Qiu Chengtong, a famous master of mathematics, said, "Mathematics is not boring, but it is boring when we teach it.". The Chinese nation has a long cultural history and profound cultural heritage of 5,000 years. According to many years' teaching practice, I deeply realize that in teaching, if poetry can be properly quoted to make math class more cultural, it can not only enliven the classroom atmosphere, but also stimulate students' enthusiasm for learning and cultivate students' sentiment. Specifically, it can be implemented from the following aspects:
First, the literature of mathematical knowledge
Compared with other disciplines, mathematics is really abstract, which is also a major feature of mathematics. However, combining mathematical knowledge with poetry can turn abstraction into concreteness and rigidity into vividness. This not only helps students to master mathematics knowledge better, but also creates beautiful teaching scenes.
Symmetry is an important term in mathematics, which refers to the invariance of graphics in motion and change. Similar to duality in literature. When explaining symmetry, we can achieve better results by means of "duality". "Moonlight in the pine forest, crystal stone in the stream" is Wang Wei's poem. Moon-clear spring, pine house-stone, sparkling-flowing, noun to noun, verb to verb, which is very similar to mathematical symmetry. Wu Jiangxue, a poetess in the early Qing Dynasty, wrote a palindrome poem about windlass. The clear water in Xiang Lian is moving and cool, while the water is moving and cool, and the summer is long.
In the long summer, the cool wind moves the water, the cool wind moves the water, and the water is fragrant.
Ten different words in the poem depict a summer picture with wind blowing water and flowers floating. Curiously, the first two sentences of the poem are read backwards, which is the standard symmetry in mathematics.
Limit is an important concept in mathematics. The ancients explained that "a foot of wooden vertebrae, a day and a half, is inexhaustible." Recently, Mr. Xu Lizhi quoted "Sailing alone, the blue sky is exhausted, and the Yangtze River is only flowing in the sky" to describe it, which is wonderful.
Coordinate system, a tool for analyzing geometry. Chen Zhiang, a poet in the early Tang Dynasty, wrote a poem: "Before me, where were those lost times?" 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 down. The content involves time, space and the author's mood at that time. A three-dimensional rectangular coordinate system can be obtained by integrating the three. If the precise parameters are given separately, the exact position of the author in the coordinate system can be obtained.
Elevation angle and depression angle refer to the angle between sight and horizontal line. Can be linked to "looking up, I found it was moonlight, and then sinking, I suddenly remembered home"; When studying the positional relationship between a straight line and a circle, we can relate to the poem "The desert is lonely and the smoke is straight, and the long river sets the yen". Wait a minute.
Application problem is a difficult point in mathematics teaching, and students are often bored. In fact, in China's mathematical treasure house, there are many mathematical problems in the form of poems. When talking about related content, if we can introduce teaching, we can inject vitality into the classroom, make mathematics more intimate and make teaching more interesting. Just give two examples:
1. Looking at the towering seventh floor from a distance, the red light doubled.
* * * light three hundred and eighty-one. How many lights are there on the top floor?
This is a problem in Nine Chapters Algorithm Analogy written by Jason Wu, a mathematician in Ming Dynasty.
Attachment: Solution of multiple sum of each layer:1+2+4+8+16+32+64 =127.
Number of lights on the top floor: 38 1 ÷ 127 = 3 (lights)
2. Li Bai walks the streets and plays with wine with a pot;
When you meet a store, double it, see flowers and drink a bucket;
I met the shop flower three times and drank all the wine in the pot.
How much wine is there in the hip flask?
This is a folk math problem (Li Bai hits the wine). The title means: Li Bai is walking in the street, drinking and carrying a hip flask. Every time he meets a hotel, he doubles the wine in the kettle. Every time he meets flowers, he drinks a barrel (barrel is an ancient unit of capacity, 1 barrel = 10 liter), so he meets flowers three times in the store and drinks the wine. How much wine is there in the pot?
P.S. There used to be a barrel of wine in the solution pot. get
[(2x-1) × 2-1]× 2-1= 0, the solution is x = 7/8.
Second, the language of literature teaching
In teaching, teachers can not only introduce mathematical concepts, abstract theorems and laws to students with professional terms, but also decorate the mathematics classroom with poems, which can not only enlighten thinking, but also increase interest, and sometimes play the role of making the finishing point.
Different results can be obtained by studying the same problem from different angles (such as observing three views). The teacher can quote the poem "From one side of the mountain, the distance is different" to explain vividly.
Mathematics problem-solving teaching, especially difficult problem teaching, will have a special flavor if it is combined with Wang Guowei's "three realms". When students see the topic, they can't find any breakthrough because of their vague ideas, but they must patiently analyze the meaning of the topic and try their best to extract relevant information from their existing knowledge system, as if they had entered the first realm: "Last night, the west wind withered the green trees, and they climbed the stairs alone to look at the horizon"; Rack one's brains and think hard for a long time, but I still don't understand. It is also like entering the second realm: "the belt is getting wider and wider, and I will not regret it, and I will be haggard for Iraq"; After repeated thinking, I finally found a way (for example, adding necessary auxiliary lines when solving geometry problems, which made me suddenly enlightened and my mood doubled), and reached the third realm: "I looked for him thousands of times and suddenly looked back, and that man was in the dim light." In this way, teachers and students not only solved the problem in a strong cultural atmosphere, but also experienced the process of "determination", "persistence" and "success" of those who achieved great things.
Specifically, students have just come into contact with the topic, and they don't understand the meaning of the topic and how to solve it, just like "I don't know the true face of Lushan Mountain, but toward which corner of the mountain"; When analyzing, grasp the essence of the problem and solve the main contradiction, as if "shooting people first shoots horses, catching thieves first captures the king"; After thinking for a long time, I finally got a clue, but I still can't completely solve the problem. I have to keep thinking, like "However, before she came to us, we called for a thousand times and urged her for a thousand times, but she still hid half of her face behind her guitar from us"; If you encounter difficulties and feel confused, you can gain new ideas through hard work. Teachers can compose a poem "There is no way to recover if there is doubt, but there is another village in the dark"; Many methods have failed to solve a problem, and they occasionally get a method to make the problem complete smoothly if they are not careful, just like "nowhere to find, you can get it as easy as blowing off dust" or "it is easy to plant flowers, but it is easy to plant willows"; After repeated thinking, the problem has finally been solved. I feel gratified and excited, but I also feel that "the apes on both sides of the strait can't stop crying, and the canoe has passed Chung Shan Man".
Third, encourage evaluation to be literary.
In the process of learning mathematics, students may encounter all kinds of troubles and setbacks. At this time, teachers need to educate students in time. If you preach to students in plain and tasteless language, it will be straightforward, lacking passion and appeal, and can't better stimulate students' self-motivation, and the persuasion effect will definitely be bad. On the contrary, in the process of education, if teachers can quote poems with aphorisms and catchy aphorisms in time, students will not only be happy to accept them, but also enhance their persuasiveness.
For example, when students don't study hard, teachers can encourage them with poems such as "Flowers will bloom again, and people will never be young again" or "Black hair doesn't know how to learn early, but a bald head regrets learning late". After students' hard work, they make little progress, and when they are discouraged, they can be guided by the poem "Learning is like a spring valley, but the days don't increase, and the months have their strengths and the years have their gains". When students are complacent and arrogant in their grades, they can use the famous saying "benefit with modesty, lose the whole game" or "make people progress with modesty, and make people lag behind with arrogance" to warn them; When students get grades, the teacher evaluates them, hoping that they will make persistent efforts and make greater progress. They can encourage them by saying "The river is sharp" or "But you can broaden your horizons by 300 miles on the next floor". Wait a minute.
In order to check students' learning situation, teachers often write test questions composed of traditional questions for testing. If some topics appear in the form of poems, it can reduce the pressure of students in exams and enjoy the beauty to a certain extent. Just give two examples:
1 Habitat tree A group of crows, the number of crows is unknown,
Three live in trees, five have nowhere to go,
Five live in one tree, and one tree is idle.
Please count carefully. What is the size of the crow tree?
Attachment: There are X trees in the solution, and (3x+5) crows are known.
3x+5=5(x- 1)，x=5 3x+5=20。
There are 5 trees and 20 crows.
2. The water is three feet and one red lotus, and the wind blows the flowers flush with the water.
Move six feet horizontally. Please calculate the water depth geometry.
Attachment: The solution of water depth x feet is obtained from Pythagorean theorem.
X2+62=(x+3)2 Then x=4.5.
So, the water depth is 4.5 feet.
The marriage of mathematics and literature is of great benefit to mathematics teaching. But in the eyes of many people, mathematics and literature are like the poles of a magnet, which repel each other. In math class, showing off literary poems not only affects students' learning math, but also takes up their precious time. I don't think so. In mathematics teaching, it is not only feasible for students to learn in a strong cultural atmosphere, but also a necessary condition for students to make achievements in mathematics in the future. Throughout the history, most of the great mathematicians have high cultural accomplishment and literary skills, and some even are literary masters.
When Gauss, the prince of mathematics, was studying at the University of G? ttingen, his two favorite subjects were mathematics and language, and he remained interested all his life. Of the 25 books he borrowed from the library in his freshman year, humanities accounted for 20. When the idea of becoming a mathematician or linguist lingered in his mind, 19-year-old gauss successfully solved the problem of drawing straightedge and straightedge with regular 17 polygon, thus strengthening his belief in teaching and research. Imagine, with his cultural accumulation in the university, if he is engaged in linguistic research, we can have reason to believe that he will have a place in the palace of linguists.
G. Polya was particularly interested in literature when he was young, especially the works of Heine, a great German poet. He was proud to be born on the same day as Heine and won an award for translating his works into Hungarian.
Russell is a famous contemporary philosopher, mathematical logician and discoverer of the famous Barber paradox. But he is also a writer, and he has published many collections of novels. To the surprise of many professional writers, he won the Nobel Prize in Literature with 1950.
Look at the mathematicians in China. Hua is good at poetry, and popular science articles are condescending and easy to understand, which is a model worthy of emulation by future generations. Sue loved old-style poetry since childhood and read many books on literature and history. He takes reading poems and memorizing words as his hobby and uses it to adjust his life. Xu Baozong studied classical literature since childhood, and learned to write ancient prose after 10. His article is concise, rich in connotation and extraordinary in skill. Li Guoping is not only one of the founders of China's reanalysis, but also an excellent poet. His collection of poems, Selected Poems of Li Guoping, was published by Wuhan University Press 1990. The preface is a ode by Su: "It is famous all over the world, with fresh sentences and fantastic words. Swallow Changhong Lian Guangyu, and wave colored pens to clean up the dust. East, west, north and south, people dream frequently in spring, summer, autumn and winter. I have always preferred chanting, and jade is not a tool. " To several altars.
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Xu Lizhi, a famous mathematician, summed up his academic experience in five aspects: cultivating interest, pursuing simplicity, attaching importance to intuition, learning to be abstract and not afraid of calculation. Recently, when he was giving lectures in Nanjing, he added a special project-he loves literature and instills after-school education, so he can't ignore literary literacy. Qiu Chengtong, a master of mathematics, also mentioned: "... how to find the soul of mathematics depends on our cultural quality".
Mathematics curriculum standard points out that the starting point of mathematics curriculum is to promote students' all-round, sustained and harmonious development and help students understand the correct mathematics concept and values. In order to meet the requirements of the new curriculum, stimulate students' enthusiasm for learning mathematics, activate the classroom atmosphere, improve the teaching quality, and make students make greater progress in mathematics, let's teach mathematics with a cultural atmosphere!