The essence of mathematical modeling thought is to cultivate students' ability to use mathematical knowledge flexibly to solve practical problems. In this process, we need to cultivate students' mathematical abilities such as abstract thinking, simplified thinking and critical thinking.

1 Mathematical modeling needs abstract thinking.

By analyzing the establishment and solving process of the above model, we can find that abstract thinking and deep understanding and thorough analysis of the basic concepts of higher mathematics are indispensable for solving problems.

When solving the 1 problem, we closely combined the concepts of "absolute water inflow" and "relative water inflow", analyzed every information contained in the concepts, found the calculation formulas of "absolute water inflow" and "relative water inflow", and established the mathematical model i. 。

It can be seen that the complex practical problems should be reduced to the related concepts and definitions of higher mathematics, and the calculation formula should be found by using the definitions, so as to establish the mathematical model. Abstract thinking plays a key role in this layer-by-layer analysis process. It is this layer-by-layer analysis that solves complex problems. So mathematical modeling needs abstract thinking.

2 Mathematical modeling needs to simplify thinking

The so-called simplified thinking is to simplify complex problems and highlight their essence. Just like x-ray, remove the flesh and leave the skeleton. Only by grasping the main contradiction quickly, abandoning the secondary factors and finding the essence of the problem can we "see through" the essence of the problem.

For example, to distinguish whether a mine belongs to a "low-gas mine" or a "high-gas mine", in essence, we need to make clear the "absolute discharge" and "relative discharge" first, and then compare them with the standard values; The possibility of coal mine explosion is actually a probability problem; The optimal (total) ventilation required by this coal mine is essentially an optimization problem, that is, a linear programming problem with constraints.

This simplified thinking has profound characteristics. It is not innate, but can be formed through careful training and strengthened through hard exercise. In the teaching process of advanced mathematics, it is necessary to cultivate students' profound insight.

3 Mathematical modeling needs critical thinking

After the mathematical model is established and solved, we need to analyze the obtained results, evaluate the established mathematical model, and improve the model in time to obtain the best results. At the same time, it is necessary to point out the practical significance of the established model and try to popularize it. All these links need good critical thinking.

In the teaching process of advanced mathematics, we need to cultivate students' critical thinking. After each problem is solved, we should carry out this kind of reflection training after solving, and keep asking questions: Is the result right? Realistic? What are the advantages and disadvantages of this solution? Is there a better solution? How to improve? Can it be promoted? ..... In this training process, students' critical thinking will be strengthened and improved.

References:

[1] Jiang Qiyuan. Mathematical Experiment and Mathematical Modeling [J]. Practice and Understanding of Mathematics, 200 1(5)

[2] Li Daqian. Integrating the idea of mathematical modeling into the main course of mathematics [J]. Journal of Engineering Mathematics, 2005(8)

[3] Geng Xiurong. Monitoring model of coal mine gas and coal dust [J]. Journal of Guilin Institute of Aerospace Technology, 2006(4)

[4] Gao Zhaolian, et al. Coal mine gas and coal dust monitoring model [J].2007-2006 National Mathematical Modeling Competition for College Students Guangxi Division experience exchange and excellent paper selection (1)