A Brief History of Mathematical Competition
Mathematics competition is similar to sports competition. It is an intelligence competition for teenagers, so the Soviet Union pioneered the term "Mathematical Olympics". In similar intelligence contests with basic science as the competition content, the mathematics contest has the longest history, the largest number of participating countries and the greatest influence. The more formal math competition began in Hungary in 1894, and has been held for more than 90 times up to now, except for seven sessions suspended due to two world wars and the incident of 1956. The mathematics competition in the Soviet Union began at 1934, while the mathematics competition in the United States began at 1938. Apart from the three years during World War II, these two countries have held more than 50 competitions. Other countries with a long history of mathematics competitions include Romania (1902), Bulgaria (1949) and China (1956).
1956, the eastern European countries and the Soviet union formally defined the plan of the international mathematical olympiad. 1959, the first international mathematical olympiad (1MO) was held in brasov. It will be held once a year. Except for 1980, which was suspended due to the economic difficulties of Mongolia, the host country, it has been held for 40 times so far. More and more countries are participating. Only 7 countries participated in the first session, and by 1980, there were 23 countries; To 1990, there are 54.
It must be pointed out that there have been some math competitions before the above history. For example, the Soviets said that a math contest was held in the era of 1886. Another example is 1926. A abacus competition was held in China and Shanghai, with students, banks and bank employees. Hua, a first-year student in China Vocational School, won the championship with his wisdom. These are all stories about math competitions, not in the official history.
Second, the development of mathematical competitions
Mathematics competitions have gradually developed from a single city to the whole country and then to the whole world. For example, the math competition in the Soviet Union started in Leningrad and Moscow, and 1962 was extended to the whole country. In the United States, there was no national mathematics competition until 1957.
Mathematical competition activities are also gradually developed from shallow to deep. In almost every country, mathematical competitions are organized by some famous mathematicians. The test questions are very close to the exercises in the middle school textbooks, and then gradually deepen. Some mathematicians spend more energy on selecting topics and organizing competitions. At this time, the test questions are gradually out of the scope of middle school textbooks. Of course, it is still required to state the questions in elementary mathematical language and solve them by elementary mathematical methods. For example, at the beginning of the Soviet Mathematical Competition, famous mathematicians such as André Andrey Kolmogorov, Aleksandrov and Tommy Tam Nie all took part in this work. In the United States, famous mathematicians such as boekhoff and his sons Paulia and Kaplanski participated in this work.
After the start of the International Mathematical Olympiad, the preparation work of the participating countries is often mainly an intensive training for athletes to broaden their knowledge and improve their ability to solve problems. This kind of training class is very difficult, much deeper than middle school mathematics. At this time, several mathematicians are needed to specialize in this activity. In countries with good math competitions, competitions often take the form of pyramid competitions and are selected at different levels. For example. The Soviet Union is divided into five levels of competitions, namely, school-level, municipal, provincial, national and all-Soviet competitions. The number of participants in each level is about110 of the previous level, and eight special math schools (or math Olympic schools) have been established to train students with good math quality.
Although the mathematics competition has a long history, it has developed and changed greatly in the recent 10 years, and the related work has become more and more specialized. We should pay close attention to its development and understand its laws.
Third, the role of mathematics competition
1. Choose young people with mathematical talent. Because the winners are selected on the basis of step-by-step competition and gradual deepening of assessment, the winners should not only have a solid and extensive mathematical foundation, but also have a flexible and witty mind and creative ability, so they are often diligent and intelligent teenagers. These people have a great chance of becoming talents in the future. More and more countries attach importance to mathematics competition, which is one of the important reasons for its rapid development in the world. In Hungary, famous mathematicians Fay, Ritz, Xie Gui, Koenig, Hal, Rado, etc. are the winners of the mathematics competition. In Poland, the famous number theory expert Zinzel was the winner of a math contest. In the United States, Milnor, Manford and Quinlan won the Fields Prize in Mathematics, and many outstanding young people became famous physicists or engineers, such as the famous mechanic Feng? Carmen.
2. Stimulate teenagers' interest in learning mathematics. Mathematics is becoming more and more important and essential in all natural sciences, social sciences and modern management. Due to the development of electronic computers, various sciences tend to be more in-depth and mature, from qualitative research to quantitative research. Therefore, it is almost necessary for teenagers to learn mathematics well for them to learn all sciences well in the future. Mathematics competition introduces healthy competition mechanism into teenagers' mathematics learning and stimulates their self-motivated and creative thinking. Because the mathematics competition is conducted at different levels, the questions before the national competition basically did not jump out of the scope of middle school mathematics textbooks, which is suitable for the majority of teenagers to participate. However, it should also be admitted that there are differences, even great differences, between people's talent and mathematical quality. National competitions and subsequent competitions and training can only be carried out among a small number of people, and a small number of teenagers with good math quality can afford it. For example, Australian teenager Tory? Tao won the bronze medal, silver medal and gold medal in the 27th, 28th and 29th International Mathematical Olympiad at the age of 10, 12 and12 respectively. Of course, some university teachers and math researchers need to take part in high-level math competitions.
3. Promoted the reform of mathematics teaching. After the mathematics competition enters a high level, the content of the test questions is often the elementary of higher mathematics. This not only adds fresh content to middle school mathematics, but also may prompt middle school mathematics teaching to reflect on a new basis and change from quantitative change to qualitative change in the process of gradual accumulation. Middle school teachers can also learn new knowledge, improve their level and broaden their horizons in the process of participating in math competitions. In fact, some math teachers have gradually tasted the sweetness in this activity. Therefore, mathematics competition may also be one of the "catalysts" for the reform of middle school mathematics curriculum, which seems to be better than the top-down "indoctrination" method. In the early 1960s, the so-called modernization movement of middle school mathematics teaching in the West tried to replace the old middle school mathematics content with some modern mathematics, but it adopted the method of top-down indoctrination, resulting in the intuitive thinking process that was divorced from the teacher's level and students' sequential learning. Now it is basically blown by the wind and declared a failure. On the contrary, math competition may be a way. In China, middle school students are under great pressure to enter the college entrance examination, and middle school teachers are rushing about for it, which makes them feel that the road is getting narrower and narrower. Mathematics competition may lead to the reform of mathematics teaching in middle schools.
Fourth, competition mathematics-Olympic mathematics
With the development of mathematics competition, a special mathematics discipline-competition mathematics, also known as Olympic mathematics, has gradually formed. The task of competition mathematics is to put advanced mathematics into elementary mathematics, express the problems of advanced mathematics in the language of elementary mathematics, and solve these problems by elementary mathematics. The background of problems and even solutions here often comes from some advanced mathematics. Mathematics can be divided into analysis and algebra according to its methods, that is, continuous mathematics and discrete mathematics. At present, calculus does not belong to the category of international mathematical Olympics, so decentralized discrete mathematics is the main body of competitive mathematics. Many topics of the International Mathematical Olympiad come from mathematical theory, combinatorial analysis, modern algebra, combinatorial geometry, functional equations and so on. Of course, it also includes plane geometry in middle school curriculum.
Competition mathematics is different from these fields of mathematics. Usually, mathematics often seeks to prove some generalized theorems, while competition mathematics only seeks some special problems. Generally, mathematics pursues to establish general theories and methods, while competition mathematics pursues to solve special problems with special methods. Once a problem comes out, it becomes an old problem and needs to continue to create new ones. Competition mathematics belongs to the category of "hard" mathematics, and usually, like pure mathematics, it takes its inherent beauty, including the simplicity of questions and the cleverness of answers, as an important criterion to measure its value.
Competition mathematics can't develop independently without the existing branch of mathematics, otherwise it will become passive water, so it is often run by experts in some fields. For example, Shan Zun, an excellent coach of China delegation who participated in the International Mathematical Olympics, is an expert in number theory.
The spirit of the International Mathematical Olympiad encourages the use of ingenious elementary mathematical methods to solve problems, but it does not exclude the use of advanced mathematical methods and theorems. For example, in the 3rd 1 international mathematical olympiad, some students used Bertrand hypothesis, that is, Chebyshev theorem, that is, when n is greater than1,there must be a prime number between n and 2n, and some students used Scherbinssey theorem when solving problems, that is, a square table becomes the general solution of the sum of s squares. These theorems can only be found in "Introduction to Number Theory" written by Hua (a textbook for graduate students of university mathematics department) or in more professional books. This is not only "killing the chicken with an ox knife", but also according to a foreign coach, "They are bombing mosquitoes with atomic bombs, but mosquitoes are killed!" This is allowed, but it is not encouraged by the International Mathematical Olympiad.
A difficult problem in the international mathematical Olympics needs to be written in three or four pages after simplification, which not only greatly exceeds the depth of middle school textbooks, but also is not lower than the depth of general courses in university mathematics departments, and certainly does not include the breadth of university courses. In fact, in the course of university mathematics department, not many people prove a theorem with three pages. A good test answer is roughly equivalent to an interesting essay. Therefore, it is quite scientific to use these questions to evaluate the mathematical quality of teenagers. Their solution requires participants to have extensive basic knowledge of mathematics, plus wit and creativity. This is completely different from a simple intelligence test. International mathematics competitions generally range from the fourth grade of primary school to the second grade of college. Because primary school students have little basic knowledge, the so-called math contest during this period is actually a quiz. For college students, systematic learning should be emphasized, and an overall understanding of mathematics is needed. Therefore, the focus of mathematics competition should be middle school, especially high school.
Now, we have accumulated a wealth of math contest question banks for middle school teachers, students and math enthusiasts to practice. There is also a special competition mathematics magazine in the world.
5. China Mathematics Competition
China's math competition began at 1956, when senior high school math competitions were held in Beijing, Shanghai, Wuhan and Tianjin. A number of famous mathematicians, such as Hua, Su, and so on, actively led and participated in this work. However, due to the "Left" influence, 1965 only opened six times sporadically. After the "Cultural Revolution" began, the mathematics competition was regarded as a set of "customs, capital and repair" and was forced to cancel it all. It was not until the downfall of the Gang of Four and the resumption of the China Mathematics Competition in 1978 that it embarked on the road of rapid development. The math contest before 1980 belongs to the primary stage, that is, the test questions are not divorced from the middle school textbooks. After 1980, it gradually entered the advanced stage. China participated in the International Mathematical Olympiad for the first time in 1985, and was among the best in 1986. 1989 and 1990 won the first place in the total score of the team for two consecutive years.
China successfully held the 3 1 International Mathematical Olympiad, which indicated that the level of China's mathematical competition reached the international leading level. First, China won the first place in the total score of the team, which shows that China's pyramid-shaped competition selection system at all levels, Olympic Mathematics school and centralized training system are all perfect. Second, mathematicians in China simplified and improved more than 100 test questions provided by 35 countries, and recommended 28 questions for leaders of various countries to choose from. As a result, five questions were selected (* * * needs six questions), which shows that the level of competition mathematics in China is quite high. Third, the test papers of students from all countries are first corrected by leaders of various countries, and then coordinated and recognized by the host country. We organized nearly 50 mathematicians as coordinators, scored accurately and fairly, and completed the coordination task half a day ahead of schedule, which shows that China's mathematics has considerable strength. Fourthly, this is the first time that the International Mathematical Olympiad has been held in Asia. China's outstanding achievements have inspired developing countries, especially Asian countries. In addition, the organization of this competition is also quite good.
In China, thousands of mathematicians from the older generation, young and middle-aged mathematicians to primary and secondary school teachers joined forces with Qi Xin to achieve the achievements of today's mathematics competition. Special mention should be made to Hua here. He not only advocated China's math contest, but also wrote five pamphlets, from Yang Hui's triangle, from Zu Chongzhi's pi, from Sun Tzu's "magic calculation", mathematical induction and mathematical problems related to the honeycomb structure. These are his competition math works. 1978 After China resumed the math competition, he personally presided over the test questions and wrote comments for the answers. China's other outstanding competition mathematics works include Duan Xuefu's Symmetry, Min Sihe's Lattice and Area, and Jiang Boju's A Pen and the Post Road. Wang Shouren should also be mentioned here. Since he cooperated with China, he has been leading and participating in mathematics competitions. Led the China team to participate in the International Mathematical Olympiad for three times, and led the work of the 3rd1International Mathematical Olympiad. After 1980, young and middle-aged mathematicians basically took over the math competition of the older generation in China, and they made positive efforts to push the level of math competition in China to a new height. Qiu Zonghu is one of the outstanding representatives. He has made outstanding contributions from cultivating students to organizing and leading mathematical competitions, from leading the China team to participate in the International Mathematical Olympiad for three times to holding the 3 1 International Mathematical Olympiad.
Six, some questions about the China Mathematics Competition.
1. We should sum up our experience seriously. We should sum up the experience of success and the lessons of failure. Especially in the 22 years from 1956 to 1977, only six mathematical competitions were held on a small scale, and they stopped completely in 16, which was more than twice as long as that in Hungary due to the two world wars, which also reflected the harm of "Left" from one side. It is necessary to allow and even encourage the expression of different views on mathematics competitions, and avoid big bang, ups and downs and "one size fits all". When there are shortcomings, we should calmly analyze and draw a clear line between the irrationality contained in the math competition and the shortcomings in our work.
2. Improve the leadership system. Can we imagine that the State Education Commission and the China Association for Science and Technology, through the chinese mathematical society Mathematical Olympic Committee (or other forms of unified leadership), will lead and coordinate the participation and training of the national mathematical competitions at all levels and the international mathematical Olympics? Set up the Mathematical Olympic Foundation to fund some mathematical competitions and reward winners of mathematical competitions and leaders, coaches and primary and secondary school teachers who have made contributions.
3. Publicity to the society. Publicize the significance and function of math contest, and eliminate misunderstandings, such as "math contest is an intellectual quiz for primary and secondary school students", "talent selection impacts normal teaching", "teachers, especially university teachers, are not in place" and so on. Facts should be used to illustrate the achievements of mathematics competition activities. For example, just before the "Cultural Revolution", in several low-level math competitions, some winners have become talents. For example, Wang Jiagang and Chen Zhihua in Shanghai, Tang Shouwen and Shihe in Beijing, are now famous middle-aged mathematicians in China, and some of them have obtained doctoral tutor qualifications. It was the Cultural Revolution that delayed 10 years, otherwise the achievements would be even greater.
4. Handle the relationship between popularization and improvement. Mathematics competitions need to be held in schools, cities, provinces, the whole country, winter camps and training courses in the form of pyramids. The first three levels are universal, and the test questions should not be divorced from the scope of middle school mathematics textbooks, but should be oriented to the majority of students and teachers. National competitions and follow-up activities are all improved, and the number of participants should decrease rapidly. As for the winter camp and training team, only dozens of students can participate. Mathematical olympiad schools should pay attention to quality, and do it with less and more precision. Students attending math schools should be strictly selected, so as not to hinder their all-round development in morality, intelligence and physique. In addition to winter camps and training courses, a few mathematicians need to concentrate on problem-setting and training. We might as well encourage mathematicians and primary and secondary school teachers to engage in math competitions in their spare time and not interfere with everyone's normal work. In a word, the popularization part and the improvement part of mathematics competition should not be antagonistic, but should be organically combined.
5. Continuing education and training the winners of mathematics competitions. On the one hand, we should fully affirm and encourage the winners' achievements, on the other hand, we should tell the winners of the competition that they must be cautious, modest and prudent, and only after a long and unremitting hoe can they become an excellent mathematician or an expert in other fields. Don't take winning the game as the sole purpose, but as a spur to encourage progress. We should also create better opportunities for the winners of mathematics competitions to study deeply and let them grow rapidly. For example, we can consider letting some universities of science and engineering select some students from the winners of the national high school mathematics competition and not take the exam.
6. Those who have made contributions to the mathematics competition activities, including organization leaders, coaches and primary and secondary school teachers, should fully affirm and reward their work achievements. In their job evaluation, as one of the basis for promotion.
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