A Study On The Correlation Between Mathematical Cognitive Structure And Mathematical Modeling Ability Of High School Students

With the deepening of curriculum reform,mathematical modeling,which plays a significant role in developing students’ mathematics inquiry ability and mathematics application consciousness,as one of the six core competencies and values and the bridge connecting the reality world and Mathematics,attaches more and more attention from educators and students.As a knowledge structure reflecting students’ degree of knowledge integration,mathematical cognitive structure is one of the influencing factors of the level of modeling ability,functions as the basis for students to carry out mathematical modeling activities.At present,few researchers select senor high school students as participants to analyze their mathematical cognitive structure and mathematical modeling ability at the same time.Thus,this study aimed at researching on students’ mathematical cognitive structure and mathematical modeling ability as well as their connections and furthermore proposing meaningful strategies is of realistic value.With the CPFS structure,the mathematical cognitive structure test paper was compiled combining the concept map theory,and the mathematical modeling ability test paper was adapted from typical college entrance examination questions with mathematical modeling features.This study selected 186 senior grade two students as research participants to have a overview of students’ current mathematical cognitive structure and mathematical modeling ability,and furthermore explore whether they are influenced by class levels,gender factors and the relationship between the two by means of data analysis.Finally,two abilities improvement strategies are given respectively.The results are as follows:(1)The level of mathematical cognitive structure of senior two students is lower-middle;the level of mathematical cognitive structure of boys is slightly higher than that of girls,but there is no significant difference;there exists significant difference in mathematical cognitive structure of students of three levels,with girls in high cognitive structure group performing slightly better and boys in middle and low cognitive structure groups performing slightly better;the mathematical cognitive structure of intensive class students is significantly better than that of ordinary class students.(2)The level of mathematical modeling ability of senior two students is upper-middle level;gender has little influence on the mathematical modeling ability;the mathematical modeling ability of the intensive class students is significantly better than that of the ordinary class students.(3)Gender has little effect on mathematical modeling ability in different cognitive structure groups.In the group with high level of mathematical cognitive structure,boys have better mathematical modeling ability than girls while in the group with medium and low level of cognitive structure,girls have better mathematical modeling ability than boys.(4)There is a significant positive correlation between the level of mathematical cognitive structure and the ability of mathematical modeling ability.The higher students’ mathematical cognitive structure level is,the better their mathematical modeling ability will be.The mathematical cognitive structure plays a significant role in the prediction of mathematical modeling ability.Finally,from the teacher’s point of view,the strategies for improving students’ mathematical cognitive structure and modeling ability are given.