Mathematics is indeed a culture.
In the article Mathematics and Application Today, Mr. Wang Zikun summed up the great role of mathematics in four aspects, one of which is to "cultivate the scientific thinking and cultural quality of all people". He further pointed out: "Mathematical culture has richer and deeper cultural connotations than mathematical knowledge system, and mathematical culture is a high generalization of mathematical knowledge, skills, abilities and qualities." We study mathematics not only to acquire knowledge, but also to be influenced by mathematical spirit, mathematical ideas and methods, so as to improve our thinking ability and exercise our thinking quality. Qin Xin, a mathematician in the former Soviet Union, also pointed out that mathematics education can not only cultivate people's integrity and honesty, but also exercise people's tenacious will and courage. No wonder many British law universities or American military academy at West Point have set up advanced mathematics courses, the purpose of which is self-evident.
After years of mathematics education, Mi Shan Kunsan, a Japanese mathematics educator, said a meaningful sentence: If students have no chance to apply the mathematics knowledge they learned in junior high school or senior high school after entering the society, then this kind of mathematics as knowledge will usually be forgotten within one or two years after leaving school. However, no matter what job they are engaged in, it is undoubtedly true that the mathematical spirit and mathematical thinking method engraved in their minds will play an important role in their work and life for a long time.
It can be seen that the cultural nature of mathematics is embodied in: it can help us better understand nature, the world and adapt to life; It can promote our orderly thinking, effective expression and communication, and use mathematics to analyze and solve problems; It can cultivate our initiative, sense of responsibility and self-confidence, and cultivate our scientific attitude of seeking truth from facts and innovative spirit of daring to explore. It can be said that good mathematical literacy is the basis of the sustainable development of human life. In the future society, if you don't have considerable mathematical knowledge, you will be illiterate.
Mathematics is a kind of culture. So, is mathematics an elite culture or a popular culture? Look at what the great mathematician Poincare said. Poincare said:
Scientists study nature not because it is useful, but because he loves it, and he loves it because it is beautiful. If it is not beautiful, it is not worth knowing. If nature is not worth knowing, people are not worth living. Of course, what I am talking about here is not the beauty that excites the senses-the beauty in quality and the beauty in appearance; It is not that I underestimated that kind of beauty, far from it, but that kind of beauty has nothing to do with science; I'm talking about the deeper beauty of harmony and order among the parts, which can be mastered by a pure heart.
Obviously, Poincare refers mainly to theoretical science, including mathematics. He also seems to support that science (including mathematics) is an elite culture.
Today, Poincare's view seems unacceptable. We believe that it is not a good thing that mathematics is too far away from the public. The objectivity of mathematics is the inevitable "fate" of any intelligent life; A mathematical problem or theory cannot be inherited if it is studied by only one person or several people. Finally, it can only be turned out from the pile of old paper by future generations. This kind of math is not good. Mathematics, as a kind of culture, is not a matter of a few mathematicians, but a matter of the masses, and it is destined to be a mass culture.
When we open the current new mathematics textbooks, whether junior high school textbooks or senior high school textbooks, the "cultural flavor" of mathematics comes to us, and the illustrations and popular books full of "humanization" all reflect the educational ideas of "humanization", "popularization" and "popularization" of contemporary mathematics education. Indeed, promoting "mathematical culture" is the purpose. Due to the long-term influence of exam-oriented education, there are still some misunderstandings in our mathematics education: the mathematics curriculum overemphasizes its "logic", "deduction" and "closure"; In classroom teaching, problem-solving teaching occupies a dominant position. Learning mathematics through a large number of exercises is the main theme of mathematics teaching in China today. It is really effective to improve students' basic calculation ability, logical reasoning ability and problem-solving ability through a lot of imitation exercises. But what can we do to train such students to solve several problems temporarily? They don't realize the cultural value of mathematics and lack the spirit of innovation, which is a serious defect in mathematics education. To completely change this situation, the reform of teaching materials is important, but in the final analysis, it depends on the reform of talent selection mechanism and the renewal of educational concepts, and teachers have an unshirkable responsibility.