Research On The Correlation Between Trigonometric Function CPFS Structure And Problem-solving Ability Of High School Students

Learners' mathematical learning is closely related to cognitive structure.The CPFS structure of mathematical learning psychology is a cognitive structure unique to mathematics learners.Enriching and improving CPFS structure theory is also an important subject for mathematics educators.At present,the proposition method adopted in the college entrance examination mainly tests students' problem-solving ability.Many mathematical teachings still use "question-sea tactics" as a means to improve students' problem-solving ability.Although it does have a positive impact on improving students' academic performance,the Creativity and interest are being lost,which runs counter to the requirements of the curriculum standards.Trigonometric functions originate from people's research on astronomy,and have been enriched and developed in marine technology and surveying.It is inseparable from modern science and technology.Trigonometric functions occupy an important position in high school mathematics learning and are also a popular test site for the college entrance examination.Taking the CPFS structural test paper and problem solving ability test paper of high school students as the carrier,208 ordinary high school students in Jiangsu were tested,and the development status and correlation of the CPFS structure and problem solving ability of high school students with SPSS software were analyzed.The conclusions are as follows: The CPFS structure of trigonometry for most high school students is at a medium level.The CPFS structure of trigonometry for high school students has no significant difference in gender,significant difference in grades,and in four-star and three-star schools.There are very significant differences between them;most high school students 'trigonometric function solving ability is at a medium level,and high school students' trigonometric function solving ability has no significant difference in gender,and there are very significant differences in grades.There are very significant differences between three-star schools;high school students' trigonometric function CPFS structure and problem solving ability are significantly positively correlated at a level of 0.01,and high school students' trigonometric function CPFS structure has a causal relationship with problem solving ability.The trigonometric function CPFS structure has an 88.1 percent explanatory power to the trigonometric function solving ability.The trigonometric function CPFS structure caneffectively predict the trigonometric function solving ability.The non-standardized regression equation between the CPFS structure and problem solving ability of high school students is Y = 1.041 X + 39.327,and the standardized regression equation is Y= 0.939 X.According to the research conclusions,put forward teaching suggestions: reveal the concepts and propositions in the trigonometric functions from multiple angles,and help students establish the concept domain and the proposition domain;attach importance to the internal and external connections between the concepts and propositions of the trigonometric functions,and help students establish the concept department And propositions;teachers guide students through the process of knowledge generation,allowing students to independently establish and improve the trigonometric function CPFS structure.