Broad sense: In addition to the above connotations, it also includes mathematicians, mathematical history, mathematical beauty and mathematical education. Humanistic elements in the development of mathematics, the relationship between mathematics and society, the relationship between mathematics and various cultures, and so on. [2]
2-value editing
In the upcoming high school mathematics curriculum standards, mathematics culture is a separate section, which has received special attention. Many teachers will ask why they do this. An important reason is that there is an isolationist tendency in mathematics at the beginning of the 20th century, which has been affecting China today. The over-formalization of mathematics makes people mistakenly think that mathematics is just a "free creation" imagined by a few geniuses. The development of mathematics does not need the promotion of society, and its truth does not need the test of practice. Of course, the progress of mathematics does not need the edification of human culture. As a result, the "revival of empiricism" appeared in the western mathematics field. White's mathematical culture theory tries to return mathematics to the cultural level. Klein's Ancient and Modern Mathematical Thoughts, Mathematics in Western Culture and Mathematics: The Loss of Determinism were published one after another, trying to create a humanistic mathematical culture.
Sun Xiaoli, a professor in Peking University, was the earliest scholar in China who paid attention to mathematical culture. The book Mathematics and Culture, co-edited by her and Deng Donghao, collected the relevant expositions of some famous mathematicians and recorded the thinking on mathematical culture from the perspective of dialectics of nature. Mathematics and Culture, published later by Qi, mainly expounds the cultural value of mathematics from the history of non-Euclidean geometry, especially points out the cultural significance of mathematical thinking. Zheng Yuxin's monograph "Mathematical Culturology" and so on. It is characterized by emphasizing the cultural effect produced by "mathematical isomorphism" with social constructivism philosophy.
The above works and many papers try to liberate mathematics from the circle of pure logical deduction and reasoning, focusing on the analysis of the history of mathematical civilization, fully revealing the cultural connotation of mathematics and affirming the value of mathematics as a cultural existence.
After entering the 2 1 century, the study of mathematical culture has deepened. An important symbol is that mathematics culture has entered the classroom of primary and secondary schools and penetrated into the actual mathematics teaching, so as to make students really be infected by culture in the process of learning mathematics, produce a cultural upsurge, experience the cultural taste of mathematics and observe the interaction between social culture and mathematics culture.
Then, how to carry out mathematical culture education in mathematics teaching in primary and secondary schools? The author thinks that we should understand and implement it from the following aspects.
Every nation has its own culture, so there must be mathematics belonging to this culture. Mathematics in ancient Greece and traditional mathematics in China have brilliant achievements and excellent traditions. However, there are obvious differences between them. Different political civilizations in ancient Greece and ancient China gave birth to different mathematics.
Ancient Greece was a slave country. At that time, Athens, Greece practiced slave-owner democracy (the majority of slaves did not enjoy this democracy). Male slave owners always elect consuls and vote democratically on some war and financial events. This political civilization contains some reasonable factors. When slave owners talk about democracy, they often need to convince each other with reasons, which makes the academic debate very strong. In order to prove that you are sticking to the truth, you need to prove it. First set some "axioms" that everyone agrees with and specify the meanings of some nouns, and then call the proposition to be stated the logical reasoning of axioms. Euclid's Elements of Geometry came into being under this background.
During the Spring and Autumn Period and the Warring States Period, China also had an academic atmosphere in which a hundred schools of thought contended, but it did not practice democratic politics among the rulers of ancient Greece, but practiced the system of king rule. The Spring and Autumn Period and the Warring States Period were also the golden age for intellectuals to express their opinions freely. Thinkers and mathematicians at that time, the main goal was to help the king rule his subjects and manage the country. Therefore, most of the ancient mathematics in China appeared in the form of "management mathematics", aiming at the practical goals of national management, such as measuring fields, building water conservancy projects, distributing labor, calculating taxes and transporting grain. Rational discussion takes a back seat here. Therefore, from the cultural point of view, China mathematics can be said to be "management mathematics" and "carpenter mathematics", and its existence form is official documents.
The cultural fashion in ancient Greece is to pursue spiritual enjoyment and gain an understanding of nature as the highest goal. Therefore, the proposition of "equal vertex angles" is included in the Elements of Geometry as a proposition 15, which is proved by axiom 3 (equal amount MINUS equal amount, equal difference). In China's mathematical culture, it is impossible to leave a place for such an intuitive proposition.
Similarly, China Mathematics emphasizes practical management mathematics, but it has made great progress in algorithm. The application of negative numbers, the root method of solving equations, Yang Hui's triangle (Jia Xian's), Zu Chongzhi's calculation of pi, the art of heaven and other exquisite calculation topics can only be born in China, but they are despised by ancient Greek civilization.
We should pay full attention to the practicality and algorithm tradition in China's traditional mathematics, and at the same time, we should absorb all the beneficial mathematical cultural creations of human beings, including the cultural traditions of ancient Greece. When we enter the 2 1 century, as the villagers of the global village, we must integrate into the world mathematical culture and organically combine the nationality with the world.
3 cultural connotation editor
Out of the shadow of mathematical isolationism, the connotation of mathematics is very rich. However, in the field of mathematics education in China, there is often the concept of "mathematics = logic". The survey shows that students regard mathematics as "a collection of absolute truths" or "a game of symbols". "Mathematics follows memorizing facts-using algorithms-executing memorizing formulas-calculating the model of answers" [1], and the formula "Mathematics = logic" has brought many negative effects. As a wise man said, a dynamic mathematical beauty has only skeleton in X-ray photos!
The connotation of mathematics includes observing reality from a mathematical point of view, building mathematical models, learning mathematical languages, charts and symbols, and conducting mathematical exchanges. Through rational thinking, cultivate rigorous quality, pursue innovative spirit and appreciate the beauty of mathematics.
More than half a century ago, the famous mathematician Courand wrote in the preface of his masterpiece What is Mathematics: "Today, the traditional position of mathematics education is in a serious crisis. Mathematics teaching sometimes becomes an empty problem-solving training. There is a trend of over-specialization and over-emphasis on abstraction in mathematical research, while ignoring the application of mathematics and its connection with other fields. Teachers, students and educated people all need a constructive change, the purpose of which is to truly understand that mathematics is an organic whole and the basis of scientific thinking and action. "
On August 20, 2002, Qiu Chengtong said in an interview with Oriental Time and Space: "I appreciate Historical Records as an opera." "Because I value history, and history is macro, so when I look at mathematical problems, it is often a macro view, which is different from others' views. "This is a mathematician's mathematical culture.
On August 2 1 2002, Wen Wei Po published Qian Weichang's article "The Pursuit of Gottingen School", which mentioned: "This made me understand that mathematics itself is beautiful, but don't be lost by it. The task of applied mathematics is to solve practical problems, not to perfect many mathematical methods. We take solving practical problems as our responsibility. From this perspective, we should be excellent butchers who solve practical problems, not knife makers, not knife makers who appreciate how sharp their knives are all their lives without solving practical problems. " This is a mechanic's mathematical culture view.
Like all cultural phenomena, mathematical culture directly dominates people's actions. The mathematical culture of isolationism, on the one hand, makes people stay away from it, making people afraid of mathematics; On the other hand, he is narcissistic and talks to himself, which makes people regard mathematicians as "weirdos". Mathematics in school, originally a favorite subject for teenagers, has become a "sieve" for filtering and a "stick" for beating people. Excellent math culture will be a beautiful and moving math queen, handy servant and clever pet. With advanced mathematics culture, mathematics teaching will become lively and radiant.
4 research editor
When it comes to mathematical culture, it is often associated with the history of mathematics. Indeed, observing mathematics from a macro perspective and observing the progress of mathematics from a historical perspective is an important way to reveal the level of mathematics culture. But in addition to this macroscopic historical investigation, there should also be a microscopic side, that is, revealing the cultural connotation of mathematics from specific mathematical concepts, methods and ideas. The following will explain some new perspectives and strive to show mathematical culture in many ways.
The thinking methods of mathematics and literature are often interlinked. For example, middle school curriculum has "symmetry" and literature has "duality". Symmetry is a transformation, but some properties remain unchanged after it changes. Axisymmetric, that is, folded in half according to the axis of symmetry, the shape and size of the figure remain unchanged. So what is the opposite? It's just that the upper couplet has become the lower couplet, but some characteristics of words and expressions remain unchanged. Wang Wei's poem says, "There is moonlight in the pine forest and crystal stone in the stream". Here, the bright moon and clear springs are all natural scenery and have not changed. Adjective "Ming" is the same as "Qing" and noun "Yue" is the same as "Quan". The rest is the same. The immutability of change exists widely in culture, literature and mathematics. The "dual theory" in mathematics and the change and invariance in topology are the embodiment of this idea. Literary artistic conception and mathematical concepts also have similarities. Mr. Xu Lizhi has long pointed out that "sailing alone, the blue sky is exhausted", which is the artistic conception of the limit concept.
Chen Ziang, a poet in the early Tang Dynasty, said, "Where was the past before me? Behind me, where are the future generations? I think of heaven and earth, there is no limit, there is no end, I am alone, and my tears fall. " This is a literary description of time and three-dimensional Euclidean space. In Chen Ziang's view, both ends of time are infinite. Taking oneself as the origin can be compared to a straight line. The sky is flat and the earth is flat. Living in this distant and empty time and space, human beings can't help but feel deeply. Mathematics formalizes this feeling of life accurately. The poet's imagination can complement our mathematical understanding.
Language is the carrier and shell of culture. A cultural expression of mathematics is to integrate mathematics into language. "Willy-nilly" involves multiplication, and "three times two divided by five will solve it" is a abacus formula. Another example is "foolproof", which is a metaphor for "absolute assurance" in China language. However, this idiom can be considered in connection with "small probability events". "One in 100,000 chance" is also not allowed on the parts of the spacecraft. In addition, "exponential explosion" and "straight rise" have entered everyday language. Their meaning can be related to the complexity of things (computational complexity), which is exactly what needs to be studied. "Career coordinates" and "life track" are also familiar words.
5 skill editing
In short, mathematical culture can not be separated from the history of mathematics, but it can not be limited to the history of mathematics. When the charm of mathematics culture really permeates the teaching materials, reaches the classroom and is integrated into the teaching, mathematics will be more approachable, and mathematics teaching will also let students further understand, like and love mathematics through the cultural level.