Why should we learn mathematics?

Why should people learn mathematics? In fact, many people are not clear about it, and there are even many misunderstandings. Some students think, “Mathematics is only useful when shopping and taking exams, but it doesn’t have much practical use.” Some students think, “Learning mathematics is all for the college entrance examination. Without the college entrance examination, no one would learn these useless things.” Something. "Actually, mathematics is a field of meaning.

1. The significance of mathematics - the scientific stance

Mathematics has always been the main force in forming human culture. Through the mirror of mathematics, we can understand the characteristics of an era. Ancient Greek mathematicians emphasized rigorous reasoning. Their concern was not the practicality of these results, but educating people to engage in abstract reasoning and stimulating people's pursuit of ideals and beauty. Therefore, ancient Greece created beautiful literature, rational philosophy, and ideal architecture and sculpture that are difficult to surpass in later generations. Ancient Chinese mathematics advocated practicality, and its biggest shortcoming was the lack of rigorous verification. "The mathematization of mathematics and various scientific hypotheses has become the backbone of modern science." The characteristics of an era are closely related to the mathematical activities of that era. Since the 17th century, due to the creation of calculus, the success achieved in seeking the laws of nature with the help of calculus tools has gone far beyond the field of astronomy. In the 19th century, the improvement of the tool of calculus into a rigorous analytical system made powerful theories of mathematical physics possible, which ultimately led to the birth of quantum mechanics and the theory of relativity, allowing people to have a deeper understanding of the basic properties of matter and space. In the 1950s, the development of mathematics created computers. Mathematics moved from behind the scenes of science to the stage, and digitization penetrated into almost all human activities.

Mathematics can give people a huge spiritual shock just like music. Russell wrote in his autobiography: "When I was 11 years old, I began to study Euclidean geometry with my brother as my teacher. This was a major event in my life, as intoxicating as first love. I have never I never imagined that there is such a wonderful thing in the world. "In people's minds, mathematics and art have few similarities, although they are both the crystallization of human wisdom. However, mathematics has always accompanied art silently, providing it with a rich source of inspiration and a solid pillar of creation. Mathematics can inspire art, and art can inspire mathematics. From the Fibonacci sequence and the decimal digits of pi to the tetrahedron and Mobius strips, artists can be inspired to create. Music is the pleasure that the human spirit derives from unconscious calculations. The French mathematician Fourier proved that all sounds, whether noise or sounds from instruments, complex or simple sounds, can be comprehensively described mathematically. Fourier's proof has profound philosophical significance. Beautiful music has been mathematically described in an unexpectedly beautiful way, so that the most abstract fields in art can be transformed into the most abstract science; and the most rational knowledge is closely related to rational music. So, mathematics is the music of reasoning, and music is mathematics of feeling. The close connection between mathematics and architecture should come as no surprise. Mathematics has always been an inexhaustible source of creativity for architects and a valuable tool for architectural design and innovation.

Not only the natural sciences, but also various social sciences are constantly turning to mathematics. With the deeper revelation of the relationship between mathematics and other sciences, mathematics has gained a new title - partner. American mathematician Steen made this analogy between mathematics and other disciplines: Many knowledgeable people, especially scientists and engineers, imagine mathematics as a tree of knowledge, with formulas, theorems and conclusions hanging on the tree. The ripe fruits are picked by passing scientists to enrich their theories. Mathematicians, on the other hand, regard mathematics as a rapidly growing tropical rain forest that needs to absorb nutrients from the world outside mathematics. At the same time, it contributes to human civilization the rich and ever-changing intelligent animals and plants. Mathematics has made many contributions to other disciplines, and at the same time, these disciplines are challenging mathematicians with interesting new kinds of problems, which in turn lead to 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. To adopt a postmodern proverb, almost nothing escapes the "text" of mathematics. It can be said that if mathematics is suddenly taken away from our world, human society will collapse instantly; if mathematics is frozen in our world, human civilization will immediately regress. Civilization without mathematics is unimaginable.

2. The significance of mathematics - the standpoint of education

Learning is a basic human quality, especially in ancient Greek society. Greek philosophers regarded knowledge as good, and the pursuit of truth, goodness and beauty was the purpose of Greek religion. Plato believes that mathematics is a prerequisite for citizenship. After the human soul is cultivated by mathematics, it is possible to transcend the world and return to the holy and supreme ideal world to be saved. People who are trained to reason logically and mathematically will be more likely to escape from the cave of ignorance. Mathematics is not only a basic human quality, but it can also enhance intelligence and talents. Plato believed that those who are naturally good at arithmetic are often quick to learn all other subjects; and those whose reactions are slow will always improve if they receive training in arithmetic.

Plato particularly emphasized that the profound things in geometry can help people grasp the concept of good more easily. People who do not know basic mathematical language, do not understand basic mathematical symbols, do not master basic mathematical reasoning, and do not understand 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, has been increasingly recognized by people. Mathematics has become a basic component of today's social culture with its thinking, rational spirit and elegance. It can be said that without mathematics, we can hardly live well; without mathematics, we can hardly work well; without mathematics, we can hardly think well; without mathematics, we can hardly communicate well; without mathematics, We can barely appreciate it very well.

Through the study of mathematics, "it can promote the development of students' learning attitudes, thinking habits, thinking patterns, thinking strategies, etc., so that each student can respond appropriately to new situations." The traditional positivist view of knowledge describes knowledge as linear accumulation and value-neutral, ignores human activities in knowledge creation, and ignores the ethical significance contained in knowledge. However, knowledge is essentially a social construction, which must reflect people's value choices and express people's ethical concerns. Mathematics is no exception. For mathematics, it can promote the formation of the following excellent qualities of people.

First, be honest and upright and uphold the truth. Calculation and proof are not a simple operation step or formal process, but a series of viewpoints and insights. Mathematical conclusions are the same for everyone and must be accepted by the court of reason. Right is right and wrong is wrong. Mathematical calculations, mathematical deductions, and mathematical proofs cannot rely on speculation, but can only rely on step-by-step calculation and reasoning. Through the study of mathematics, we can cultivate the good character of being honest and upright, convincing others with reason, adhering to the truth, and correcting mistakes.

Second, be diligent in thinking and brave in innovation. To inspire this unique and noble innovative ability of human beings, there is nothing better than mathematics. No subject can focus, accelerate, and sharpen people's attention like mathematics. It turns out that the success of mathematicians does not depend on how talented they are, but mainly depends on their diligence and innovation.

Third, perseverance and courage to climb. There is no path to success in geometry, and mathematical research requires strong perseverance. Because the proof of mathematical propositions is like climbing a mountain, only those who are persevering and brave enough to explore can reach the other side of victory. Mathematics is an excellent school of thinking. Mathematics is a wise training subject. Mathematics is an abstract mode of thinking. The precise language of mathematics allows us to think about complex decisions methodically, rather than relying solely on anecdotes, guesswork, 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 would be no organized logical thinking. Mathematics can make people's thinking methods strict and develop the habit of reasoning step by step.

Mathematics is the key that opens the door to opportunity. Mathematics is not only the language of science but contributes in direct ways to business, finance, economics, defense and opens career doors for students. The more mathematics a person knows, the more career doors will be open to him. Today, those who understand mathematics and can do it will have greater opportunities than those who do not. From insurance company statisticians, systems analysts, marketing experts, network managers, to financial analysts, and more. In fact, mathematics has historically played an important role in helping education authorities identify students who deserve society's rewards. To a certain extent, differences in mathematics level and ability determine a person's future career and development prospects. In the future world, the best opportunities for job hunting and promotion will be available 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, and just as future scientists and engineers will need a broad range of mathematics, future citizens will need an extremely diverse range of mathematics to cope with the vast array of mathematics-based tools, devices, and technologies at work. When students leave school and enter their working lives, mathematics greatly determines what kind of jobs a person can and cannot do.

In all countries in the world, the content of mathematics courses in primary and secondary schools is relatively consistent and has outstanding similarities. Specifically, the mathematics curriculum content selected by each country is closely related to the needs of society, the development of mathematics, and the development of students. Mathematics occupies a central place in the curriculum and no other subject is taught for as long across countries or cultures. We rarely see students who do well in mathematics but poorly in other subjects. It is rare in secondary schools for a student to be first in mathematics but among the worst in other subjects. On the contrary, those so-called "poor students" often fail to learn mathematics well in the first place, and mathematics has become a "sieve" for these students. Screening out their employment opportunities and screening out their development opportunities. Mathematics has truly become the door to the future, and everyone's development depends on the success of mathematics education. Across all civilizations, generations of children learn mathematics to achieve a better life.

3. Inspiration for mathematics education

In the context of mathematics curriculum reform, why should we learn mathematics? What does mathematics mean for student development? What exactly does mathematics want to shape students? What exactly can mathematics shape students? These problems may seem ordinary, but in fact they are extraordinary; they may seem simple, but in fact they are complex; they may seem simple, but in fact they are far-reaching. In fact, every question is a basic question in the philosophy of mathematics education that our educators must understand. Facts have shown that mathematics is an area of ??significance that cannot be ignored, whether from the perspective of the development of human civilization or the personal development of students. Mathematics is the highest intellectual achievement of mankind, the most unique creation of the human mind, and the core part of human civilization. Mathematics is one of the main keys to understanding the world and its development. Mathematics, as a symbol of the development of human civilization, plays an important role in human development. Mathematics has become a basic condition for individuals to participate in society, and everyone needs to learn mathematics. Mathematics should enter students' living world and become an integral part of each student's life, inspiring their love for life and reflecting more humanistic care. Mathematics should promote students' development, shock students' minds, cultivate students' curiosity, and reflect the cultural value of mathematics. Mathematics should develop students' abilities and reflect the value of mathematical thinking. Mathematics should cultivate students’ pursuit of beauty and reflect the artistic value of mathematics. Therefore, mathematics teaching does not instill fragmented knowledge in various fields of mathematics into students. It does not treat mathematics as a closed system and start from those perfect mathematical conclusions. Instead, it starts from the real life and existing mathematical experience that students are familiar with, and integrates mathematics into as a basic human activity. There should be less coercion and less annoying mechanical training. Get students thinking! think! Think again! Teachers do not teach for exams, and students do not learn for exams. Mathematics is not meaningless symbols, mathematics is not a meaningless game of formulas, and mathematics is not meaningless operations and reasoning. Mathematics is a field of meaning. Mathematics is not ethereal, but the life of ideas sprouts in it. Today, all kinds of confusion and confusion in mathematics education are closely related to the loss of the meaning of mathematics. Mathematics education moving towards meaning is the call of the times. Here, mathematical meaning is not a logical concept but is understood as a manifestation of life. Mathematical meaning is not extracted from text but created from dialogue. The meaning of mathematics is contained in operations and reasoning, in the learning of every mathematical concept, in the exploration of every mathematical theorem, and in the study of every mathematical problem. Mathematics education that moves toward meaning should give every student a piece of sunshine, awaken their souls, and become an unforgettable life experience for students. It exposes students to inspiring concepts in modern mathematical thinking, as refreshing as drinking ice water in the summer. It allows students to appreciate mathematics and feel the beauty of mathematical theorems and mathematical concepts, which is as exciting as art. It allows students to discover beautiful theorems and the formation process of concepts to create a more connotative and meaningful mathematical culture, as natural as breathing. In mathematics education, when questions, exams, and scores become the focus of mathematics education, mathematics becomes a meaningless list of formulas, definitions, and processes. The meaning of mathematics—either scientific or educational. ——Just stay away from us. However, mathematics education that is far away from meaning is fundamentally far away from students' lives. Thus, mathematical knowledge is limited to epistemological stereotypes, one-sided emphasis is placed on the objectivity, abstraction and certainty of mathematical knowledge, and the world of meaning contained in mathematical knowledge is obscured. Therefore, mathematics education must transcend the abstract world, the world of symbols, the world of logic, the world of knowledge, the world of absolute truth and the world of study tools, and move towards the world of meaning. It can be said that returning to the meaning of mathematics is the sacred mission of every mathematics educator. Mathematics education that moves towards meaning should of course become a new educational direction and a new educational pursuit.