A study of the precision effect of modeling ideas in the teaching of advanced mathematics applications

Mathematical modeling as a means of application of mathematical knowledge is used to solve all kinds of problems in the real world, based on the simplification of real scenarios to get the simulation linkage model, and further generate mathematical models. In this paper, we design a teaching method for integrating mathematical modeling ideas into higher mathematics, and construct a path for cultivating modeling abilities. To develop the relevant analysis, a principal component analysis framework for assessing college students’ self-efficacy in modeling ability is proposed, and its influencing factors are analyzed by multiple linear regression. To have a more comprehensive understanding of the current status of students’ modeling ability, students’ self-efficacy for mathematical modeling and mathematical modeling ability were mapped based on the scale and the pre-test paper, respectively. It was found that most of the students’ perceived self-modeling hypothesis ability scored between [4,5] points, and the scores would significantly affect the two dimensions of self-efficacy in model building (0.001) and model analyzing (0.004) ability. Regarding the number of high scores, the experimental class was 13 and the control class was 8. Regarding the percentage of high scores, the experimental class is higher than the control class in all cases. Mathematical modeling ideas integrated into the real-problem teaching mode can improve students’ academic performance compared to traditional teaching modes.