Why study math culture and what is math culture?

Mathematical culture refers to the ideas, spirit, methods, opinions, and language of mathematics, as well as their formation and development. In addition to the above connotations, it also includes mathematicians, history of mathematics.

Mathematical beauty, mathematics education. The humanistic component of the development of mathematics, the connection between mathematics and society, the relationship between mathematics and various cultures, and so on.

The connotation of mathematics includes observing reality from a mathematical point of view and constructing mathematical models.

Learn the language, diagrams, symbolic representation of mathematics, and communicate mathematics. Through rational thinking, cultivate rigorous qualities, pursue innovative spirit, and appreciate the beauty of mathematics.

The culture of mathematics is inseparable from the history of mathematics, but it cannot be limited to the history of mathematics. When the charm of mathematics culture truly penetrates into the teaching materials, reaches the classroom, and integrates into teaching, mathematics will be more approachable, and mathematics teaching will allow students to further understand, like, and love mathematics through the cultural level.

Mathematics culture refers to the integration of mathematics with people's daily life and cultural activities, and is the combination of mathematics and humanities education. In modern society, mathematics has penetrated into all walks of life and has had a huge impact on people's daily life, cultural activities and other aspects.

Traditionally, mathematics has been considered a "secluded" subject, somewhere between the sciences and the liberal arts, lacking neither the rich perceptual image of a linguistic discipline nor the direct evidence of experimental science. However, when we understand the nature and connotation of mathematics, we will find that mathematics is actually a discipline full of cultural connotations.

First of all, mathematics is a manifestation of the crystallization of human wisdom. From ancient Greece to China's Song, Yuan, Ming and Qing dynasties, from Galois to Gauss, from Turing to Shannon, many great mathematicians in history are representatives of human wisdom. Through long-term thinking and practice, they creatively put forward a series of important mathematical theories and methods, which promoted the development of the entire society and culture.

Second, mathematics is the embodiment of an abstract way of thinking. Mathematics is a discipline based on symbolic language, which focuses on the use of symbols, formulas, numbers, and other tools to describe. Therefore, mathematics does not depend on concrete matter or events, but on abstract descriptions of these things, which requires us to have strong abstract thinking ability to understand and apply mathematical knowledge.

Third, mathematics is closely linked to other disciplines. From natural sciences to social sciences, from economics to arts, literature and other cultural fields, mathematics is inseparable. For example, in physics, there are a large number of mathematical applications in sub-disciplines such as optics and electromagnetism; In economics and finance, mathematical analysis methods such as calculus and statistics have become indispensable tools for discipline research.

Finally, the specific embodiment of mathematical culture is very diverse, such as mathematics museums, mathematics festivals, mathematics competitions, mathematical games, books, sculptures and even **, etc., are all important parts of mathematical culture. Through these forms, we can better enjoy the aesthetics of mathematics and make mathematics an important element in our daily lives.

In short, mathematical culture is a new cultural form, which is not only the combination of mathematical knowledge and humanities education, but also a cultural phenomenon that has attracted widespread attention around the world. Mathematical culture has greatly broadened people's thinking horizons and cultural levels by promoting the characteristics of human wisdom, abstract thinking and practical application, and has played a positive role in promoting the development of the whole society and culture.

1 The rational spirit of mathematics.

The cultivation and development of this rational spirit is of special significance, and it is the core of human civilization, especially Western civilization. Since the first crisis of mathematics, philosophers represented by Plato (ancient philosophy and mathematics are inseparable) began to realize the unreliability of human intuition, and the rational spirit of mathematics began to develop. Therefore, in teaching, students should be trained to think independently and have the courage to criticize.

With this as the focus, we should consistently cultivate the rational spirit of human beings through mathematics teaching, which should be the highest level of mathematics education.

2 Mathematical Ideas and Methods.

Mathematics is the product of human abstract thinking, it is a rational thinking paradigm and cognitive mode, it is not just some rules of operation and transformation skills, its essence is that people can benefit for life is the method of thinking. Therefore, in teaching practice, we should always pay attention to this essential feature of mathematics, avoid the tendency of simply pursuing the intellectualization of mathematics learning, and pay attention to the cultivation of ability and thinking, so that students can benefit for life.

The mathematical ideas in primary school mainly include: axiomatization, symbols, sets, models, reduction, identity and inequality, number and form combination, function and correspondence, infinity and other important mathematical ideas. Math Method:

Important mathematical methods such as comparison, analysis, synthesis, abstraction, generalization, induction, deduction, classification, transformation and transformation, correspondence, hypothesis, conjecture, observation, simplification, reasoning and proof.

3 The beauty of mathematics.

Mathematics is beauty, a spiritual space with a new aesthetic dimension. As the famous British philosopher Russell said, "Mathematics not only has truth, but also has supreme beauty."

The beauty of mathematics is not as distinct, bright and chic as the beauty of nature and art, nor is it even as intuitive and concrete as the beauty of other societies, it is abstract, rigorous, deep, cold and subtle, and it is a kind of intellectual beauty. Therefore, in teaching practice, we should strive to discover the unique intellectual beauty of mathematics and guide students to appreciate and appreciate the beauty of mathematics. The aesthetic value of mathematics at the primary level mainly includes:

Dynamic beauty, static beauty, symmetrical beauty, asymmetrical beauty, intuitive beauty, abstract beauty, .......

4 The application value of mathematics.

The cultural significance of mathematics lies not only in the knowledge itself and its connotation, but also in its application value. Therefore, the connection between mathematics and practical life should be strengthened in teaching, and the applicability of mathematics should be enhanced, so that students can experience the application value of mathematics.

5 History and Culture of Mathematics.

The connotation of mathematical culture is not only manifested in the knowledge itself, but also in its history, which is a kind of historical existence. Therefore, in the teaching process, the whole process of the generation and development of mathematical knowledge is fully revealed. We believe that mathematics is both creative and inventive, as large as a discipline or as small as a symbol, and is always produced by a certain kind of thinking in a certain cultural context.

Our mathematics education should strive to restore and reproduce the process of discovery or invention, explore the source of mathematical knowledge, and reconstruct the connection between the separated mathematical knowledge and the real background.

1. Mathematical sciences are becoming more and more comprehensive, and now they have formed a huge scientific system that includes hundreds of sub-disciplines and various disciplines are intertwined and infiltrated, which fully demonstrates the unity of mathematical sciences.

2. The intersection, penetration and interaction between mathematics and other disciplines not only further expand the depth and breadth of mathematics, but also promote the vigorous development of many emerging interdisciplinary and marginal disciplines, such as financial mathematics, biomathematics, control mathematics, quantitative sociology, mathematical linguistics, quantitative history, military operations research, and so on. This convergence has greatly contributed to the development of various related disciplines, making the application of mathematics ubiquitous.

3. The early code method of mathematics is the soul of mathematical technology, and if it is removed, mathematical technology will only be an empty shell, and mathematical technology plays a great role in promoting the modernization of human society.

4. Mathematics can cultivate people's rational thinking well. In addition to being the foundation and tool of science, mathematics is also a very important way of thinking and cultural spirit.

Mathematics is the science of studying numbers and shapes, which is the best in production and serves life, and is not a castle in the air. In ancient Egypt, the Nile River flooded periodically, and the need to remeasure the land developed geometry; In ancient China, the development of mathematics was also promoted by the developed agricultural production and the need for astronomical observations. Mathematics and culture have always been closely linked.

Mathematics is not a proudly isolated tree. It has grown up under the influence of human material needs and spiritual life, and at the same time, it has also had a profound impact on different areas of human culture with its own unique charm. The following three characteristics of mathematical culture:

First, mathematics pursues a kind of knowledge that is completely certain and reliable. Second, the simplicity, profundity, and unity of mathematics. Thirdly, mathematics can be self-reflective and self-improving.

The history of the development of mathematics is the history of gradual improvement through continuous exploration.