? Academician Li Da thinks: (1) The influence and function of mathematics can be said to be everywhere. Everything in the world has a tangible tree. As a science to study the quantitative relationship and spatial form in the real world, these two aspects of mathematics exclude other specific characteristics of matter and only study the whole world from the perspective of number and form. The role and position of mathematics can be summarized as follows:
? 1. Mathematics is evergreen knowledge. Many human discoveries are like clouds in the past, and many disciplines have established new theories by overthrowing previous conclusions; However, the development of mathematics in past dynasties is not that future generations destroy the achievements of predecessors, but that each generation of mathematicians adds a new layer of architecture on the basis of the original architecture. Therefore, the conclusion of mathematics often has eternal significance. Euclid was an ancient Greek mathematician more than 2000 years ago. However, Euclidean geometry named after him still plays an important role today. The valley theorem is not only dismissed as outdated, but also called the eternal first theorem, which has been highly praised and used repeatedly, which fully illustrates this point.
2. Mathematics is a scientific language. Galileo once said, "naturally this book is written in mathematical language ... unless you learn its language first ... this book can't be read." The scientific language of mathematics is very accurate, which is the characteristic of mathematics, and this language is universal in the world. Addition, subtraction, multiplication, division, square root, exponent to exponent, differential integral, constant, etc. Although these mathematical languages and symbols may be varied at first, they have long been unified into a fixed style, which is very convenient for us to master and use all over the world.
? 3. Mathematics is a powerful tool. In modern times, mathematics, as an important weapon of modernization, plays a key and even decisive role in many important fields.
? 4. Mathematics is the same foundation. Not only in natural science and technical science, but also in economic science, management science and even humanities and social sciences, mathematics has become an indispensable and important foundation in order to accurately and quantitatively consider problems and get a well-founded regular understanding.
? 5. Mathematics is an important science. Mathematics ignores the concrete forms and attributes of matter, and studies the real world purely from the perspective of quantitative relations and spatial forms. Similar to philosophy, it has the characteristics of transcending specific disciplines and universal application, which is of guiding significance to all disciplines.
Mathematics studied in middle schools generally belongs to the category of elementary mathematics, while advanced mathematics studied in undergraduate courses has a history of more than 300 years, marked by calculus founded by Newton and Leibniz in17th century. In the past, in the arithmetic class of the sixth grade of primary school, "chickens and rabbits in the same cage" was a top-level problem. For example, given that the number of heads is 10 and the number of feet is 28, how many chickens do you ask? How many rabbits? Because the chicken is 1 the first two legs and the rabbit is 1 the first four legs, the problem is complicated. The requirement of arithmetic class is to write the answer in one step, which is more difficult. But when I was studying algebra in middle school, I listed a binary simultaneous equation according to the meaning of the question, and I could find the answer to the question at once.
Really good mathematics is more and more in-depth, more concise and more useful.
6. Mathematics is a key technology. It seems strange that mathematics, which used to be done with a pen and a piece of paper, can become a technology. However, the combination of mathematical ideas and methods with highly developed computing technology does form a technology, and it is a key and realizable technology, which has become "mathematical technology". For example, when a hospital looks at a CT film, its essence is to restore the three-dimensional shape of an object (such as a tumor) in the body by using many plane photos taken from different angles by X-rays. This is the connotation of mathematics. Materializing computer software and hardware has become an important part and key of technology, which can be directly transformed into productivity.
? 7. Mathematics is an advanced culture. Mathematics is an important foundation of human civilization. With the development of human civilization, it has been playing an important role in promoting and occupying a decisive position. Primitive people can only distinguish between 1 and many, and they feel a lot when they meet 3. Three people are probably so "numerous" Then there was the decimal system. With 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, plus each decimal point (and a decimal point), you can represent any number in the world. This is a fact that people have known since childhood, and it seems to be taken for granted. However, it has gone through a long historical process and is an indelible great contribution that mathematics has brought to human civilization. Without it, a slightly larger number will make people dizzy, not to mention a huge astronomical number or an extremely small number. In today's financial industry or scientific experiments, it is impossible to carry out all kinds of complex or high-precision mathematical operations. Can there be such a highly developed civilized society?
? The ancients said, "Zhong Ni was not born in heaven, but will last forever.". Let's think about it. If there is no mathematics and there is no progress in mathematics, people may still live in ignorance and live the life of big sleep. Why don't we attach importance to mathematics and the leading and edifying role of mathematical culture?
For a long time, mathematics, as an accurate language and a powerful tool, has been playing a decisive role in people's understanding and transformation of the world. At present, mathematics, as an important weapon of economic construction, as an important foundation of various sciences and as an important pillar of human civilization, plays a key and even decisive role in many fields. Mathematical technology has become a prominent symbol and an indispensable part of high technology, and its influence and function can be said to be everywhere, and its importance has been recognized by more and more people.
(2) Mathematics education seems to be just a kind of knowledge education, but it is essentially a kind of quality education. If you only regard mathematics learning as accepting a lot of mathematics knowledge, then even if you recite more theorems and formulas, it will inevitably become a pile of rigid dogmas and it will be difficult to play its role. If we only understand the quality of mathematics learning as the quantity and speed of "brushing questions", we can only become a skilled mathematics craftsman at best. Mathematics is a creative science that emphasizes thinking, understanding and strict training. Only by mastering the thinking method and spiritual essence of mathematics can we deduce ever-changing vivid conclusions from a few formulas and show infinite power.
? For example: the concept of conscious quantity. People will seriously pay attention to the quantitative aspects of things and their changing laws, instead of "countless in their chests", and make decisions and do things by feeling and "patting their heads".
Strict logical thinking ability. Keep people clear-headed, clear-headed, and handle all work in an orderly manner.
High abstract thinking ability. In the face of complicated phenomena, people can distinguish between primary and secondary, grasp the main contradictions, highlight the essence of things, and solve problems step by step and effectively, without being at a loss, scratching their eyebrows and beards.
Mathematical deduction requires that every symbol and decimal point should not be vague and perfunctory, which is helpful to cultivate serious and meticulous style and habits.
? Mathematics pursues the most useful (extensive) conclusion, the least condition (cost) and the simplest proof. Through strict mathematics training, we will gradually form the habit and style of Excellence and perfection.
Paying attention to the context of mathematics and understanding the origin and development of mathematical concepts, methods and theories will improve the consciousness, belief and ability of establishing mathematical models and using mathematical knowledge to deal with various complex problems in the real world. Mathematics, as an ideological gymnastics and competition, will enhance people's fighting spirit and adaptability. By constantly analyzing contradictions, we can sort out the difficulties and finally solve the problems.
The study and thinking of mathematics will open a vast world of free creation for students, stimulate their exploration spirit, innovative consciousness and innovative ability, make them more flexible and proactive, and give full play to their intelligence, and so on.
It can be seen that mathematics education seems to be just a kind of knowledge education, but it is essentially a kind of quality education.
This kind of quality education is not imposed by the outside world, but is inherent in mathematics education itself. With imparting and learning mathematics knowledge as the carrier, through strict and earnest mathematics study and training, we can unconsciously and consciously imprint these qualities and abilities in our hearts, practice them, imprint them in our hearts, form habits, and gradually become our own mathematics education.