The Correlation Between CPFS Structure Level And Problem Solving Ability Of High School Students

Vector has the dual properties of algebra and geometry.It is an important carrier to solve the problem of form by number operation.It embodies the important mathematical thoughts such as the combination of number and form,and is an excellent problem-solving tool.It can also be related to many mathematical knowledge points.Vector has a rich physical background and is the link to realize interdisciplinary communication.However,most students do not have a deep learning depth of plane vector and stay in the operation stage of plane vector.They do not have a deep understanding of the tool of plane vector and are not strong in solving problems with the application of plane vector.To learn mathematics is to develop the individual cognitive structure of mathematics.The development of high school students’ mathematical cognitive structure will have an important impact on their mathematical problem-solving ability.CPFS structure,as a unique mathematical cognitive structure,guides students to understand the relationship and rule between concepts and propositions from more angles and more logically,which is conducive to enhancing students’ interest and sense of achievement in learning mathematics.At the present stage,the main way to investigate the effect of students’ learning of high school mathematics is to solve problems,so most teachers use "Excessive Assignments Tactic" to improve students’ problem-solving ability.Although there is a certain memorization effect,mechanical training is far worse than students’ active understanding of problem-solving methods,such as improving their CPFS structure.In this paper,some students in Grade two and Grade three of high school were investigated on the structure and problem solving ability of planar vector CPFS by the method of test paper.SPSS26.0 was used to complete the statistical analysis of the data.Some teachers were interviewed on the confusion of planar vector teaching by the method of teacher interview.Combined with the above research results,this paper analyzes the structure of planar vector CPFS and the current situation of problem solving ability of high school students and their correlation,and concludes the following conclusions:1.The CPFS structure of the overall plane vector of the subjects was at the lower level.Gender does not affect the structure of planar vector CPFS for high school students.Grade difference will affect,specifically in the high CPFS structure group;Liberal arts and sciences were also one of the influencing factors.The main students in the low CPFS group were liberal arts students.In the middle CPFS structure group,there were differences in grade,arts and sciences,but the differences were not significant.2.The overall plane vector problem solving ability of the subjects was at a medium level.Grade and subjects choosing(arts and sciences)are important factors affecting the plane vector problem solving ability of high school students.The difference of grade mainly affects group A,while the difference of arts and sciences mainly affects group C,and gender does not affect the plane vector problem solving ability.3.The P value of the significance of CPFS structure and problem-solving ability of high school students was 0.000(less than 0.01),and the Pearson coefficient was0.946(more than 0),indicating that there was a significant positive correlation between CPFS structure and problem-solving ability,and there was a causal relationship between them.4.In the teaching of plane vectors,teachers have problems such as insufficient natural and fluent explanation of concepts,and lack of derivation of propositions in proposition teaching,which leads to students’ mechanical memorization of relevant propositions and weak application ability of solving analytic geometry,trigonometric functions,inequalities and other mathematical problems with plane vectors.Combined with the research results,the teaching strategies based on CPFS structure theory to improve students’ plane vector problem solving ability are proposed as follows:(1)Attach importance to the concept formation process and optimize the concept domain;(2)Attach importance to teaching students in accordance with their aptitude and form an appropriate conceptual system;(3)Effectively ask questions in class and make clear the connection between propositions;(4)To strengthen the application of vector,students can experience the instrumentality of vector.