Why are China people good at math and why are they not?

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, you can't do four operations. If sinx/n is counted as "six", American students make jokes one after another. Every once in a while, public opinion calls for "saving children". In contrast, most American middle school students are astounded by the ability of China students.

jokes made by American students on math test papers that are widely circulated on the Internet

Why is China's math good

In the programme for international student assessment (PISA) sponsored by the OECD, Shanghai's middle school students surpassed 75 other cities in the math proficiency test, ranking first. The British were so envious that they immediately invited 6 math teachers from Shanghai middle schools to introduce their experiences in Britain.

Source: programme for international student assessment (PISA) of OECD in 212

In addition, the mainland has not yet taken the test as a whole, but Shanghai, China ranks first, and the United States ranks only 36th.

In addition to daily teaching, the results of competitions 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, it has won the first total score for 19 times. Outside China, only South Korea, Romania, Bulgaria and the Soviet Union (Russia), Iran and the United States have won the first place in the total score, of which the United States has only won once.

Good American media will certainly reflect. In September, The Wall Street Journal quoted the research results of two professors, Northeastern University in Boston and Texas A&M University, and summarized the reason for backwardness as a language problem.

That is to say, languages in China, Japan, South Korea and Turkey have natural mathematical advantages. For example, in Chinese, 1 basic Chinese characters can present all the numbers, while in English, 2 different words are needed, which affects the efficiency of mental operation.

In different languages, Chinese, Japanese and Turkish can all use the method of ten to represent numbers, but English can't. Source: wsj

In the operation process, the application of "make a ten" also has a profound influence. That is to say, it seems clearer and faster if the number can be rounded up to ten first. For example, "9+5" can be decomposed into "9+1" and then "1+4" by "ten-point method", but native English speakers cannot decompose it smoothly. Similarly, "11+17" can be replaced by "1+1+1+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. Malcolm Gladwell, in his book Alien: Different Apocalypse of Success, specifically analyzed and studied the phenomenon why China people's mathematics is particularly good with the title of Paddy Field and Mathematics.

Gladwell's explanation seems very convincing. In addition to the 1 basic Chinese characters mentioned above, he also believes that the monosyllabic Chinese makes China people naturally have faster mental arithmetic speed when dealing with numbers; Another advantage of China people in language is that the way of expressing scores in Chinese is naturally more concise and intuitive than other languages.

However, Gladwell believes that China people's good mathematics is not only the above-mentioned linguistic advantages, but also the agricultural farming culture dominated by rice in China is equally decisive. Because Gladwell noticed that the mathematical ability of Japanese and Koreans who mainly grow rice is equally outstanding-in areas suitable for rice planting, farmers are busy all year round, and in order to make full use of land and time, they will be far more careful than wheat farmers. In addition, China has always been a scattered small farmer in ancient times, and the economic independence makes every farmer have to learn to calculate like an entrepreneur. Competitive selection in the long history will make the social mathematics ability dominated by rice farming more prominent.

However, although Gladwell's analysis is clear-headed, there are serious errors and omissions in both his observation and explanation of the phenomenon. This may even make his research worthless.

Malcolm? Gladwell and his work Alien: Different Revelations of Success

Are China people good at math?

the first question is, what are the criteria for good math?

If we say that a certain group of people is good at mathematics, we mean the level of mathematics research, then the problem comes. Once mathematics is extended to universities or research fields, stupid Americans immediately stand up, and China's mathematical advantage is magically reduced.

The United States, France and Russia are in the undisputed leading position in the world mathematics research. Subsequently, countries such as Israel and Japan were also ahead of China. Even in the United Kingdom, where middle school mathematics learned from China, mathematics research is also far ahead. If the discussion scope of the topic is extended to the field of research and application, instead, a new question will arise, why China people's mathematics research is not good.

Take the International Mathematical Olympiad as an example. Except China, many gold medal winners after 1985 have made their mark in the international mathematical field. Competitors from France, Russia, the United States, Hungary, Brazil and other countries have all won Fields Prize and Clay Prize in Mathematics, but the contestants from China are behind their defeated opponents in research level as a whole.

American mathematics research is particularly strong, leading not only in the field of pure mathematics, but also in physics, chemistry, finance which requires a lot of mathematical knowledge and basic computer science which requires discrete mathematics. The United States has gathered a large number of talents in these fields that depend on mathematics, and the overall mathematical level of its natural scientists and engineers is by no means inferior to that of their counterparts in China.

liuzhiyu (left), a "mathematical genius" who won the gold medal in the International Mathematical Olympiad with full marks, has now become a monk in Longquan Temple, with the legal name Shengyu

Why did China perform so well in the middle school mathematics competition, but she lacked stamina in her backward development?

Another problem is that if the standard of good mathematics is that middle school students have a high level of mathematics competition, Gladwell and others have obviously forgotten a period of history. Before the 199s, the gold medal winners in the international mathematical olympiad were the Soviet Union and eastern European countries-the international Olympic Games were originally initiated by eastern European countries, and the Soviet Union and Russia * * * won the first place in the total score of 16 international mathematical olympiads.

China began to replace the Soviet Union and Eastern European countries in mathematics competitions after the drastic changes in the Soviet Union and Eastern Europe-just as the Soviet Union stopped concentrating all the resources and strength of the country to win the gold medal in the Olympic Games, China began to surpass the Soviet Union and Eastern Europe in the gold medal in the Olympic Games.

Soviets have no innate linguistic advantages in mathematics, and they have never had 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, and they are the people farthest from the qualities of careful calculation and hard work.

No matter the Soviet Union and Eastern Europe in the past, or 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 the computing ability of junior high school and senior high school is also different from that of college mathematics.

Tao Zhexuan, an Australian mathematician who won the gold medal and Fields Prize in the International Mathematical Olympiad at the same time, once said in an article: Mathematical contests are very different from mathematical learning. Especially in the postgraduate career, students will not encounter problems with clear descriptions and fixed steps like mathematical competition problems. Although competitive thinking is very fast in solving some research-oriented problems, it cannot be extended to a wider field of mathematics. More problems still depend on patient and persistent work-reading literature, using skills, modeling problems and finding counterexamples.

In p>1988, at the age of 13, Tao Zhexuan received the Olympic gold medal in international mathematics from then Australian Prime Minister bob hawke.

In addition, although the topics in the Olympic Games are more difficult, they test skills and require less creativity, but the latter is one of the core competencies in the research field.

Generally speaking, mathematics competition requires proficiency and skill, and depends on talent, but it can also achieve success by relying on a lot of intensive training. The research and study of advanced mathematics depends on persistent work and in-depth understanding. Different from arithmetics, mathematical research emphasizes abstraction and the use of logical reasoning. It is far more important to have a deep understanding of complex and diverse mathematical problems than to solve specific types of problems.

William, a famous mathematician? Thurston once compared a math contest to a "spelling contest". In his opinion, winning a place in the word spelling competition does not mean becoming an excellent writer, and so does the math competition: good grades do not mean really understanding mathematics.

Mathematics learning tests the depth and quality of learning and thinking, while mathematics competition needs "precocity". It is necessary to race against time and learn faster than peers. For a clever student, the latter is easier. Moreover, even with limited talent, you can make progress in the latter with high-intensity training.

Obviously, exam-oriented education in East Asia can provide the most abundant training. Yuri, a behavioral economist? Uri Gneezy and Aldo? Aldo Rustichini's experiment found that even if the contestants are similar in level, the contestants can get the best results by giving a competition with higher single-question reward, which is precisely the strength of China, Eastern Europe and other countries: higher competitive pressure, more competition rewards, and the whole middle school education takes arithmetic ability as the training point.

This is not required in the United States or other western European countries. For ordinary students, as long as they have achieved basic math scores, for example, in Massachusetts, the difficulty of the unified examination is about knowing 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 difference in math scores between China and the United States began to reverse. Why?

Why is China's mathematics research not good

Perhaps the key reason is American classified education. The basic requirements of the United States for ordinary middle school students' mathematical computing ability are not high, and talented and interested students can complete Advanced Placement in middle schools. After completing AP, you will take the prerequisite exam.

AP textbooks for middle school students in the United States are not limited to mathematics, but also cover many disciplines.

The difficulty of prerequisite courses is much higher than that of ordinary high school mathematics in the United States. Compared with mathematics competitions, its setting is more conducive to the understanding of mathematical problems. For example, in the pre-university courses in the United States and Canada, the two courses in calculus cover all the knowledge of one-dimensional 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. However, China High School, which emphasizes competition, seldom pays attention to this kind of knowledge.

From the perspective of personal growth in the future, it is more appropriate to finish the pre-university courses ahead of time than to spend time on math competitions. The former is closer to real math research. For the same reason, universities will also take the scores of pre-university courses as an important consideration when enrolling students.

As for the research field, 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 competitions, but at the same time they are the top countries in mathematical research-in the past 1 years, the Soviet union and Russia have always been the top countries in mathematical research, and are recognized as the top countries in mathematical research along with the United States and France. Its sharp contrast with China is precisely this reason.

The Soviet Union (Russia) has an excellent and long tradition of mathematical research, which has almost never been interrupted. As early as the 18th century, Leonhard, a pioneer of modern mathematics? Euler worked in Petersburg for more than 3 years, which led to 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 times of Stalin and Khrushchev, the tradition of mathematical research in the Soviet Union was not interrupted. On the contrary, mathematicians escaped the impact of political movements because of the needs of war and planned economy. Not only is there considerable security in life, but also there is relative freedom to do interesting research.

In the late 195s, Soviet middle school students were taking a math class under the lens of photographer erich Lessingsheng.

At the same time, they also had a special discussion class system, which was presided over by a famous mathematician and was open to all interested parties regardless of their age and qualifications. This is very helpful for the continuation of tradition. A large number of young mathematicians emerged in the discussion class of the Soviet Union, forming the famous Moscow School.

The Soviet Union is also different from China in training younger mathematics talents. The Soviet Union and China also have a large number of math summer camps, but the Soviet summer camps rely on interest registration 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 for exams. For example, top mathematicians, such as Andrey Kolmogorov, attend middle school math summer camp every year. This will not only make students interested in mathematics, but also give gifted students a chance to talk to the master and learn about 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. The French bourbaki School of Mathematics, which was extremely prosperous at that time, 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, contemporary mathematicians in China are much more miserable. Even if you can escape death, you can only do research according to the arrangement of the leader. For example, Hua Luogeng, a famous analytic number theorist, was humiliated less than two years after returning to China, but attempted suicide. Since then, we have to study and promote the optimization method of "steamed steamed bread". Hua Luogeng's teacher, Xiong Qinglai, the founder of the Department of Mathematics of Tsinghua University, was directly persecuted to death.

In the winter of p>1974, Hua Luogeng went deep into the workshop in Guangxi to explain the optimization method

And the students in China were not 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 those who have real talent can shine in the research field. Of course, good competition results will enable them to enter the first-class universities, and the school leaders will be rated as advanced, even not bad for the country-these students studying in the United States in the future will make Americans feel that China people's mathematical calculation ability is really strong.

Wen/Hu Xiuzhuo

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, you can't do four operations. If sinx/n is counted as "six", American students make jokes one after another. Every once in a while, public opinion calls for "saving children". In contrast, most American middle school students are astounded by the ability of China students.

The laughter made by American students on the math test paper, which is widely circulated on the Internet.