Study On The Correlation Between CPFS Structure And Mathematical Modeling Ability Of Individual High School Students

CPFS structural theory is a cognitive theory unique to mathematics.The establishment of mathematical models to solve real problems in mathematics is a sign of the close relationship between mathematics and life.In General High School Mathematics Curriculum Standard(2017 Edition),mathematical modeling is included in the curriculum system as one of the six core qualities of mathematics,and is a separate chapter incorporated into the new lyse A-version of the high school mathematics textbook.Therefore,in order to measure the cognitive ability and level of high school students on mathematical modeling by CPFS theory,it is of great significance for the development of mathematical modeling teaching and improvement of the mathematical modeling ability of high school students.In this dissertation,based on the structure theory of CPFS,the CPFS structure of mathematical modeling of high school students is measured,and some correlations and test results between the fine structure of CPFS and the level of mathematical modeling ability are analyzed and given.Segments and full class-time teaching examples,as well as outclass extracurricular development cases of mathematical modeling,are designed.Some teaching materials suitable for teaching part of mathematics modeling content in the new textbooks for high school are put forward.Some teaching suggestions for improving CPFS structure of the mathematical modeling are given.Firstly,the CPFS structure of different levels has significant differences in the test results of mathematical modeling.The students with better CPFS structure have higher levels of mathematical modeling,while the students with imperfect CPFS structure have lower levels of mathematical modeling.At the same time,it is also concluded that the influence of sex on the structure of CPFS in mathematical modeling is not significant.Secondly,through the analysis of the test results of individual CPFS structure and mathematical modeling levels,the test subjects were divided into three groups of high,medium and low CPFS in high school.The students of the high CPFS group have good understanding of the connotation and extension of mathematical modeling.They can form the knowledge chain of mathematical knowledge and explain the idea that can use mathematical combination to solve problems.They can use various methods to verify the correctness of propositions,establish the relationship model between variables and carry out hypothesis tests,and have strong mathematical ability.Students of the medium CPFS group can master the basic knowledge,but their basic skills are weak,their method is single.They cannot be flexible.They have low mathematical abstraction,intuitive imagination and mathematical computation.They can make judgments on the problem but can't provide a rigorous argument in the mathematical calculation of the relatively high frequency of errors,but they are lack of accurate calculation ability,and so they cannot do numerical combination better.The students in the low CPFS group do not have a solid grasp of the basic knowledge and cannot be connected to a good knowledge network.They are difficult in understanding mathematics,so they can not extract important text information into mathematical symbol language.They have very large obstacles on the models,so they cannot judge and prove the proposition.It is easier for them to give up solving the problem.Thirdly,based on the theory of CPFS structure and the results of the mathematical modeling test for high school students,some typical problems are selected.The segments of teaching,full class-time teaching examples,and outclass extracurricular development cases of mathematical modeling,are all designed.Finally,in view of the new teaching textbooks in high school,parts of suitable contents are present as mathematical modeling teaching.Furthermore,detailed teaching suggestions are given for improving the students' CPFS structure with respect to high,medium and low group are put forward by teaching student depending on their different levels of CPFS structure.