Infiltrating math culture Enhancing math literacy

Infiltration of mathematical culture Enhancement of mathematical literacy is a sample paper I bring to you.

Abstract In the traditional mathematics classroom, people always regard mathematics as a tool subject, ignoring the cultural educational value of mathematics, so that the students' mathematical literacy can not be improved, resulting in the extinction of spirituality and creative degradation.

Mathematics classroom teaching must go deep into the cultural level, so that the mathematical culture penetrates the classroom, so that the mathematical culture highlights the students' life wisdom.

This article describes and analyzes how to carry out the penetration of mathematical culture in mathematics classroom teaching to improve students' mathematical literacy.

The proposal to open ? Mathematical culture? class, is an effective way to improve the mathematical literacy of college students, and further specifies the ? The math culture class is an effective way to improve the mathematical literacy of college students, and further specifically elaborates the? The characteristics of the class, the entry point.

Keywords mathematical culture; mathematical literacy; ? Mathematical culture? class

In the traditional mathematics classroom, people always regard mathematics as a tool subject, ignoring the cultural educational value of mathematics, so that the students' mathematical literacy can not be improved, resulting in the degradation of creativity, spirituality extinction.

With the deepening of the curriculum reform, it has become clearer and clearer to me that this narrow, one-sided, and simplistic view of mathematics has brought about a great deal of negative impact on mathematics education.

First of all, it obscures the true nature of mathematics, distorts the true image of mathematics, and leads to the inability of mathematics teachers to understand mathematics comprehensively, objectively, and y.

Second, a narrow view of mathematics leads to a radical view of mathematics education, curriculum, teaching and evaluation.

What's more, it will lead students to form distorted and deformed beliefs about mathematics.

It is not uncommon to hear students ask their teachers what math knowledge will come in handy when they leave school. Often feel the situation: some students in the effort to learn mathematics at the same time, but tired, bored with mathematics, and with the abundance of mathematical knowledge, the degree of boredom is also intensifying; once the task of mathematical problem solving is completed, the function of mathematical education also disappeared.

Such a learning experience also leaves too much shadow on the students, and this shadow will always be accompanied by their growth, and even affect their attitude towards life.

Thinking that mathematics is deduction, calculation, can not experience the history of mathematics, can not understand the humanity of mathematics, culture, can not appreciate the mathematical thinking and spiritual temperament, and can not feel the inner beauty and harmony of mathematics.

At the beginning of the twenty-first century, mathematical culture courses into the classroom, so that mathematics into life, so that students into mathematics.

The Mathematical Culture Program is characterized by the intermingling of arts and sciences, and is a course that infiltrates humanities education and science education, and has accumulated a lot of successful experiences in the reform.

The mathematical knowledge we need is relatively little, while the mathematical literacy of mathematics, i.e., the spirit of research, the method of thought, and the training of thinking, is absolutely necessary for everyone.

Therefore, no matter what kind of business they are engaged in, the only thing that is y engraved in the mind of the spirit of mathematics, mathematical methods of thinking, research methods, reasoning methods, and focus, etc., but at any time, but the role of life-long benefit.

Improvement of students' mathematical literacy, that is, to improve the students to adapt to society, participate in the production and further study of the necessary basic knowledge and basic skills of mathematics, which is the need of the times, but also the need for students to realize their own value.

So how do we improve the mathematical literacy of college students? In this paper, we will start from ? Mathematical culture? This perspective into the discussion.

First, the mathematical culture

? Mathematical culture? The term, is 20 years ago appeared.

It is professionally described as the literacy to actively explore and be good at grasping the background and essence of mathematical problems; the literacy to skillfully express one's own mathematical ideas in accurate, concise, and standardized mathematical language: the literacy to have a good scientific attitude and a spirit of innovation, and to reasonably put forward new ideas, concepts, and methods: the literacy to think about a variety of problems in a ? mathematical way. s rational thinking, from multiple perspectives to explore ways to solve the problem of literacy: good at the reality of the phenomenon and the process of reasonable simplification and scenarios, the establishment of mathematical models of literacy.

Mathematics has a close relationship with human civilization, with human culture.

Therefore, many people are more willing to pay attention to mathematics from the perspective of culture and emphasize the cultural value of mathematics for certain needs.

As a matter of fact, mathematics is a product of the progress of human society and one of the driving forces of social development.

Currently, there is a lot of discussion about ? The term "mathematical culture" has both narrow and broad meanings. The term, there are two interpretations of the narrow and broad sense.

The interpretation in the narrow sense refers to the idea, spirit, method, point of view, language of mathematics, as well as their formation and development; the broader `interpretation' is that in addition to these, it also includes the history of mathematics, mathematical beauty, mathematical education, the intersection of mathematics and the humanities, and the relationship between mathematics and various cultures.

The content, ideas, methods, and language of mathematics are an important part of modern civilization.

Mathematics is essentially a culture, a crystallization of human wisdom.

Its values have permeated every corner of human society.

Mathematics education is not only the teaching of knowledge and the cultivation of ability, but also a kind of cultural cultivation and quality enhancement.

Therefore, mathematics should be as a culture into the classroom, so that students in the process of learning mathematics is really infected by culture, produce cultural **** Ming, experience mathematical culture.

Mathematical culture has its important characteristics.

(1) Mathematical culture is an important way to spread human thought.

Mathematics as a culture is rooted in the fertile soil of rich human thought and is the crystallization of human wisdom and creation.

The development of ancient mathematics in different periods of history and the mathematical exchanges between the same peoples were largely influenced by the spread of culture.

From ancient to modern times, mathematics has had a profound influence on philosophy, art, literature and other disciplines, and Chinese mathematicians of all times and their great achievements in mathematics have had a significant impact on cultural dissemination.

Yin Dynasty, China used the decimal system and place value system; Confucian scripture "Zhouyi" in the eight trigrams contain the germ of the binary system; heavenly stems, earthly branches constitute China's hexadecimal system; the Song Dynasty, Yang Hui authored the "renewal of the ancient extracts of strange algorithms on the Volume" (1275) contains the fourth, fifth, sixth and seventh order of the then-called longitudinal and transverse map; the world-famous Yang Hui triangles; the "Thighs Calculations" and "Nine Chapters" recorded the hook-and-square theorem, which is the basis for the mathematical system. Nine chapters" recorded the hook and strand theorem, 500 years earlier than Pythagoras; Zu Chongzhi calculated pi (called the rate of density) than the Westerners a thousand years earlier.

Liu Hui's cut circle, for the calculation of pi to lay the theoretical foundation; negative numbers of the earliest application of our country, the Eastern Han Dynasty has used the red chips to indicate the positive, black chips to indicate the negative; the Yuan Dynasty Zhu Shijie's "arithmetic Enlightenment" gives the multiplication and division of the positive and negative numbers of the law, but also explains the quadratic equation; the "Nine Chapters of the Mathematical Art" with the ? surplus and shortage? The method of solving quadratic equations; 1600 years ago, "Sun Tzu's Arithmetic" also introduced the method of solving indeterminate equations, called? The method of "Danyan" was also introduced in Sun Tzu's "Arithmetic Classic" 1600 years ago. In the Song Dynasty, Zhou Mi's book called it? Ghost Valley Calculation?

Shen Kuo in the Northern Song Dynasty, Zhu Shijie and Guo Shoujing in the Yuan Dynasty, and later Li Shanlan in the Qing Dynasty wrote about ? stacking? (i.e., higher-order isomorphic series) have all made their mark.

Modern Chinese mathematicians have made important contributions to the study of Goldbach's Conjecture.

Pan Chengdong proved (1+5), Wang Yuan and Pan Chengdong collaborated to prove (1+4), and especially Chen Jingrun proved (1+2), which is only one step away from a successful solution of the conjecture (of course, half a dozen of those who walk a hundred miles are ninety, and this last step is bound to be the toughest of them all); Hua Luogeng, in order to use mathematics for practical purposes, researched the method of preferences, the 0.618 method, and other popular applications of mathematics. He has also done considerable research on the problem of extreme values.

(2) The high degree of unity of the language of mathematics.

Language is the most important system of symbols in a society, and it is more capable of clarifying and conveying subjective meaning than any other system of symbols.

Mathematical language originated from human natural language, but with the development of mathematical abstraction and rigor, gradually evolved into a relatively independent language system, mathematical language symbolization, high degree of precision, which can distinguish between the confusion and ambiguity caused by everyday language.

At the same time, the language of mathematics is concise, and Descartes, the founder of analytic geometry, argued that algebra mechanizes mathematics, thus making the steps of thinking and arithmetic simple.

The language of mathematics used in mathematical cultures is global in the way that painting and music are global, and it has even been speculated that it may have a breadth that transcends the cultures of the Earth, and that mathematics is becoming a universal language because of the tendency of mathematical language systems to unify and harmonize as they develop.

This characteristic enables the culture of mathematics to transcend the limitations of some cultures and to achieve wide and direct dissemination.

(3) The logical constructiveness of mathematical objects.

Mathematical objects are the product of abstract thought, which is not a real existence in the material world.

In this sense, therefore, mathematics is a culture.

But the object of mathematics has a clear objective independence in relation to the subject of cognition.

This independence comes from mathematical abstraction.

In the strict study of mathematics, it can only be deduced on the basis of the corresponding definitions, without recourse to intuition.

Thus, as opposed to possible prototypes of reality, mathematical objects are defined with the help of explicit ? Logic has? gets constructed.

(4) Mathematical culture is relatively stable and independent.

Mathematics is an activity, mathematical activity is a complex of multiple activities, which includes both mathematical knowledge and mathematical tradition.

As a mathematical culture, in modern society, mathematicians obviously constitute a special group and have a relatively stable mathematical tradition.

Mathematics in the course of its historical development, there is a great change in the mathematical tradition, and at the level of the object shows a clear continuity, and previous theories are often preserved in a new form.

Thus the constant change of mathematical tradition is dialectically united with the continuity of mathematical knowledge.

Since mathematical culture is a continuum of positive and progressive whole.

Thus its basic components have a relatively unchanging significance in a given period of time.

Mathematics has its own special standards of value and development, and the development of mathematical culture has a certain degree of independence in relation to the whole cultural environment.

(5) Mathematical culture has a high degree of permeability and unlimited development possibilities.

The permeability of mathematical culture is manifested in the deep penetration of the rational spirit of mathematics into human thinking.

Every major discovery in mathematics has given rich inspiration to human thought.

For example, non-Euclidean geometry has changed the long-standing conception that Euclidean geometry comes

from the a priori comprehensive judgment of human beings.

This was manifested in the growing range of applications of mathematics.

In particular, computer and information sciences have energized the concepts and methods of mathematics, opening up many new fields of research and application.

The infinite nature of the development of mathematical culture is reflected in the fact that, although some mathematicians claim from time to time that their subjects have been nearly? completely solved? and that all the fundamental results have been obtained, the opposite is true: the solution of a mathematical problem has only a relative significance.

Because of the above features, it is clear that mathematical culture is an open system.

Mathematics originally developed as part of human culture.

With the progress of mathematics itself and human civilization as a whole, mathematics has shown relative independence again and has its own special development law.

Therefore, we can regard mathematics as a relatively independent cultural system.

Second, the importance of mathematical culture in university mathematics education

Mathematics in today's society has a greater influence and role than at any time, so the position of mathematics education in university education is also increasingly important.

It is no longer just for science and engineering students; all students need to learn math as well.

Although different majors need to master different mathematical knowledge, but the fundamental purpose of university mathematics education is to improve students' mathematical literacy, mathematical knowledge as a carrier, to show mathematical ideas, methods, and cultivate students' rational thinking, rational spirit.

Mathematical culture puts mathematics in the cultural system of mankind, so that college students realize that the formation and development of mathematics is not simply a pile of mathematical knowledge, skills and logical deduction, and that every major discovery in mathematics is often accompanied by a breakthrough in scientific understanding.

At the same time, it also enables students to understand the role of mathematics in the development of society, the impact of human progress, the status of mathematics in the system of scientific thought, the relationship between mathematics and other disciplines.

Recognize that mathematics is an organically related, vivid, exploratory knowledge of science and cultural image, rather than a fixed, rigid and dogmatic, divided into blocks of knowledge and memory.

This is conducive to students' understanding of the source and flow of knowledge, so that they have a horizontal and vertical penetration of mathematics, so as to understand the nature of mathematics, and to promote the learning and teaching of university mathematics.

Therefore, through the establishment of mathematical culture courses to improve students' mathematical literacy has its important practical significance.

Mathematicians' pursuit of truth, goodness, beauty and dedication, the spirit of fearlessness and courage to explore, so that students can not only see the rigorous and rich mathematics, but also see the living mathematicians, mathematical activities in the spirit of questioning, criticism and innovation, truth-seeking, pragmatism and the spirit of cooperation are full of rich humanistic spirit.

The rational way of thinking in mathematical research, the comprehensive and systematic way of dealing with problems, and the scientific spirit of combining theory and practice are all complementary to the humanistic spirit.

This fusion of scientific and humanistic spirit is indispensable for the development of students' personality and spiritual education.

While improving students' mathematical literacy, it also improves their cultural literacy and intellectual literacy.

Therefore, mathematical culture is a very important part of university mathematics education.

Third, the opening of ? Mathematical culture? class, effectively improve the mathematical literacy of college students

Mathematics classroom teaching must go deeper into the cultural level, so that the mathematical culture penetrates the classroom, so that the mathematical culture highlights the students' life wisdom.

The mathematics classroom should show the charm of mathematical culture from multiple sides and perspectives, and use the spiritual ideas of mathematics to enhance students' cultural literacy, from scientific mathematics to cultural mathematics.

(a) Explore mathematical problems, sense of mathematical culture

Mathematics education is not only the transmission of knowledge, ability training, but also a cultural cultivation, quality enhancement.

It is the interpenetration of humanities education and science education.

We have a responsibility to make math education full of culture and life.

Therefore, mathematics should be as a culture into the classroom, so that students in the process of learning mathematics is really culturally infected, cultural **** Ming, experience mathematical culture, sense of mathematical culture.

Cut from the perspective of mathematical problems, such as: 1, the rabbit problem and the golden section; 2, Zeno's paradox and infinity; 3, the length of the coastline and the separation and mixing of purity; 4, the reasonableness of the voting election and the distribution of quotas on behalf of the problem; 5, the root solution of the quintuple equations and the recent algebra; 6, Fermat's Great Theorem and ? The hen that lays golden eggs? , 7, Hilbert's 23 Problems; 8, The New Millennium Clay Problem, and so on.

In teaching through the exploration of the problem, showing the development of mathematics itself and the beauty of harmony.

Students focus on the substance, focus on understanding, the pursuit of ? The first step is to understand the concept of "the realm of the realm of the realm of the realm. The realm of the.

(ii) collect mathematical stories, feel the scientific spirit of mathematicians

In the teaching of the value of mathematical culture, penetration of mathematical culture and history, so that students can experience the emergence of mathematical knowledge, the development of the form of lively and interesting, easy to read, to introduce to the students of some of the stories of mathematicians, mathematical discoveries, mathematical history of the knowledge, etc.

In this way, we will be able to understand the value of mathematical culture and the development of mathematical knowledge.

This can not only develop students' overall knowledge of mathematics learning, but also stimulate students' interest in learning, and also allow students to appreciate the connection between mathematics and human life experience and practical needs, appreciate the history of the development of mathematics and the great achievements, and experience the cultural heritage of mathematics.

From the perspective of mathematical allusions to cut, such as: 1, the history of the three mathematical crises; 2, "Zhou Thigh Calculus" and the hook and strand theorem; 3, Pu Feng cast the needle story; 4, from heliocentricity to geocentricity, and then Kepler's Three Laws; 5, more than a hundred years of international mathematical conferences, the 1900 Hilbert's speech on the 23 problems, more than seventy years of the Fields Medal; 6, Hanson's story and Chinese surplus theorem. story and the Chinese remainder theorem;7. The origin and development of non-Euclidean geometry;8. On the ? Foundations of Mathematics? s three schools of logic, intuitionism, and formalism.

For example, the introduction of quotations and stories of mathematicians, so that the masters of mathematics, such as Zu Chongzhi, Chen Jingrun, Hua Luogeng, Gauss, Descartes and so on, have become the figures that students often discuss and admire, so that students can have a deeper understanding of mathematics.

Students learned that the mathematicians to solve mathematical problems of the arduous journey, their kind of sleep and food, tireless attitude; repeated failures, never give up the spirit of great encouragement.

Through the study of these stories of mathematicians, students and successful people closer to the emotional distance between the students to set an example of learning, set the goal of struggle.

In short, mathematical culture can not be separated from the history of mathematics, but can not be limited to the history of mathematics.

Through the history of mathematics, the structure of the discipline, interesting problems and so on to explore the meaning of learning mathematics.

When the charm of mathematical culture really penetrates into the textbook, reach the classroom, dissolve into the teaching, mathematics will be more approachable, mathematics teaching will be through the cultural aspects of the students to further understanding of mathematics, like mathematics, love mathematics.

(C) Appreciate the famous mathematical problems and cultivate mathematical thinking

Watch mathematical movies such as ? Black Dream Empire?

Watching math movies such as? etc. to appreciate famous mathematical problems, cultivate mathematical thinking methods and the ability to use mathematized processing methods to solve real problems.

Mathematical methods, on the other hand, are the concrete expression of mathematical ideas, and are the means and important tools for realizing mathematical ideas.

From the perspective of mathematical methods, the method of reduction; the method of transformation; the method of analogy; the method of induction; the method of logical reasoning; the inverse method; the method of combining figures and shapes; sampling; classification method; observation method and so on.

From the mathematical point of view of entry: approximate point of view; abstract point of view; one-to-one correspondence point of view; symmetrical point of view; diversity and unity point of view;? The change in the unchanging? point of view; contingency and necessity point of view; arithmetic and structure; game point of view; relationship, equivalence, order, correlation, proportionality, functional relationship and so on.

Cutting from the perspective of mathematical ideas, such as: the idea of symbolic and variational representation; the idea of sets; the idea of correspondence; axiomatization and structural ideas; the idea of combining numbers and shapes; the idea of recursion; the idea of functions and equations; the idea of the whole; the idea of the limit; the idea of sampling statistics; propositions need to be proved; proofs rely on logic; quantitative ideas; mathematical modeling ideas; the idea of optimization; mathematical mechanics; data processing and mathematical statistics; the idea of the proofs of the propositions; proofs rely on logic; quantification ideas; mathematical modeling ideas; optimization ideas; mathematical mechanization. Data processing and mathematical statistics; mathematical aesthetic ideas; decomposition ideas; inductive ideas; deductive ideas and so on.

Mathematics is permeated with mathematical ideas, they are the soul of the basic knowledge, if they can make them implemented in our learning and application of mathematics, then we get a lot.

(D) link to the practical, reflecting the value of mathematics

The significance of mathematical culture lies not only in the knowledge itself and its connotation, but also in its application value.

Therefore, in teaching, we should strengthen the connection between mathematics and real life, enhance the applicability of mathematics, and let students experience that the value of mathematical culture lies in the fact that mathematics is used in all areas of life.

Mathematics for students is often a kind of their life experience of mathematical phenomena ? interpretation?

If the teaching can be closely linked to the reality of their lives, the use of their enjoyable material to evoke their original experience, learning is bound to be friendly, real, interesting, easy to understand.

In this kind of math classroom, students appreciate that the culture of mathematics is a culture of life continuation.

Generally speaking, mathematics education provides a powerful tool - practical value; provides a way of thinking and methodology - the value of formal training; provides a value - cultural value; advocate a spirit - centrally manifested as the role of mathematical concepts in the formation and development of human concepts, as well as the concepts of society.

The development of mathematics today, we want students to recognize the depth of mathematics, the value of the culture of mathematics, mathematics, the great role of mathematics and the intrinsic charm of mathematics, so that the students can really appreciate the interesting mathematics, promote the idea of mathematics, to recognize the vastness of mathematics, the vastness of mathematics and mathematical underpinnings, the value of mathematics, go to the real love of it, so that our students to mathematics to produce a deep feeling of attachment.

With the advanced mathematical culture, mathematics teaching will become vibrant, flesh and blood, brilliant.

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