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History of Modern Mathematics in China

19 19 After the May 4th Movement, the study of modern mathematics in China really began. The development period of modern mathematics is a period from the beginning of the 20th century to the present, which is often divided into two stages marked by the establishment of 1949 New China. Feng Zuxun of China who studied in Japan in recent three years, 1908 Zheng who studied in America, 19 10 Hu Mingfu who studied in America, 19 165438 Jiang Lifu who studied in America, 1965438 who studied in France. Most of them became famous mathematicians and mathematicians after returning to China, and made important contributions to the development of modern mathematics in China. Among them, Hu Mingfu received his doctorate from Harvard University in the United States on 19 17, becoming the first mathematician in China to receive his doctorate. With the return of foreign students, mathematics education in universities all over the world has improved. At first, only Peking University 19 12 set up the Department of Mathematics, Jiang Lifu 1920 set up the Department of Mathematics in Tianjin Nankai University, Xiong Qinglai 1926 set up the Department of Mathematics in Southeast University (now Nanjing University) and Tsinghua University, and soon Wuhan University, cheeloo university University and Zhejiang University were also established. 1930, Xiong Qinglai initiated the establishment of the Mathematics Research Department in Tsinghua University, and began to recruit graduate students. Chen Shengshen and Wu Daren became the earliest mathematics graduate students in China. In 1930s, (1927), (1934), Hua (1936) and Xu (1936) went abroad to study mathematics, and they all became the backbone of modern mathematics development in China. At the same time, foreign mathematicians also come to China to give lectures, such as Russell in Britain (1920), boekhoff in the United States (1934), osgood (1934), Wiener (1935) and Adama in France (/kloc-0). 1935 the inaugural meeting of chinese mathematical society was held in Shanghai, attended by 33 delegates. The publication of 1936 annals of chinese mathematical society and Journal of Mathematics marks the further development of modern mathematics research in China. Before liberation, mathematical research focused on the field of pure mathematics, and more than 600 theories were published at home and abroad. In terms of analysis, Chen's trigonometric series theory and Xiong Qinglai's research on meromorphic functions and whole functions are representative works, as well as functional analysis, variational methods, differential equations and integral equations; In the field of number theory and algebra, Hua's analytical number theory, geometric number theory, algebraic number theory and modern algebra have achieved remarkable results; In geometry and topology, Su's differential geometry, his algebraic topology, his fiber bundle theory and indicator theory have all done pioneering work: in probability theory and mathematical statistics, Xu obtained many basic theorems and strict proofs in univariate and multivariate analysis. In addition, Li Yan and Qian Baoyu initiated the study of the history of Chinese mathematics, and they did a lot of basic work in the annotation and textual research of ancient historical materials, which made our national cultural heritage shine again. China Academy of Sciences was established in June 1949 1 1. 195 1 March, China Journal of Mathematics (1June, 952 was changed to Journal of Mathematics), 195 1 year1October, China Journal of Mathematics (. Those who went abroad to study mathematics earlier: 190 made great progress. In the early 1950s, Hua's theory of heap primes (1953), Su's introduction to projective curves (1954), Chen's sum of series of rectangular functions (1954) and Li Yan's theory of the history of middle arithmetic (5 series, 65434) were not only continued in number theory. At the end of 1960s, China's mathematics research basically stopped, education was paralyzed, personnel were drained, and foreign exchanges were interrupted. After many efforts, the situation has changed slightly. 1970, Mathematics Magazine was reissued, and Practice and Understanding of Mathematics was founded. 1973, Chen Jingrun published a paper "A big even number is expressed as the sum of the products of a prime number and no more than two prime numbers" in China Science, which made outstanding achievements in the research of Goldbach conjecture. In addition, mathematicians in China have some original opinions on function theory, Markov process, probability application, operational research and optimization methods. 1978 165438+ the third congress was held in the Chinese mathematical society on 10, which marked the revival of mathematics in China. 1978 National Mathematics Competition resumed, 1985 China began to participate in the International Mathematical Olympiad. 198 1 year, Chen Jingrun and other mathematicians won the National Natural Science Award. 1983, the state awarded the first batch of 18 young and middle-aged scholars with doctorates, among which mathematicians accounted for 2/3. 1986, China sent representatives to the international congress of mathematicians for the first time and joined the international mathematical union. Wu Wenjun was invited to give a 45-minute lecture on the history of ancient mathematics in China. In the past ten years, mathematical research has achieved fruitful results, and the number of published papers and monographs has doubled and the quality has been rising. At the annual meeting of 1985 to celebrate the 50th anniversary of the founding of chinese mathematical society, the long-term goal of mathematics development in China was determined. The delegates are determined to make unremitting efforts to make China a new mathematical power in the world at an early date.

The Application of Mathematics in Life

First, walk into life and observe and understand things around you with a mathematical eye:

The world is big, and there are important contributions of mathematics everywhere. Cultivating students' mathematical consciousness and ability to solve practical problems with mathematical knowledge is not only one of the goals of mathematics teaching, but also the need to improve students' mathematical quality. In teaching, let students get in touch with reality, understand life, and understand that life is full of mathematics, and mathematics is around you.

For example, in the introduction of "the meaning and basic nature of proportion", I designed a passage like this: Do you know that there are many interesting proportions in our human body? The ratio of the length of the fist to the length of the sole is about 1: 1, and the ratio of the length of the sole to the height is about 1: 7 ... It is very useful to know these interesting ratios. If you buy socks in the store, just wrap them around your fist for a week and you will know whether they are suitable for you. If you are a detective, as long as you find the footprints of the criminal, you can estimate the height of the criminal ... these are all interesting proportions that make up the body proportion. Today we will learn "the meaning and basic nature of proportion";

In addition, teachers can also design some practical assignments such as "investigation", "experience" and "operation" according to the age characteristics of students, so that students can consolidate their knowledge and improve their abilities in all aspects. For example, before teaching the relationship between unit price, quantity and total price, students can be arranged to be a small investigator and complete the following form:

Cucumber, cabbage, radish and pork

Unit price (yuan)

Quantity (kg)

Total price (yuan)

In this way, students have a perceptual knowledge of what they have learned, which slows down the slope of learning and helps students deeply understand the relationship between unit price, quantity and total price. For another example, after learning the stability of triangles, students can observe where the stability of triangles is used in their lives; After learning the knowledge of circle, ask the students to explain why the shape of the wheel is round and triangular from a mathematical point of view. Students can also find out where the center of the pot cover and washbasin is; ..... This greatly enriches the knowledge students have learned, and makes them really realize that mathematics is everywhere around them, and mathematics is in our life, which is not mysterious. At the same time, we unconsciously realize the true meaning of mathematics, thus arousing students' feelings of loving, learning and using mathematics since childhood, promoting students' thinking to develop into a scientific way of thinking, and cultivating students' consciousness of consciously applying what they have learned to real life.

Second, realize life and build a bridge between mathematics and life;

"Everyone learns useful mathematics, and useful mathematics needs to be learned by important people" has become the slogan of mathematics teaching reform experiment. In teaching, I contact the reality of life, close the distance between students and mathematics knowledge, and explain mathematics problems with concrete and vivid life examples.

1, solving mathematical problems with life experience

In the content of the lesson "Numbering by Letters", I used CAI courseware to demonstrate the scene of Li Lei's students finding money, and then played a "lost and found notice":

Claim the lost property.

Li Lei found RMB A near the flag-raising platform on campus, and asked the owner to come to the Young Pioneers Brigade to claim it.

Xiao young pioneers team headquarters

2002.3

The students were surprised at the way the teacher talked about lost and found in math class. By analyzing and discussing the meaning of monism,

Teacher: Can one yuan be 1 yuan? Student 1: One yuan can be 1 yuan, which means 1 yuan has been found.

Teacher: Can one yuan be 5 yuan money? Health 2: Yes! Said to change 5 yuan.

Teacher: How much can a dollar have? Health 3: It can also be 85 yuan, which means you found 85 yuan's money.

Teacher: How much can a dollar have? Health 4: It can also be 0.5 yuan, which means you got 50 cents. ……

Teacher: So can one yuan be 0 yuan? Health 5: Absolutely not. If it is 0 yuan, then this lost and found notice is a big joke to everyone!

Teacher: Why not just say how much you found and use one yuan instead? ……

Because it is easy for students to know concrete and definite objects, and the numbers represented by letters are uncertain and changeable, it is often difficult for students to understand when they start learning. The "lost and found notice" in this topic is a familiar activity for students, which stimulates their desire to learn new knowledge, and students can participate in the problem-solving process involuntarily. In discussion and communication, brainstorming enables students to learn new knowledge in a pleasant atmosphere and to understand and master what they have learned more firmly; On the other hand, it also improves interpersonal skills, enhances the awareness of mutual assistance and cooperation, receives a good ideological education, and also exercises students' insight into society.

2, using mathematical knowledge to solve practical problems

For example, after learning the calculation of rectangular and square areas and the calculation of combined graphics, I try my best to let students use what they have learned to solve practical problems in life. The teacher's home has a two-bedroom apartment, as shown in the picture. Can you help him calculate the living area of two rooms and one living room? To calculate the size of the area, which area should we measure first? Let the students calculate after giving some data; Next, I asked the students to go home and measure the actual living area of their home. In this practical calculation process, not only the interest is improved, but also the ability of practical measurement and calculation is cultivated, so that students can learn and use it in their lives.

For example, after learning the addition and subtraction within 100, the teaching situation of "buying a car" was created: the price of a mini-car was greatly reduced, and Kobayashi spent 100 yuan to buy several cars. How many cars did he buy? Which ones?

Through observation, thinking and discussion, with my encouragement and guidance, the students expressed the following in an orderly way:

(1) decompose 100 into the sum of two numbers: (2) decompose 100 into the sum of three numbers:

50+50= 100 40+60= 100 30+70= 10020+80= 100 60+20+20= 10050+20+30= 10040+40+20= 10030+30+40= 100

(3) decompose 100 yuan into the sum of four numbers (4) decompose 100 yuan into the sum of five numbers 40+20+20 = 100.

20+20+20+20+20= 100 30+30+20+20= 100

Students explore, innovate and seek original answers with the mentality of discoverer, which also verifies what Suhomlinski said: "In the deep heart of people, there is a deep-rooted need, that is, I hope to be a discoverer, researcher and explorer." This kind of illustrated application problem makes students feel that they are not solving application problems, but solving problems in life, which trains students' ability to capture information and improves the application taste of application problems: the form of cartoons is closer to children's real life, students get information about various car prices from pictures, and also get the information of "Kobayashi spent 100 yuan" from words. Because the question has practical significance, it cannot be rigidly classified into which one. Combining with the problems in real life, we can get different solutions. The whole learning activity provides students with a broad thinking space, allowing them to experience the learning process of observation, analysis, generalization and induction. It not only consolidates the understanding and addition within 100, but also promotes the exchange of mathematics, cultivates students' ability to analyze and solve problems, which is conducive to teaching students in accordance with their aptitude, reflects the different levels of learning mathematics by different people, and makes students feel the close connection between mathematics and life and the ubiquitous interest and role of mathematics in life.

Third, create life and solve mathematical problems in life.

In the teaching after the two-step application problem, I asked the students to "create" the application problem, and the students actively thought and used their imagination: "A chicken wing 8 yuan and a hamburger are more expensive than it. 4 yuan, I ate a chicken wing and a hamburger. How much do you think I spent? " ; "My mother bought a catty of vegetables in the morning and bought twice as many radishes as vegetables. How many Jin of vegetables did my mother buy? ; There are 62 episodes of Journey to the West and 5 episodes of Journey to the West. How many episodes are there in The Journey to the West? " Students are very happy, exaggerated actions and humorous language when compiling application questions, which often cause laughter. Because the theme comes from things that students are familiar with, students speak actively and fluently, and their thinking is multipolar and diversified. They came to a new view that "after snow melts, it is spring, not water". They are very excited about creation, and they realize that there is mathematics everywhere in life.

For example, after learning the knowledge of "proportional distribution", let students help parents calculate how much water (electricity) each household in this residential building should pay; After learning the knowledge of "interest", calculate how much principal and interest you can get after the money deposited in the bank expires; For example, after learning the knowledge of scale, let the students draw "I designed a plan for the future campus" and "I designed a plan for the living area" and so on. The richness of the chart content and the degree of social concern are amazing!

Life is the center of education, and the theory of "life is education" has opened up a vast Yuan Ye for the reform of mathematics teaching in primary schools. "Let students learn mathematics in life" makes students feel close to mathematics, feel that mathematics and life are together, enhance students' initiative in learning mathematics, develop students' thinking of seeking differences, cultivate students' style of study of integrating theory with practice and the spirit of being brave in exploration, bold innovation and continuous progress, and let students experience the pleasure of participating in applying what they have learned to solve practical problems.