Question 1: What is model thinking? Model thinking method is one of the most common and widely used mathematical thinking methods in senior high school teaching. Mathematics in senior one is the starting point for students to learn in senior high school. Teachers should properly infiltrate the mathematical model thinking method in the teaching process of this book, which can not only visualize the mathematical problems in this book and make them easy for students to understand, but also improve students' initiative and thinking ability to analyze problems independently and form good thinking habits. At the same time, as an undergraduate majoring in normal mathematics, he will generally engage in the teaching of mathematics in senior one, and this paper can play a certain guiding role. This paper refers to all kinds of literature and combines with the current relevant mathematics teaching theories. Starting from the specific processes and methods that appear in mathematics classroom, it mainly discusses how to infiltrate the mathematical model thinking method in senior one mathematics teaching and what problems should be paid attention to in the use process. Mathematical model of keywords; Thinking; Teaching; Generally speaking, the mathematical model is a mathematical structure model expressed abstractly, generally or approximately by using formal mathematical language and referring to the main characteristics and relations of an objective thing. All mathematical concepts, mathematical theoretical systems, various mathematical formulas, various equations, various functional relationships, and an algorithm system composed of a series of formulas can be called mathematical models. These models are organically combined through the processing and logical processing of teaching methods, which constitutes the middle school mathematics knowledge system. In this sense, we can say that middle school mathematics teaching is actually the teaching of mathematical models, and the method of solving related problems by constructing mathematical models is called mathematical model thinking method. With the development of science and technology, especially the wide application of modern computers and the digitalization of science and technology, the method of solving practical problems by constructing mathematical models has been widely used in natural science, engineering technology and social science. Appropriate infiltration of mathematical model thinking method in middle school mathematics teaching can visualize abstract mathematical knowledge and play a great role in cultivating students' observation and analysis ability and logical thinking ability. Make it easier for students to understand, deepen their memory and use their knowledge and mathematics flexibly. Senior one mathematics is the starting point for students to learn mathematics in senior high school. Because students have just entered junior high school, they have mastered some elementary mathematics knowledge and formed a basic way of thinking, but they have not yet formed a systematic understanding of mathematical model thinking methods and have not had enough practical experience. Moreover, the teaching of mathematics in senior one involves the most widely used content in senior high school-function. Therefore, infiltrating mathematical model thinking method at the beginning of senior high school will help students gradually form good thinking habits and improve their mathematical knowledge and problem-solving ability. At present, quality education advocates the change from the method of emphasizing teaching to the method of emphasizing learning. Students are the main body of learning and teachers are the instructors. How to explore the potential mathematical model thinking methods in the content of teaching materials and guide students to apply them imperceptibly in teaching is the ability that a middle school mathematics teacher should have. The thinking method of mathematical model can be applied to conventional mathematical problems and other practical problems in the teaching of this textbook. To establish a mathematical model of practical problems requires some insight and imagination, screening and discarding secondary factors, highlighting the main factors, and making appropriate abstraction and simplification. The whole process is generally divided into several stages: expression, solution, explanation and verification, and through these stages, the cycle from physical object to mathematical model and then from mathematical model to physical object is completed, which can be expressed as follows: Figure 1 application flow chart of mathematical model thinking method Of course, in the process of solving conventional mathematical problems, it is more common to transform the mathematical model reflected by existing problems into another mathematical model in order to obtain the best way to solve problems. Therefore, in most cases, the specific steps are different when using mathematical model thinking method for different topics, but the most important thing is how to establish a suitable model to make the problem easier to solve.

Question 2: What is the idea of mathematical modeling? The essence is to cultivate students' ability to solve practical problems flexibly by using mathematical knowledge. 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 thorough understanding and analysis of the basic concepts of higher mathematics are indispensable in 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 can be found by using the definitions, so as to establish the mathematical model. Abstract thinking plays a key role in this process of layer-by-layer analysis. It is this layer-by-layer analysis that enables complex problems to be solved. So mathematical modeling needs abstract thinking.

2 Mathematical modeling needs to simplify thinking

The so-called simplified thinking is to simplify complex problems and then highlight the essence. Just like X-rays, the flesh and blood are removed, leaving only 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, we should also point out the practical significance of this model and 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.

Question 3: What advanced mathematical ideas are mainly used in establishing mathematical models? All thoughts and ideas may be involved.