Keywords: economic mathematics; Teaching resources; quality of teaching
First of all, talk about the problems faced by economic mathematics teaching.
Economic mathematics is an important basic course for economic management majors in colleges and universities. Through the study of this course, on the one hand, students can acquire the basic concepts, basic theories and basic operational skills of calculus, linear algebra, probability theory and mathematical statistics, and lay the necessary mathematical foundation for learning the following courses and further acquiring mathematical knowledge. On the other hand, through various teaching links, students' abstract thinking ability, logical reasoning ability, spatial imagination ability and self-study ability are gradually cultivated, and they have relatively skilled computing ability and the ability to comprehensively apply what they have learned to analyze and solve practical problems in economics, management and other disciplines. It plays a very important role in cultivating the comprehensive quality and innovative consciousness of students majoring in economic management. Because of this, the teaching and curriculum construction of economic mathematics are paid more and more attention by the education administrative departments and teachers. However, because the teaching of economic mathematics has not been carried out for a long time, the curriculum system and teaching content are not perfect, and the curriculum construction is relatively backward, some problems have been encountered in the mathematics teaching of science and engineering universities: for example, how to deal with the relationship between the new content reflecting the progress of the discipline and the traditional classic content? How to carry out inquiry teaching and heuristic teaching to stimulate students' thinking, guide students to learn independently and cultivate their innovative consciousness? Under the situation of popularization of education, how to cultivate some outstanding talents while ensuring the comparison of basic teaching quality and college students' benefits? How to combine the idea of mathematical modeling and mathematical experiment with the teaching content of mathematics? How to give students the feeling of mathematical beauty in mathematics teaching, turn abstraction into image, stimulate students' learning enthusiasm and improve teaching quality? How to deal with the relationship between the reduction of studious hours and the teaching content ... These problems are more prominent in the teaching of economic mathematics.
In the past ten years, we have taken the teaching of economic mathematics as the breakthrough point, strengthened teaching research, strengthened the construction and reform of economic mathematics, handled the relationship between tradition and modernity, theory and application, and made full use of modern teaching methods and means to form a relatively complete teaching system of economic mathematics, and achieved a series of teaching research and reform results, resulting in relatively complete teaching resources. The series of textbooks of Economic Mathematics edited by Wu Chuansheng is one of the national planning textbooks for general higher education in the Tenth Five-Year Plan and the Eleventh Five-Year Plan. It has been published by Higher Education Press, and has been widely used and praised in many universities across the country. The expanding and guiding teaching materials such as mathematical modeling, mathematical experiments, economic mathematics tutoring materials and economic mathematics electronic teaching plans, which are matched with the series of economic mathematics teaching materials, have been or will be officially published. The research results of the key research project "Calculus Exercise Learning System" in the Ninth Five-Year Plan have been published by Higher Education Press. The project of "Three-dimensional Teaching Material Construction of Economic Mathematics" is a calculus course examination system developed by "Hundred Colleges and Universities", which has been widely used in more than ten colleges and universities, and the online version is being reformed. The developed "Economic Mathematics Material Database" and "Economic Mathematics Network Courseware" have been running on the school campus network, and are welcomed by teachers and students. It should be said that we have been engaged in the teaching construction and teaching reform of economic mathematics for many years, and have accumulated more teaching resources and teaching achievements, which have produced certain influence and radiation in China. In 2006, the course "Economic Mathematics" in our school won the title of excellent course in Hubei Province and passed the evaluation of national excellent course, which marked a new starting point for the course construction of economic mathematics in our school.
After years of research and practice, we realize that to solve the problems encountered in the above-mentioned economic mathematics teaching, in addition to teaching management, teaching organization and teachers' personal quality, very important and effective measures are: on the one hand, we should establish a scientific economic mathematics teaching system, choose appropriate teaching content, and carefully make and create high-quality paper teaching resources; On the other hand, it is necessary to build various electronic teaching resources, including online teaching resources, to match with paper teaching resources and form a complete teaching resource pool. In teaching, give full play to the respective functional advantages of paper teaching resources, electronic teaching resources and network teaching resources, make them complement each other, and promote the coordinated development of students' mathematical knowledge, ability and quality.
Second, the reform of teaching content and textbook construction of economic mathematics are the core and foundation of the construction of teaching resources of economic mathematics.
For more than 20 years, although many mathematics educators and experts at home and abroad have done a lot of work on the construction and reform of the curriculum system and teaching content of economic mathematics, they have still failed to achieve the "mathematics teaching" proposed by Professor Li Daqian. Students should not only learn many important mathematical concepts, methods and conclusions, but also learn mathematical thinking methods, understand the spiritual essence of mathematics, understand the ins and outs of mathematics, and thrive under the influence of mathematical culture. Therefore, it is necessary to combine the teaching process to make students understand that the concepts, theorems and formulas they are learning now, which seem boring but seem to be taken for granted, are not rooted trees, passive water, falling from the sky, nor are they inherent in people's minds, but have their realistic sources and backgrounds. Generally speaking, there are some problems as follows:
1. The teaching content is simple and outdated, lacking modern mathematics content.
2. The combination of economy and mathematics is not enough to meet the teaching needs of economic mathematics.
3. The idea of economic mathematical model and experiment has not penetrated into the teaching content.
4. There is no good practice in teaching students in accordance with their aptitude.
In recent ten years, we have also made a systematic study on the teaching content reform and textbook construction of the basic course of economic mathematics. We believe that the teaching of economic mathematics should organically combine mathematical knowledge with relevant contents of economic management, emphasize the cultivation of mathematical thinking mode of students majoring in economic management, adapt to the trend of higher and higher requirements for mathematics in economic management specialty on the basis of maintaining classic traditional teaching contents, pay attention to properly infiltrating modern mathematical ideas and methods, and integrate theory with practice. Strengthen the cultivation of students' ability to apply mathematical knowledge and methods to solve economic problems, properly adjust and optimize the system, highlight the basic concepts, theories and methods of mathematics, highlight the basic ideas and application background of mathematics, emphasize scientific, systematic, accurate and intuitive, pay attention to readability, and pay due attention to using calculation software to drive mathematical calculation.
Based on the above ideas, since 2003, a series of textbooks "Economic Mathematics", the national tenth five-year plan textbook for general higher education, have been published one after another, and some explorations and attempts have been made in the following aspects:
1. Mathematical concepts come from geometric intuition, numerical results and economic application examples as far as possible, and can give economic significance, so that students can deeply understand mathematical concepts, establish the relationship between mathematical concepts and economic concepts, and gradually cultivate students' mathematical thinking mode and mathematical application ability of economic management. Important concepts come from various practical problems in economy and management or explain their economic significance.
2. Based on the basic content of mathematics, this paper organically combines the useful basic knowledge of mathematics in economic management science with the related contents of economics and management. Based on cultivating students' scientific spirit, innovative consciousness and comprehensive ability to solve problems with mathematical knowledge, combining basic mathematical knowledge with simple economic mathematical modeling methods and mathematical experiments to achieve the perfect unity of science, application and interest as far as possible can enable students to gradually establish mathematical concepts and mathematical ideas, improve their learning interest and improve their ability to analyze and solve economic problems with mathematical knowledge. For example, in calculus, functions, limits, continuity, derivatives, integrals, series, differential equations and difference equations all form bright lines. With simple economic function model, compound interest and continuous compound interest, margin, elasticity (cross elasticity), economic optimization model, present value and future value of capital flow based on integral (based on continuous compound interest), present value and future value of single fund based on series, establishment and solution of various basic differential equations and difference equation models in economics as black lines, the basic methods of calculus-approximation method, element method, optimization method and their economy are highlighted.
3. Optimize the structure, handle the connection between middle school mathematics and college mathematics teaching, pay attention to the connection between several courses of economic mathematics, and form a harmonious system and style; Properly strengthen the content of geometry, strengthen the useful content of multivariate function calculus in the discipline of economic management, and strengthen the connection between geometry and algebra, so that students can learn the follow-up courses better; Update the teaching content appropriately, and introduce the ideas, viewpoints and methods of modern mathematics such as stability, fixed point theory, optimization and stochastic optimization of differential equations in a simple way under the existing basic framework of the basic course of economic mathematics and the requirements of the development of modern economics.
4. Reform the way of writing and narration, and try to be both "closed" and "open"; From simple to complex, from concrete to abstract, theory is integrated with practice, readability is emphasized, and affinity exists. Grasp the essence of the course deeply, and try to "lift weights as easily as possible" and "lift weights as easily as possible". Low starting point, accurate selection of materials, smooth words, clear narration and strong readability; Rich examples, large amount of information, and many teaching options. The exercises are arranged step by step. In addition to some basic exercises, it fully absorbs the advantages of foreign textbooks and is equipped with colorful and lively exercises that are close to real life and the development of economic management.
5. Pay attention to the flexible advantages of tutoring materials and electronic teaching materials. Tutoring materials not only help students master the basic knowledge of the main textbook, but also extend and supplement the main textbook, introduce the history of mathematics and more modern mathematical knowledge and economic application cases appropriately, improve students' comprehensive quality, realize the teaching concept of teaching students in accordance with their aptitude, and make a beneficial discussion on how to cultivate outstanding talents with innovative spirit under the situation of popular education. Make full use of the advantages of electronic teaching materials that are easy to carry and use, provide teachers with a variety of teaching design schemes and teaching materials, and integrate personalized teaching plans according to different teaching directions.
6. Pay attention to using calculation software to drive mathematical calculation.
Thirdly, under the guidance of modern educational theory, we should build an economic mathematics teaching resource database and give full play to its educational function.
In the process of constructing excellent courses of economic mathematics, we have published relatively complete paper teaching resources, and accumulated digital teaching resources including CAI, electronic lesson plans, learning software, tutoring system, exercise lesson learning system, network courseware, material library, examination system and quality assurance system of several courses of economic mathematics. Then, how to develop more abundant and high-quality teaching resources, scientifically build a digital teaching resource database of economic mathematics, and give full play to its role in teaching?
With the rapid development of computer science and technology, the application of network technology in education is increasingly extensive and in-depth, especially the connection between the Internet and campus network, which provides broad prospects and rich resources for school education and produces the possibility of network teaching. It is a variety of educational attempts based on information technology, network technology and multimedia computer technology, covering a variety of educational forms and contents. Multimedia network teaching has been rapidly developed and applied in teaching with its advanced technology, powerful functions, high integration and diversity of teaching resources. Computer network technology can not only realize the sharing of computer hardware resources and software resources, but also realize the information exchange across time and space, which will certainly have an important impact on the school's educational concept, educational thinking, teaching content, teaching means and methods. Due to the constraints of financial resources, material resources and manpower, as well as the influence of traditional educational concepts and teaching methods, the current teaching reform mainly stays on the improvement of media means, lacking the design of teaching content, mode and strategy.
The scientific and rational design of economic mathematics teaching resource base based on computer technology and network technology is of great significance. It is conducive to personalized education and teaching students in accordance with their aptitude: it is conducive to giving full play to students' main role; It is beneficial to broaden the channels of learning information exchange between teachers and students and between students; It is conducive to promoting inter-school cooperation and realizing resource sharing; It is conducive to promoting the formation of learning socialization. So it should be vigorously promoted.
The construction of economic mathematics teaching resource base aims at cultivating talents with innovative spirit and practical ability, paying attention to visualization, openness and hierarchy, correctly handling the internal relationship between economic mathematics series courses and subsequent related courses, correctly handling the relationship between basic content of economic mathematics, comprehensive improvement, economic mathematics model and mathematical experiment, promoting heuristic inquiry teaching, promoting teaching interaction, guiding students to learn consciously, and strengthening the cultivation of students' mathematical knowledge and applied mathematics ability in all directions.
Based on the above understanding, we believe that the teaching resource database of economic mathematics should be divided into three modules or levels for construction:
1. Basic teaching module. The basic teaching module focuses on the choice of teaching breakthrough points. According to the characteristics of computer multimedia technology and the new achievements of current economic mathematics teaching research and teaching reform, this paper focuses on solving the problems that traditional teaching methods are difficult to describe and explain. Through the careful design of teaching content, mode and teaching strategy, some highly abstract mathematical concepts, formulas, theorems, complex applications and other contents are well integrated with various forms of information such as graphics, images and words, so as to achieve an illustrated, intuitive and vivid effect. This part should include various ways and examples derived from important concepts of corresponding knowledge points, various teaching designs and teaching solutions for important teaching contents, problem solving, simple application, graphic images, numerical simulation, dynamic demonstration, etc.
2. Integrated lifting module. The content of the comprehensive improvement module mainly consists of three aspects: (1) the deepening and expansion of classical economic mathematics theories and methods; (2) Introduce some useful modern mathematical knowledge in economics, such as the stability of solutions of differential equations, fixed point theory, economic control theory, fractal and chaos, operational research methods and some simple algorithm design and analysis; (3) Wide and comprehensive application.
3. Ability and quality training module. The core of the ability and quality training module is to design several mathematical modeling and mathematical experiment cases, which are divided into three parts: teaching, experiment and application. Teaching cases mainly provide teaching explanations and demonstrations for problem analysis and knowledge application, so that students can intuitively understand the meaning of knowledge points. On the basis of teaching cases, experimental cases provide students with data for direct verification, and observe and test different results of solving the same problem under different conditions. On the basis of teaching and experimental cases, application cases inspire students to solve the same problem with different mathematical methods and expand into method learning to solve similar problems. Through the variable problems, conditions and methods of the case, the variability of the solution results of the case problem is observed, and the heuristic, inquiry and discussion methods are organically combined to expand students' independent thinking space, encourage students to study problems independently and stimulate students' innovative consciousness.
In the construction of economic mathematics teaching resource database, we should carefully handle the following two relations:
1. Relationship between content and form: According to the nature and characteristics of economic mathematics teaching content, choose appropriate technical means and expression forms, and make full use of the characteristics of various media means to make the complex simple, the difficult easy, the abstract concrete and the boring vivid.
2. Promote the relationship between teaching and learning: focus on helping students understand the teaching content and improve the learning effect. In other words, students' learning situation should be considered when designing teaching process and making multimedia courseware. The application of multimedia network technology in the teaching field will eventually promote the reform of teaching methods, realize the teacher-led and student-centered teaching methods, and promote the formation of students' autonomous learning atmosphere and environment under the guidance of teachers.
[Editor: Wen Heping]
Wu Chuansheng, Vice President and Professor of School of Science, Wuhan University of Technology; Li Yanfu, Dean of Mathematics Branch of Higher Technical College, Higher Education Press.