Why should we study math?

Why do people study mathematics? In fact, many people are not clear about it, and there are even many misunderstandings. Some students think that "mathematics is a little useful except when shopping, but it is a little useful when taking exams, and it is of little practical use." Some students also think that "learning mathematics is for the college entrance examination." Without the college entrance examination, no one will learn these useless things. " In fact, mathematics is a meaningful field.

1, mathematical meaning-scientific standpoint

Mathematics has always been the main force in the formation of human culture, and the characteristics of an era can be understood through the mirror of mathematics. Ancient Greek mathematicians emphasized strict reasoning. What they care about is not the practicality of these achievements, but educating people to make abstract reasoning and inspiring people to pursue ideals and beauty. So ancient Greece created beautiful literature, rational philosophy, and idealized architecture and sculpture that later generations could not surpass. China ancient mathematics advocated practicality, but its biggest shortcoming was the lack of strict proof. "Mathematicization of mathematics and various scientific hypotheses has become the pillar of modern science". The characteristics of an era are closely related to the mathematical activities of this era. Since17th century, due to the establishment of calculus, the success of seeking natural laws with the help of calculus tools has gone far beyond the field of astronomy. /kloc-in the 9th century, due to the perfection of calculus as a strict analytical system, the powerful theory of mathematical physics became possible, which eventually led to the birth of quantum mechanics and relativity, and made people have a deeper understanding of the basic properties of matter and space. In 1950s, the development of mathematics created computers, and mathematics moved from behind the scenes of science to the front of the stage, and digitalization penetrated into almost all human activities.

Mathematics, like music, can give people great spiritual shock. Russell wrote in his autobiography: "When I was 1 1, I began to learn Euclidean geometry, and my brother was my teacher. This is a great event in my life, as intoxicating as my first love. I never imagined that there were such wonderful things in the world. " In people's impression, mathematics and art have little in common, although they are both the crystallization of human wisdom. However, mathematics has been silently accompanying art, providing a rich source of inspiration and a solid creative pillar for art. Mathematics can inspire art, and art can also inspire mathematics. From Fibonacci series and decimal places of pi to tetrahedron and Mobius belt, it can be used as inspiration for artists' creation. Music is the pleasure that human spirit obtains through unconscious calculation. Fourier, a French mathematician, proved that all sounds, whether noise or sounds from instruments, complex or simple, can be described comprehensively in a mathematical way. Fourier's proof has profound philosophical significance. Wonderful music is described by mathematics in an unexpected and wonderful way, which transforms the most abstract field in art into the most abstract science; The most rational knowledge is closely related to rational music. Therefore, mathematics is music in reasoning, and music is mathematics in feeling. The close relationship between mathematics and architecture should not be surprising. Mathematics has always been an inexhaustible creative source for architects and a valuable tool for architectural design and innovation.

Not only natural science, but also various social sciences are constantly turning to mathematics. With the further revelation of the relationship between mathematics and other sciences, mathematics has gained a new title-partner. Steen, an American mathematician, makes an analogy between mathematics and other disciplines: many learned people, especially scientists and engineers, imagine mathematics as a tree of knowledge, and formulas, theorems and conclusions are like ripe fruits hanging on the tree, which can be picked by passing scientists to enrich their theories. Mathematicians, on the other hand, regard mathematics as a rapidly growing tropical rain forest, which needs to absorb nutrients from the world outside mathematics, and at the same time devote itself to the rich and changeable wisdom of human civilization. Mathematics has made a lot of contributions to other disciplines. At the same time, these disciplines are challenging mathematicians with some interesting new problems, resulting in new applications, and the more basic mathematics is, the more useful it is. It is conceivable that with the development of human society, mathematics will become the most basic subject and the framework of all sciences. If the post-modern proverb is adopted, it is that there is almost nothing that can avoid the "text" of mathematics. It can be said that if mathematics is suddenly taken away from our world, human society will collapse in an instant; If mathematics is frozen in our world, human civilization will go backwards immediately. Civilization without mathematics is unthinkable.

2. Mathematical significance-the position of education

Learning, as a basic quality of human beings, is particularly obvious in ancient Greek society. Greek philosophers regard knowledge as good, and the pursuit of truth, goodness and beauty is the purpose of Greek teaching. Plato believes that mathematics is the premise of citizenship. After mathematical practice, the human soul may be extraordinary, return to the holy world and be saved. People who have been trained in logic and mathematical reasoning will be more likely to escape from the cave of ignorance. Mathematics is not only the basic quality of people, but also can improve intelligence and talent. Plato believes that those who are naturally good at arithmetic are often sensitive to learning all other subjects; And those who are slow to respond, if they have been trained in arithmetic, their responses will always improve. Plato particularly emphasized that abstruse things in geometry can help people to grasp good ideas more easily. People who don't know basic mathematical language, basic mathematical symbols, basic mathematical reasoning and basic statistical charts will not be able to adapt to the rapid development of modern society. In the information society, mathematics, as the basic quality of modern people, is increasingly recognized by people. Mathematics has become a basic part of today's social culture with its thinking, rational spirit and aesthetic feeling. It can be said that without mathematics, we can hardly live well; Without mathematics, it is difficult for us to do a good job; Without mathematics, it is difficult for us to think hard; Without mathematics, it is difficult for us to communicate well; Without mathematics, we can hardly appreciate it well.

Through the study of mathematics, "it can promote the development of students' learning attitude, thinking habits, thinking patterns and thinking strategies, so that every student can make an appropriate response to the new situation." "The traditional positivist view of knowledge describes knowledge as linear accumulation and value neutrality, ignoring human activities in knowledge creation and the ethical significance of knowledge. However, knowledge is a kind of social construction in essence, which inevitably embodies people's value choice and shows people's ethical concern. Mathematics is no exception. For mathematics, it can promote the formation of the following excellent qualities.

First, honesty and integrity, advocating truth. Calculation and proof are not a simple operation step or a formal process, but a series of viewpoints and opinions. Mathematical conclusions are the same for anyone and must be accepted by the rational court. What is right is right, and what is wrong is wrong. Mathematical calculation, mathematical derivation and mathematical proof cannot rely on opportunism, but only on gradual calculation and reasoning. Through the study of mathematics, we can cultivate the good character of honesty and integrity, convincing people by reasoning, upholding the truth and correcting mistakes.

Second, be diligent in thinking and be brave in innovation. There is nothing better than mathematics to stimulate this unique and noble innovation ability of human beings. No subject can concentrate, accelerate and strengthen people's attention like mathematics. Facts have proved that the success of mathematicians lies not in talent, but mainly in diligence and innovation.

Third, persevere and dare to climb. There is no king in geometry, and mathematical research needs strong perseverance. Because the proof of mathematical proposition is like climbing a mountain, only those who persevere and dare to explore can reach the other side of victory. Mathematics is an excellent school of thinking, a training subject of wisdom and an abstract way of thinking. Accurate mathematical language allows us to think about complex decisions in an orderly way, rather than relying solely on anecdotes, guesses and eloquence. People who study mathematics can think more effectively. Developing people's thinking ability is an important cultural function of mathematics. Without mathematics, there is no organized logical thinking. Mathematics can make people's way of thinking rigorous and gradually form the habit of reasoning.

Mathematics is the key to the door of opportunity. Mathematics is not only a scientific language, but also contributes to business, finance, economy and national defense in a direct way, opening the door for students' career. The more mathematics a person knows, the more open the door to his career will be. Today, people who know math and know math will get more opportunities than those who don't. From insurance company statisticians, system analysts, marketing experts, network managers to financial analysts, and so on. In fact, mathematics has been playing an important role in helping education authorities to determine which students should be paid by society. To some extent, the difference of mathematics level and ability determines a person's future career and development prospects. In the future world, the best job hunting and promotion opportunities will be provided to those who have the confidence to cope with mathematics. As the foundation of science and technology, mathematics provides the key to success. The information age is the age of mathematics. Just as future scientists and engineers need a wide range of mathematics, future citizens will need extremely diverse mathematics to deal with a large number of tools, equipment and technologies based on mathematics in their work. When students leave school and enter the working life, mathematics largely determines what one can and cannot do.

In all countries of the world, the contents of mathematics courses in primary and secondary schools are relatively consistent, with outstanding similarities. Specifically, the content of mathematics courses chosen by countries is closely related to the needs of society, the development of mathematics and the development of students. Mathematics occupies a central position in the curriculum. No subject has been taught for so long in different countries or cultures. We seldom see students who are good at math but not good at other subjects. It is rare for a student to be the best in mathematics, but the worst in other subjects. On the contrary, those so-called "poor students" often can't learn mathematics well at first, and mathematics has become a "sieve" for these students. Screen out their employment opportunities and their development opportunities. Mathematics really opens the door to the future, and everyone's development depends on the success of mathematics education. In all civilizations, generation after generation of children learn mathematics in order to get a better life.

3. Enlightenment to Mathematics Education

Under the background of mathematics curriculum reform, why should we study mathematics? What does mathematics mean to students' development? What does mathematics want to shape students? What can mathematics shape students? These problems seem ordinary, but in fact they are extraordinary; Seemingly simple, but actually complicated; It seems simple, but in fact it has far-reaching significance. In fact, every problem is the basic problem of mathematics education philosophy that we educators must understand. Facts show that mathematics is an important field that can not be ignored, whether from the development of human civilization or from the personal development of students. Mathematics is the highest intellectual achievement of mankind, the most unique creation of human mind and the core part of human civilization. Mathematics is one of the main keys to understand the world and its development. As a symbol of the development of human civilization, mathematics plays an important role in human development. Mathematics has become the basic condition for individuals to participate in society, and everyone needs to learn mathematics. Mathematics should enter the students' life world, become an indispensable part of every student's life, stimulate their love for life and show more humanistic care. Mathematics should promote students' development, shock their hearts, cultivate their curiosity and embody the cultural value of mathematics. Mathematics should develop students' ability and reflect the thinking value of mathematics. Mathematics should cultivate students' pursuit of beauty and embody the artistic value of mathematics. Therefore, mathematics teaching is not to indoctrinate students with fragmented knowledge in various fields of mathematics, not to regard mathematics as a closed system, and to proceed from those perfect mathematical conclusions, but to regard mathematics as a basic activity of human beings from the real life and existing mathematical experience that students are familiar with. There should be less coercion and less disgusting mechanical training. Let the students think! Think about it! Think again! Teachers don't teach for exams, nor do students study for exams. Mathematics is not a meaningless symbol, mathematics is not a meaningless formula game, and mathematics is not a meaningless operation and reasoning. Mathematics is a meaningful field, it is not illusory, and the life of thought sprouts in it. All kinds of puzzles and confusions in today's mathematics education are closely related to the loss of mathematical meaning. It is the call of the times to move towards meaningful mathematics education. Here, mathematical meaning is not a logical concept, but is understood as the expression of life. Mathematical meaning is not extracted from the text, but created from the dialogue. Mathematical meaning is included in operation and reasoning, in the study of every mathematical concept, in the exploration of every mathematical theorem and in the study of every mathematical problem. Mathematics education towards meaning should give every student a piece of sunshine, awaken their hearts and become an unforgettable life experience for students. It makes students realize the exciting concepts in modern mathematical thought, just as refreshing as drinking ice water in summer. It allows students to appreciate mathematics, feel the beauty of mathematical theorems and concepts, which is as wonderful as art, let students discover the formation process of the theorems and concepts of beauty, and create a more meaningful and meaningful mathematical culture, which is as natural as breathing. In mathematics education, when doing problems, exams and grades become the focus of mathematics education, mathematics becomes a meaningless list of many formulas, definitions and processes, and the significance of mathematics, whether scientific or educational, is far from us. However, mathematics education far from meaning is fundamentally far from students' lives. Therefore, mathematical knowledge is limited to the mode of epistemology, which emphasizes the objectivity, abstraction and certainty of mathematical knowledge unilaterally, and obscures the meaningful world contained in mathematical knowledge. Therefore, mathematics education must go beyond the abstract world, the symbolic world, the logical world, the knowledge world, the absolute truth world and the tool world to the meaningful world. It can be said that returning to the meaning of mathematics is the sacred mission of every mathematics educator. Mathematics education towards meaning should naturally become a new educational direction and new educational pursuit.