An Empirical Study Of The Influence Of Cognitive Structure Of Junior Middle School Students On Mathematical Modeling Ability

With the deepening of mathematics teaching reform, people pay more and more attention to the relationship between mathematical knowledge and the real life. Note that mathematical modeling is one of important parts related to students’ learning. It is quite sensible for the teachers to know the level of students’ mathematical modeling ability and corresponding influencement. In this paper, we study the level of the mathematical modeling ability of the junior high school sophomores, and further explore the factors that influence the ability of mathematical modeling. 195 junior high school sophomores were randomly chosen as experimental subject, who were tested through cognitive structure questionnaires that compiled by the concept map and CPFS structure and test paper that is the integrated from the PISA and secondary exam in the respect of mathematical modeling capability. We then explore the level of the students’cognitive structure and mathematical modeling ability. Besides the differences in cognitive structure and mathematical modeling ability between the students of different gender are also disussed. At last, we analyze the relationship between the cognitive structure and the ability of mathematical modeling among the grade-two juniors.The conclusions are drawn as followed:(1) In general, the cognitive structure of the second grade students were at the middle level, in which there was no significant discrimination between girls and boys while the former was slightly higher. A significant difference was found between the low, middle and high cognitive groups. Equally, there was no significant difference in gender among these groups. However, the average cognitive structure of boys in the high and the middle cognitive structure groups was higher than that of girls. In contrast,the average cognitive structure of girls in the low cognitive structure group was higher than that of boys.(2) The average mathematics modeling level of the second grade students is not high that most of the students are in the level one and some students are at the level two.The students’ mathematical modeling ability is significantly dependent on genders, that the average level of the boys’ mathematical modeling is higher than that of the girls.(3) The mathematics cognition structure of grade two students was positively correlated with the mathematical modeling level.(4) There differences in the level of mathematical modeling are found significantly among various cognitive groups. In particular, the students with the high, middle and low cognitive show a higher, moderate and lower level of mathematical modeling respectively.(5) There was no significant difference in the level of mathematical modeling between different genders of various cognitive groups, but the average mathematical modeling level of boys was higher than that of the girls. In addition, the main effect of gender and cognitive structure on mathematical modeling level was significant,whereas the interaction between gender and cognitive structure had no significant effect on the mathematical modeling level.(6) It is suggested that the level of students’ cognitive structure can be served as predictor of their mathematical modeling ability.