The traditional teaching of economic mathematics emphasizes the introduction of its own theoretical system and basic theory. This solidified teaching mode often makes students feel that the content of this course is obscure and abstract, thus losing their interest and enthusiasm for active learning.
I will talk about some methods to improve the teaching of economic mathematics based on my own teaching practice.
1? Strengthen the introduction of subject background knowledge
The concept of economic mathematics is abstract. If pure definition, theorem and deduction are adopted, students will easily lose interest and it is difficult to deeply understand related concepts. At present, many teachers pay too much attention to the integrity of mathematics knowledge in class, but have no time to take into account the relevant background of this course. In order to avoid this phenomenon, it is necessary for us to trace back the relevant history of this subject. This not only helps students to understand the ins and outs of knowledge points in a relaxed environment, deepen their understanding of concepts, but also helps to broaden their knowledge.
For example, limit is the first abstract concept of this course, and it is also the main line running through the course of economic mathematics. When teaching the concept of limit, the development of its theory can be introduced as follows. The simple idea and application of limit can be traced back to ancient times. As early as more than 2,000 years ago, there was a famous saying in Zhuangzi's "The World": "One foot pestle, half a day pestle, inexhaustible." This is the bud of China's ancient extreme thoughts. The cyclotomy founded by Liu Hui in the Three Kingdoms period uses the limit of "the area of a regular polygon in a circle" as the area of a circle to approximately calculate pi, and points out: "If you cut carefully, you will lose less, and if you cut more, you will lose nothing." With the appearance of calculus, the concept of limit was clearly put forward, but the theoretical basis was ambiguous. It was not until the19th century that the limit theory was established on a strict theoretical basis through the research of A.L. Cauchy and K. Weierstrass and the establishment of real number theory.
The introduction of these background knowledge is helpful to enrich the teaching content, and the explanation of these mathematicians' historical contributions and interesting life stories will make students curious and admire these familiar or unfamiliar mathematicians. They are eager to know the specific work of these mathematicians, and naturally they will actively seek answers in the learning process.
2? Pay attention to the geometric meaning of knowledge points.
The combination of numbers and shapes is a common way of thinking to solve mathematical problems. The combination of numbers and shapes can make some abstract mathematical problems intuitive and vivid, change abstract thinking into image thinking, and help to grasp the essence of mathematical problems. In addition, due to the combination of numbers and shapes, many problems can be easily solved, and the solutions are simple.
For example, how to calculate definite integral? fly dx(a & gt； 0)。
Solution: let x=asint, then dx=acosdt, and t = 0； when x=0; When x=a, t=
So what? Dx=a？ Costdt=？ (1+cos2t)dt=t+sin2t=, whose geometric meaning is the area of a quarter circle with (0,0) as the center and A as the radius.
Judging from the actual teaching effect, adopting this graphic processing method is helpful for students to intuitively deepen their understanding of the geometric meaning of definite integral.
3? Calculate with Mathematica software
The traditional teaching mode focuses on the theoretical system of economic mathematics itself, emphasizes the introduction of basic theories, and pays insufficient attention to the methods and applications of economic mathematics. With the wide application of computers today, modern education urgently needs to break through the traditional teaching mode and organically combine mathematics with computer calculation. Mathematics experiment is a new teaching mode. Combining mathematical knowledge with computer application by using mathematical software can not only stimulate students' interest in learning mathematics, but also cultivate their practical ability.
We take the linear programming problem as an example to illustrate the function of Mathematica software.
In Mathematica system, ConstrainedMax and ConstrainedMin functions are used to solve linear programming problems, and the calling format is as follows:
Constrained max [f, {inequality}, {x, y, ...}] means to find the unconstrained inequality {inequality} of non-negative variables x, y, ...
Constrained min [f, {inequality}, {x, y, …}] refers to finding the minimum value of the objective function [f] under the set of constrained inequalities {inequality}.
For example, solving linear programming problems: max z = 4000x+3600x S.T. 3x+2x ≤122x+x ≤ 9x+3x ≤ 8x≥0, and x ≥ 0.
Solution: in [1]: = clear [x, y]
In [2]: =←ConstrainedMax[4000x+3600y, {3x+2y≤ 12, 2x+y≤9, x+3y≤8}, {x, y}]
Out[2]= 17600，x→，y→？ shake
According to out [2], the optimal solution of this problem is 0 and the optimal value is 17600.
4? Cultivate students' consciousness of applying economic mathematics.
Nowadays, higher education pays more and more attention to the cultivation of students' ability and practical consciousness, and emphasizes quality education. In fact, economic mathematics, as a tool course for economic management majors in higher vocational colleges, has been widely used in various fields. Therefore, the application of economic mathematics in various fields should be introduced to cultivate students' application consciousness. For example, cost analysis, logistics and transportation, credit investment, financial budget and so on are all based on economic mathematics, and many students are very interested in this aspect. In the teaching process, we can introduce some applications of economic mathematics in these aspects according to relevant knowledge points and give some guidance. These contents seem to occupy teaching time, but they are helpful for students to understand the application value of economic mathematics and deepen their understanding and mastery of the concepts of economic mathematics. At the same time, it can help students broaden their horizons, stimulate their interest in learning, cultivate their awareness of application, and lay a certain foundation for future professional courses and practical work.