Research On The Influence Of CPFS Structure On Mathematical Modeling For Second-year Students

With the development of modern science and technology,the relationship between mathematics and real life is more and more close.Mathematical modeling,as a bridge between the two,shows strong vitality.Mathematical modeling literacy has become one of the core mathematical literacy that students must have.As a special cognitive structure in mathematics,what is the relationship between CPFS structure and mathematical modeling ability? How does it affect the ability of mathematical modeling? Based on the analysis of the existing development of CPFS structure and mathematical modeling,this study designs two mini experiments based on the combination of research and experimental research in the empirical research.Taking173 junior middle school students in Nanjing and Suzhou of Jiangsu Province as subjects,the paper investigates the development of CPFS structure and mathematical modeling ability and the relationship between the two.The main conclusions are as follows:(1)The CPFS structure of Grade 8 students is lower than the medium level,and the CPFS structure level of students is quite different.Overall,the CPFS structure level varies from boys to girls,with a significantly better result of boys than girls.But the local diversity is not significant.(2)As a whole,the mathematical modeling ability of Grade 8 students is in the upper middle level.There are great differences among different students.A small number of students have very low mathematical modeling ability,so they need to establish basic mathematical modeling ability.The results of boys are a little higher than that of girls,but no significant difference between the two.In addition,through the analysis of the students’ specific answers,it is found that the proficiency of the Grade 8 students in the use of equation model needs to be improved,and the awareness of model testing also needs to be improved.(3)There is a remarkable and positive relationship between the CPFS structure and mathematical modeling ability of Grade 8 students,and students in three groups of CPFS structure group of high,middle and low show great difference in the mathematical modeling at zero point five level.This shows that if students have good CPFS structure,then they also have higher mathematical modeling ability;while students with poor CPFS structure have lower mathematical modeling ability.The ability of mathematical modeling can be predicted by the level of CPFS structure.(4)The linear regression model with CPFS structure score as independent variable and mathematical modeling score as dependent variable is Y = 11.266 +0.327 X,and 39.9% of mathematical modeling ability is caused by CPFS structure.(5)The results show that individual CPFS structure has a direct and significant impact on mathematical modeling ability;whether there is prompt or not has no direct impact on students’ mathematical modeling ability,that is,whether the level of CPFS structure is high or low,adding prompt information to subjects can not improve their mathematical modeling ability;the interaction between individual CPFS structure and whether there is prompt or not has no significant impact on students’ mathematical modeling ability.(6)Individual CPFS structure plays a key role in the development of mathematical modeling ability.Students with high-level CPFS structure can solve mathematical modeling problems more effectively and show higher mathematical modeling ability.For the students with low level of CPFS structure,even the training of mathematical modeling source problem can not effectively improve their mathematical modeling ability.(7)According to the results of empirical research,this paper puts forward some teaching strategies to improve students’ CPFS structure which include strengthening variant training to form CPFS structure;paying attention to classroom reflection to realize knowledge connection;establishing knowledge network to improve knowledge system.And the teaching strategies to improve students’ mathematical modeling ability include paying attention to daily teaching to infiltrate mathematical modeling ideas;summarizing mathematical models to cultivate mathematical modeling literacy;improving CPFS structure to improve mathematical modeling ability.