teaching practice is carried out in two classes,one is the experimental class and the other is the control class.During the experiment,the experimental class was intervened with CPFS structure teaching,and the control class was taught according to the original teaching plan.After the experiment,the students' ability of trigonometric function solving was tested.The test results show that the ability of solving trigonometric functions of the students in the experimental class has been improved.Based on the experimental results,this paper puts forward some teaching suggestions to improve the students' problem-solving ability by improving the triangle function CPFS structure of senior high school students.(1)Pay attention to the integrity and systematization of mathematical concepts;(2)Pay attention to guide students to experience the generation process of mathematical knowledge;(3)Pay attention to reveal the essence of concept at multiple levels,and gradually improve the conceptual domain and system;(4)Pay attention to the infiltration of mathematical thinking and methods,and improve the individual CPFS structure.Finally,the author analyzes the shortcomings of this study from the aspects of sample selection,program implementation process,cause mining,and looks forward tofurther research work from the aspects of research breadth,teaching content,knowledge structure,etc.