Mathematical modeling, as a way of mathematical learning, is a form of cultivating students' awareness of applying mathematics and cultivating students' mathematical literacy. The following is what I collected for you. Welcome to read the reference!

On the Practice of Mathematical Modeling in Higher Vocational Colleges

This paper briefly introduces mathematical modeling and its development history, discusses the design and implementation of mathematical modeling activities in higher vocational colleges, and carries out effective practice from three aspects.

Keywords: Mathematical Modeling and Mathematical Application Mathematics Teaching in Higher Vocational Colleges

With the deepening of educational reform and the strengthening of "mathematics application consciousness", the knowledge economy society has put forward new requirements for higher vocational mathematics. Mathematics teaching in higher vocational colleges should aim at solving practical problems with mathematics, and take mathematical modeling as the breakthrough of reform, so that students can learn to know and think about their living environment and society with mathematical thinking in the process of modeling [1], and cultivate students' innovative thinking ability and comprehensive quality.

A, mathematical model, mathematical modeling and the development of mathematical modeling [2]

There is no uniform and accurate definition of mathematical model. Generally speaking, "a mathematical model is an abstract simplified structure about a part of the real world and used for special purposes." Specifically, for a specific object in the real world, for a specific purpose, according to its unique internal laws, it is necessary to simplify assumptions and use appropriate mathematical tools to get a mathematical structure. Mathematical models involving practical problems also have the characteristics of abstraction, accuracy, non-prefabrication and deduction. According to the performance characteristics of the model and the different phenomena and processes described, there are four kinds of mathematical models: deterministic mathematical model, stochastic mathematical model, catastrophe mathematical model and fuzzy mathematical model. Of course, due to the complexity and diversity of real-world relations, some mathematical models may also be mixed mathematical models with several characteristics.

Mathematical modeling is the process of establishing mathematical model. Modeling is a process of scientific analysis, simplification and abstraction of the research object. The general steps of solving practical problems by mathematical modeling are: model preparation-model hypothesis-model composition-model solution-model analysis-model test-model application.

As early as 1970s, people of insight in many developed countries began to study and carry out mathematical modeling activities, and various modeling cases emerged one after another. Around the end of 1970s and the beginning of 1980s, the famous British University of Cambridge set up a mathematical modeling course for graduate students, and established the "OSGI" for research cooperation between Oxford University and industry. At the same time, in Europe, the United States and other industrialized countries, the content of mathematical modeling began to be formally included in the teaching plan of graduate students, college students and even middle school students, and the biennial "International Conference on Mathematical Modeling and Applied Teaching" was held in 1983 for regular exchanges. Since 1980s, mathematical modeling has become the main theme of international mathematical education reform, and the curriculum standards of all countries in the world more or less require that mathematical modeling be included in the curriculum of all grades. The Chinese Society of Industrial and Applied Mathematics began to hold the "National Mathematical Modeling League for College Students" from 1992, and developed into the "National Mathematical Modeling Competition for College Students". Taking the mathematical modeling competition as an opportunity, many universities in China integrate mathematical modeling into the teaching of mathematical courses, and set mathematical modeling, mathematical experiments and other related courses as basic courses and compulsory courses to cultivate students' comprehensive mathematical ability. Mathematics teaching must adapt to the actual needs of society. Introducing mathematical modeling into the classroom of higher vocational colleges not only meets the needs of mathematics teaching reform, but also conforms to the trend of social development. For higher vocational mathematics education and teaching, students should not only master mathematical calculation methods and logical thinking, but also cultivate their awareness and ability to analyze and solve practical problems by using mathematical tools and software. The traditional teaching system of higher vocational mathematics course is undoubtedly biased towards the former, and the introduction of mathematical modeling is a useful attempt to strengthen the latter.

Second, the design of mathematical modeling activities in higher vocational colleges

1. Activity design goal of mathematical modeling in higher vocational education

① Systematically master the basic knowledge, theories and methods of mathematical modeling. (2) Cultivate the consciousness of mathematics application and reflect the practical application value of mathematics. ③ Improve students' interest in learning mathematics, cultivate students to learn to unite and cooperate, and improve their ability to analyze and solve practical problems. ④ Understand the process of mathematical modeling and cultivate the innovative ability and comprehensive quality of mathematical modeling.

2. Design principles of mathematical modeling activities in higher vocational colleges

The teaching design of mathematical modeling should reflect the direction of the development and reform of mathematical education. Specifically, we should emphasize the development of students' mathematical application ability, logical reasoning ability, software use ability and autonomous learning ability.

3. Activity design content of mathematical modeling in higher vocational education

① Theoretical knowledge: According to the principle of combining theory with practice, students are required to master the methods of establishing and solving mathematical models. Basic contents: elementary model, mathematical programming model, differential equation model, graph theory and network model, probability and statistics model, etc. ② Practical skills: Students are required to master the basic methods of data processing, be able to use Lindo and Lingo to solve various planning problems, use Matlab to solve calculus and differential equations, and carry out data fitting, demonstration estimation, hypothesis testing, regression analysis and other probability problems.

Third, the practice of mathematical modeling activities in higher vocational colleges in our college

1. Integrating mathematical modeling into the main courses of higher vocational mathematics

The key to introducing mathematical modeling into mathematics teaching is to introduce cases from real life applications and create real learning situations from the aspects of finance, engineering, aesthetics and economy. In recent years, we have been organically combining mathematical modeling with mathematical courses, and from the learning situation, we have achieved initial results. Through the application of mathematical modeling in mathematics teaching, students realize the importance of mathematics knowledge and pay more attention to mathematics learning. Mathematical modeling is integrated into the main courses of mathematics in higher vocational colleges, and teaching reform is actively promoted in teaching. In the comprehensive review of each module, the knowledge of mathematical modeling and mathematical experiment has been added, which has better mobilized the students' learning enthusiasm.

2. Actively offer elective courses related to mathematical modeling.

Under the guidance of the Outline of National Medium-and Long-term Education Reform and Development Plan and the Ten-year Development Plan of Education Informatization, in order to further promote information-based teaching, we abandoned the traditional methods of mathematics education and tried mathematical modeling and experiments many times in teaching. Since 2005, we have offered elective courses such as mathematical model, mathematical experiment, mathematical modeling and mathematical experiment to freshmen and sophomores, which have been warmly welcomed by students. The opening of this course has greatly promoted the comprehensive cultivation of college students' mathematical quality and mathematical knowledge needed by related majors. After the practice and exploration of many teachers, the school-based textbook "Mathematical Modeling and Mathematical Experiment" edited by Xie Shan, presided over by Qin and edited by Qin has been put into use, which has been widely praised by teachers and students.

3. Seriously organize mathematical modeling activities.

Every year, the teachers in the Mathematics Teaching and Research Section of the College carefully organize the advanced mathematics competitions and mathematical modeling activities of the College, which enriches the students' extracurricular life, and also makes some achievements in the mathematical modeling competitions: they won the second prize of the State once, the second prize of the province twice and the third prize of the province twice. Practice has proved that students who actively participate in the learning of mathematical modeling knowledge have greater development potential after graduation, and the reform mode of mathematical modeling teaching has achieved good results in benefiting students and improving the comprehensive quality of college students [3].

It is a long-term, arduous and meaningful work to integrate mathematical modeling into higher vocational mathematics and cultivate students' comprehensive quality. Teachers should locate accurately according to students' actual level, find the starting point and breakthrough point of mathematical modeling teaching, improve students' application and modeling ability, enable them to consciously use mathematical ideas and methods to analyze, observe, understand and solve problems, enhance their ability to cope with future social competition, integrate mathematical modeling ideas into teaching, make abstract teaching content concrete and clear, and enable students to actively learn, actively think and attach importance to mathematical application, thus improving teaching quality [4]. There is no end to learning, and the integration of mathematical modeling into higher vocational mathematics teaching reform should be supplemented with fresh blood in time with the accumulation of mathematical practice and teaching experience. The popularization of mathematical modeling in our college has cultivated students' comprehensive quality and practical ability and promoted the reform of mathematics teaching.

References:

[1] Xie shan et al. update the concept of higher vocational mathematics education and deepen the teaching reform [J]. modern enterprise education, 201* *1* *: 58.

Jiang Qiyuan, Xie Jinxing, Alfred. Mathematical model [M]. Beijing Higher Education Press, 2003: 3- 18.

[3] Cao Xiujuan et al. Exploration on the teaching reform mode of popular mathematical modeling [J]. China off-campus education, 2010 * *1* *:131.

[4] Meng Ling. On the Strategies and Methods of Mathematical Modeling Teaching in Higher Vocational Colleges [J]. Education and occupation, 201* *1* *:107.

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