Cultivation of Modeling Consciousness in Middle School Mathematics Teaching Application and Modeling in Middle School Mathematics

Abstract: Cultivating the consciousness of mathematical modeling in middle school mathematics teaching is a direction of middle school mathematics teaching reform. This paper discusses the ways to cultivate students' awareness of mathematical modeling, and expounds the significance of mathematical modeling in changing students' learning methods, cultivating students' awareness of applied mathematics and innovative ability, so that students can experience the role of mathematics in solving practical problems, promote students to gradually form and develop their awareness of applied mathematics, and improve their practical ability.

Keywords: innovative ability of mathematical modeling application consciousness

First, the empirical analysis of cultivating modeling consciousness in middle school mathematics teaching

1. Possibility certificate

There are many problems in daily life, such as mortgage to buy a house, profit maximization of enterprises, shopping, tourism and production scheme selection, which can be solved by using the basic knowledge of middle school mathematics and establishing elementary mathematical models. Here is a concrete example to illustrate the application of mathematical modeling in middle school mathematics teaching and the possibility of cultivating mathematical modeling consciousness.

For example, how to design the ratio of the height to the radius of the bottom of the can, so as to save the material of the can.

Model assumption: to simplify the discussion, we set it as a right cylinder, and the thickness of the top and bottom is three times that of other parts (because the strength of the top and bottom of the tank must be greater to ensure the opening). The corresponding variables and parameters are:

V- the volume of canned drinks

R radius

B- thickness of aluminum material for tank

P- Flange length that must be required in the manufacturing process.

H- cylinder height

It is almost exactly the same as the above calculation! You can also take the folding factor into account, then get the corresponding mathematical model and solve it, and finally see how it conforms to the actual situation.

Model generalization: in this problem, our research object is only cans. In fact, there are many problems similar to cans in our life, such as beer bottles, shampoo bottles, cups and so on. Therefore, we can completely extend this model to any shape container with volume V(V optional), and even to any shape tank with mass M. It can be seen that this model has a wide range of applications for similar tanks, and we can all get the optimal design of many graphics through this model.

2. Necessity analysis

Schumfield, an American math educator, has a math test worth thinking about: "There are 75 cows and 32 sheep on a boat. How old is the captain? " Such a topic has actually been done by students: 75-32=43 years old. Why is there such a ridiculous answer? I think the reason is that exams have almost become the only purpose for students to learn mathematics, and the knowledge they have learned has little connection with daily life and other disciplines, which makes students lack the consciousness of applying mathematics to practice.

In recent international conferences on mathematics education, "problem solving, modeling and application" has been included in several major research topics. In the new mathematics syllabus of senior high schools in China, it has also been clearly stated that it is necessary to "effectively cultivate students' ability to solve practical problems", and it is required to "enhance the awareness of using mathematics, be able to initially solve practical problems by using mathematical models, gradually learn to reduce practical problems to mathematical models, and then use mathematical methods to explore, guess, judge, prove, calculate and test, so as to solve problems". Therefore, the current middle school mathematics teaching is gradually changing from simple mathematics theory teaching in the past to applied mathematics teaching close to real life, and mathematical modeling is the source of mathematics application and the breakthrough of new curriculum reform, so it is imperative to cultivate students' mathematical modeling consciousness in middle school mathematics teaching.

Second, master mathematical modeling methods and cultivate mathematical modeling consciousness.

1. Mathematical modeling and mathematical modeling methods

The so-called mathematical model refers to a mathematical structure obtained by a specific research object in the real world, making some necessary simplified assumptions and using appropriate mathematical tools for a specific purpose and in accordance with unique internal laws. Mathematical structures can be mathematical formulas, algorithms, tables, charts, etc. Many basic concepts in mathematics are mostly abstracted from their corresponding realistic prototypes. Many mathematical formulas, equations and theorems are concrete mathematical models. For example, exponential function is a mathematical model, and many mathematical problems and even practical problems can be transformed into exponential functions to solve. By mathematicizing the problem, building a model and solving the test, it is called mathematical model method. Specifically, the operating procedure of the mathematical model method is roughly as follows:

2. Cultivate the consciousness of mathematical modeling

How to express a practical problem in production and life into a mathematical problem-mathematical modeling through appropriate assumptions, processing and abstraction, and then choose an appropriate and correct mathematical method to solve it, which is the key to applying mathematical knowledge to solve practical problems. This requires students not only to have certain abstract ability, but also to have considerable observation, analysis, synthesis and analogy ability. Of course, students' acquisition of this ability will not happen overnight. This requires that the consciousness of mathematical modeling should run through the whole teaching process, that is, constantly guiding students to observe, analyze and express various things, spatial relations and mathematical information from the viewpoint of mathematical thinking, and abstracting our familiar mathematical models from complex concrete problems, so as to achieve the purpose of solving practical problems with mathematical models and make mathematical modeling a method and habit for students to think about problems.

Third, the basic ways to cultivate the consciousness of mathematical modeling

1. According to the actual level of students, step by step. In mathematics teaching activities in middle schools, teachers should choose questions close to students' reality according to the principle of acceptable teaching and students' cognitive level, cultivate students' interest in mathematical modeling and develop students' mathematical application ability. At the same time, our mathematical modeling teaching should not stick to the form. We should choose typical problems close to life and social reality, excavate application examples from textbooks, conduct in-depth analysis, and gradually infiltrate the idea of mathematical modeling, so that students can change from "listening to mathematics" to "doing mathematics and using mathematics".

2. Fully tap the teaching materials to make the mathematical model come alive. Mathematics teaching reform pays more attention to the application of mathematics, emphasizing the extraction of mathematics problems from the reality of life and the knowledge of students. Therefore, we can use the current mathematics textbooks to introduce some commonly used and typical basic mathematical models to students, such as function model, equation model, inequality model, sequence model, probability model, geometric model, geometric curve model and so on. For example, in the teaching of exponential function, we can associate y= with bacterial reproduction, population growth, material decay, earthquake intensity and so on. As the arithmetic of the independent variables X, A, 2a, 3a, …, na, …, and the geometry of the dependent variable Y increase, there is an exponential function relationship between them. In a word, the idea of mathematical modeling should be constantly infiltrated in mathematics teaching, and at the same time, students should learn to bring mathematical models into life and experience the practicality of mathematical models, thus stimulating students' interest in applying mathematical modeling; At the same time, we should strengthen mathematics which is widely used in teaching, such as derivative, statistics, probability, linear programming, system analysis and decision-making.

3. Combining theory with practice, mathematical modeling of life problems. When integrating theory with practice, we should combine classroom teaching with students' actual level, and pay attention to the content that will help students adapt to their future life and cultivate their intelligence. For example, the derivative knowledge of senior three can be seen everywhere in life. For example, a cruise ship in a park paddles to the shore. When the waiter pulls the boat to the shore with a rope, he asks what is the relationship between the speed and acceleration of the boat and the speed of the rope. The problem of "pulling the boat to the shore", such as the optimization of grain storage in the school cafeteria, is an excellent example of derivative application.

Concluding remarks

Mathematical modeling is one of the best carriers to embody mathematical problem solving and mathematical thinking process. In teaching, we should persist in taking students as the main body, give full play to students' subjective initiative, let students consciously establish mathematical modeling consciousness in the learning process, free themselves from simple problem-solving skills and proofs, let students learn real mathematics, and realize that mathematics is living mathematics and closely related to life. In this way, the consciousness of mathematical modeling can be injected into students' skin with the flowing water of knowledge, transformed into beliefs and become the wealth that students enjoy for life. Only in this way can our mathematics education really embark on the correct track of quality education from exam-oriented education.

References:

[1] Yan Meilin. Cultivating Mathematical Modeling Consciousness and Developing Students' Innovative Thinking [J]. Journal of Jiangxi Institute of Education (Comprehensive Edition), Volume 26, 2005: 52-55-55.

[2] And Hui Fen. Set up modeling consciousness and cultivate innovative ability [J]. Exploration of Science Teaching, 2006, (4).

[3] Li Shangzhi. Teaching focuses on cultivating students' innovative vitality [J]. China Higher Education, 2004, (6).

[4] Wang Qidong. Innovative Education in Mathematics Teaching [J]. Bulletin of Mathematics, 200 1, (2).

Thanks, Fan Zhengsen. Mathematical modeling technology [M]. Beijing: China Water Resources and Hydropower Press, 2003.

[6] Ordinary high school mathematics curriculum standards (experimental draft) [M]. People's Education Press .2003.4.

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