People all over the world are too lazy to complain about the math level of American students, just as they are used to marveling at the genius of China students.
Without a calculator, there would be no four operations, and sinx/n counts as "six". American students make jokes one after another, and every once in a while, public opinion calls for "saving children." In contrast, most American middle school students are surprised by the ability of China students.
A joke played by American students on math test papers, which is widely circulated on the Internet.
Why is China good at math?
In the programme for international student assessment (PISA) sponsored by the OECD, Shanghai middle school students surpassed 75 other cities in the math proficiency test, ranking first. The British were so envious that they immediately invited 60 math teachers from Shanghai Middle School to introduce their experiences in Britain.
In addition, the mainland as a whole did not take the exam, but China and Shanghai ranked first, and the United States only ranked 36th.
In addition to daily teaching, the results of the competition also reflect this gap.
The International Mathematical Olympiad is one of the most famous competitions for middle school students. Since China entered the competition in 1985, she won the first place in the total score with 19 times. Outside China, only South Korea, Romania, Bulgaria and the Soviet Union (Russia), Iran and the United States won the first place in the total score, of which the United States won only once.
Good American media will definitely reflect. In September, The Wall Street Journal quoted the research results of two professors, Northeastern University in Boston and A&M University in Texas, and summarized the reason for backwardness as a language problem.
In other words, the languages of China, Japanese, Korean and Turkish have natural mathematical advantages. For example, Chinese, 10 basic Chinese characters can present all the numbers, while English needs 20 different words, which affects the efficiency of mental arithmetic.
In different languages, Chinese, Japanese and Turkish can all use the method of adding ten to represent numbers, but English can't. ?
In the process of operation, the application of "making a ten" has also had a far-reaching impact. In other words, it seems clearer and faster if the number can be rounded to ten first. For example, "9+5" can be decomposed into "9+ 1" and then into "10+4", but native English speakers can't decompose it smoothly. Similarly, "1 1+ 17" can be replaced by "10+10+7" in Chinese, but "eleven+seven" cannot.
Some scholars have repeatedly thought about this issue, and the most classic one should be Malcolm, who is known as a geek. In his book "Heterogeneity: Different Enlightenment of Success", Malcolm Gladwell specifically analyzed and studied the phenomenon that China people were particularly good at mathematics with paddy field and mathematics as the topic.
Gladwell's explanation seems very convincing. In addition to the basic Chinese character 10 mentioned above, he also believes that monosyllabic Chinese makes China people naturally have a faster mental arithmetic speed when dealing with numbers; Another advantage of China people in language is that the way Chinese expresses scores is naturally more concise and intuitive than other languages.
However, Gladwell believes that the number of people in China is not only the above-mentioned language advantage, but also the agricultural farming culture dominated by rice in China is decisive. Because Gladwell noticed that Japanese and Koreans who mainly grow rice are equally outstanding in math ability-in areas suitable for growing rice, farmers are busy all year round, and in order to make full use of land and time, they will be far more careful than farmers who grow wheat. In addition, China has always been a scattered small farmer in ancient times, and its economic independence makes every farmer learn to calculate like an entrepreneur. Competitive selection in the long history will make the social mathematics ability based on rice farming more prominent.
However, although Gladwell's analysis is sober, there are serious mistakes and omissions in his observation and explanation of this phenomenon. This may even make his research worthless.
Malcolm. Gladwell and his work Alien: Different Revelations of Success?
Are China people really good at math?
The first question is, what is the standard of good mathematics?
If a certain number of people learn well, it means the level of mathematical research, then the problem comes. Once mathematics was extended to universities or research fields, stupid Americans immediately stood up, and China's advantage in mathematics was magically reduced.
In the world mathematics research, the United States, France and Russia are in the undisputed leading position. Subsequently, countries such as Israel and Japan were also ahead of China. Even in Britain, where middle school mathematics learns from China, mathematics research is far ahead. If the discussion scope of the topic is extended to the research and application fields, it will lead to a new problem, why can't China people study mathematics?
Take the International Mathematical Olympics as an example. Except China, many gold medal winners after 1985 have made their mark in the international mathematics field. Participants from France, Russia, the United States, Hungary, Brazil and other countries have all won the Fields Prize and Clay Prize in mathematics, but the research level of China players lags behind the defeated opponents as a whole.
Mathematics research in the United States is particularly strong, not only in the field of pure mathematics, but also in the fields of physics, chemistry, finance and basic computer science that require a lot of mathematical knowledge. The United States has gathered a large number of talents who depend on mathematics in these fields, and the overall mathematics level of its natural scientists and engineers is by no means inferior to that of their counterparts in China.
Liu Zhiyu (left), a "mathematical genius" who won the gold medal in the International Mathematical Olympics with full marks, has now become a monk in Longquan Temple, and his legal name is Yu Sheng.
Why did China perform so well in the middle school mathematics competition, but she lacked stamina in the backward development?
Another problem is that if the standard of good mathematics is that middle school students have a high level of mathematics competition, then Gladwell and others have obviously forgotten a period of history. Before 1990, the gold medal winners of the International Mathematical Olympiad were the Soviet Union and Eastern European countries-the International Olympic Games was originally initiated by Eastern European countries, and the Soviet Union and Russia * * * won the first place in the group with the total score of 16.
After the drastic changes in Soviet Union and Eastern Europe, China began to replace the Soviet Union and Eastern European countries in mathematics competitions-just as the Soviet Union no longer concentrated all its resources and strength to win the Olympic gold medal, China began to catch up with the Soviet Union and Eastern Europe in the Olympic gold medal.
Soviets have neither innate language advantages in mathematics nor a history of rice cultivation. What's more, farmers in Russia and eastern Europe are almost the most loose and extensive farmers in the world in the eyes of westerners. They are the last people who have the qualities of careful calculation and hard work.
Whether in the Soviet Union and Eastern Europe in the past, or in China, Japan, South Korea and other East Asian countries today, the only uniqueness of these areas with strong mathematical calculation ability and high level of mathematical competition is that they have a strong national examination-oriented education system.
In fact, there are essential differences between mathematics competition and mathematics research, and there are also differences between junior and senior high school's computing ability and college mathematics.
Tao Zhexuan, an Australian mathematician who won the gold medal in the International Mathematical Olympiad and the Fields Prize, once said in an article: Mathematics competition is very different from mathematics learning. Especially in the postgraduate career, students will not encounter problems with clear description and fixed steps like math competition questions. Although competitive thinking is very fast in solving research-oriented problems, it cannot be extended to a wider range of mathematics fields. More problems still depend on patience and persistent work-reading literature, using skills, modeling problems and looking for counterexamples.
1988, 13-year-old Tao Zhexuan took the gold medal of the International Mathematical Olympiad from then Australian Prime Minister bob hawke.
In addition, although the topics in the Olympic Games are more difficult, they test skills, but the requirements for creativity are lower, but the latter is one of the core competencies in the research field.
Generally speaking, mathematics competition needs proficiency and skills, and depends on talent, but it can also be successful by a lot of concentrated training. The research and study of advanced mathematics depends on persistent work and in-depth understanding. Different from arithmetic, mathematical research emphasizes the application of abstraction and logical reasoning. It is far more important to deeply understand complex and diverse mathematical problems than to solve specific types of problems.
Famous mathematician William? Thurston once compared a math contest to a spelling contest. In his view, ranking in the spelling contest does not mean becoming an excellent writer, and so does the math contest: good grades do not mean really knowing math.
Mathematics learning tests the depth and quality of learning and thinking, while mathematics competition needs "precocity". Race against time and learn faster than your peers. For a clever student, the latter is easier. Moreover, even if the talent is limited, you can make progress in the latter through intensive training.
Obviously, exam-oriented education in East Asia can provide the richest training. Yuri, a behavioral economist? Yuri Gnitz and aldo? Aldo Rustici's experiment found that even though the level of the contestants is similar, as long as they are given a competition with a higher single-question reward, the contestants can achieve the best results, which is precisely the strength of China, Eastern Europe and other countries: the competition pressure is greater, the competition rewards are more, and the whole middle school education takes arithmetic ability as the training point.
This is not needed in the United States or other western European countries. For ordinary students, as long as they have achieved basic math scores, such as Massachusetts, the difficulty of unified examination is probably to know the basic trigonometric function operation.
It can be said that the difference of training intensity in education has caused the gap of mathematics level among ordinary middle school students. The intensity of intensive training has also greatly affected the competition results.
Then after entering the university, the gap between Chinese and American math scores began to reverse. Why?
Why is China's math research not good?
Perhaps the key reason is classified education in the United States. The basic requirements of the United States for ordinary middle school students' mathematical calculation ability are not high, and talented and interested students can complete advanced placement in middle school. After completing AP, you will take the preliminary exam.
AP textbooks for American middle school students are not limited to mathematics, but also cover many subjects.
The difficulty of preparatory courses is much higher than that of ordinary high school mathematics in the United States. Compared with the mathematical contest, its setting is more conducive to the understanding of mathematical problems. For example, in the pre-university courses in the United States and Canada, calculus covers all the knowledge of unitary calculus, which is equivalent to the contents of two semesters of mathematics courses in American universities. Through these trainings, the understanding of calculus can be improved more reasonably. China high schools, which emphasize competition, pay little attention to this kind of knowledge.
From the perspective of personal future growth, it is more appropriate to finish the pre-university course ahead of time than to spend time on the math contest. The former is closer to real mathematical research. In the same way, universities will also take the results of pre-university courses as an important consideration when enrolling students.
As far as the research field is concerned, the effectiveness of high-intensity mathematical calculation training is very low. Modern mathematics, like many basic disciplines, has a continuous research tradition and school atmosphere, which often determines its achievements. At this point, there is a huge gap between China University and European and American universities.
The Soviet Union and Eastern European countries have also achieved excellent results in the competition, but at the same time they are the top countries in mathematical research-in the past nearly 100 years, the Soviet Union-Russia has been the top country in mathematical research, and it is recognized as a big country in mathematical research on an equal footing with the United States and France. Its sharp contrast with China is precisely for this reason.
The fine and long tradition of mathematical research in the Soviet Union (Russia) has almost never been interrupted. As early as18th century, Leonhard, the pioneer of modern mathematics? Euler worked in Petersburg for more than 30 years, and made the famous Petersburg Mathematics School in Russia. Since then, mathematicians such as Lobachevsky, Chebyshev, Lyapunov and Markov have emerged in Russia and the Soviet Union.
During the most turbulent political period of Stalin and Khrushchev, the tradition of mathematical research in the Soviet Union was not interrupted. On the contrary, due to the needs of war and planned economy, mathematicians escaped the influence of political movements. There is not only a sense of security in life, but also a relative freedom to do interesting research.
1at the end of 950, middle school students in the Soviet Union had a math class under the lens of photographer erich Lessingsheng.
At the same time, they also have a unique seminar system-presided over by well-known mathematicians, regardless of age and qualifications, interested parties can participate. This is very helpful for the continuation of tradition. A large number of young mathematicians emerged in the Soviet seminar class, forming the famous Moscow School.
The Soviet Union is also different from China in training younger mathematical talents. The Soviet Union and China also have a large number of math summer camps, but the Soviet summer camps rely on interest to register, and do not emphasize exams and scores. It is often masters in a certain field who give lectures, rather than middle school teachers who focus on training students to take exams. For example, top mathematicians, such as André Andrey Kolmogorov, attend the middle school math summer camp every year. This will not only make students interested in mathematics, but also give talented students the opportunity to talk to the master and get to know the real mathematics as soon as possible.
In addition, the mathematical circles in the Soviet Union have always kept in touch with the international mathematical circles. At that time, the extremely prosperous French bourbaki Mathematics School was very popular in the Soviet Union. The speed of translation of international mathematical works by the Soviet mathematical community is also a must.
In contrast, the contemporary mathematicians in China are much worse. Even if you can escape death, you can only do research according to the arrangement of the leader. For example, the famous analytic number theorist Hua was humiliated and attempted suicide less than two years after returning to China. Since then, we have to study and popularize the optimization method of "steamed bread". Xiong Qinglai, the teacher of Hua and the founder of the Department of Mathematics of Tsinghua University, was directly persecuted to death.
1in the winter of 974, Hua went deep into the workshop in Guangxi to explain the optimization method.
Students in China are not so lucky. They received intensive training too early and won the gold medal in the competition, but there is no open higher education atmosphere and continuous mathematics tradition ahead, so that truly talented people can shine in the research field. Of course, good competition results will enable them to enter first-class universities, and school leaders will rate them as advanced, even not bad for the country-these students will study in the United States in the future, which will make Americans feel that China people's mathematical calculation ability is really strong.