I am a Chinese student. The school encourages us to recite some famous essays, poems and English words. We may also be encouraged to remember historical facts and events, but the same rules obviously do not apply to mathematics or any other natural science education.
我是一名中国学生。学校鼓励我们背诵一些著名的散文、诗歌和英语词汇。我们可能也会被鼓励去记忆历史事实和事件，但同样的规则明显不适用于数学或任何其他自然科学教育。
Generally speaking, Chinese students' mathematical problems in middle school or high school are more challenging than those in other countries. I do not believe that all these problems can be solved by pure theorem memory. These challenging problems have improved the average level of Chinese students' mathematical problem-solving ability.
一般来说，中国学生在中学或高中所做的数学问题比其他国家的数学问题更具挑战性，我不相信通过纯粹的定理记忆可以解决所有这些问题。这些具有挑战性的问题提高了中国学生数学问题解决能力的平均水平。
The most important reason why Chinese students perform well in international competitions is that they are good at math in middle school or high school, even in primary school, which is a great honor. Therefore, most "smart" students are very active in spending their time on improving their math skills. At the same time, a student who is good at other courses, such as Chinese, English, history, politics, and even sports, has no chance to get the same honor.
中国学生在国际赛事表现优异的最重要原因是，他们在中学或高中，甚至在小学，数学都很好。因此，大多数“聪明”的学生都非常积极地将时间花在提高数学技能上。同时，一个擅长其他课程的学生，如汉语、英语、历史、政治，甚至体育，都没有机会获得同等的荣誉。
Being good at mathematics also means having the opportunity to skip the college entrance examination and enter the most famous university in China. Winning the first prize in the national mathematics competition (ranking the top 40 in a province, among about 100000 to 1 million students) will guarantee admission to top universities. Over the years, this policy has undergone some changes, but being good at mathematics still helps college enrollment.
擅长数学也意味着有机会跳过高考，进入中国最著名的大学。在全国数学竞赛中获得一等奖（在一个省中排名前40位，在大约10万至100万名学生中）将保证获得顶尖大学录取。这些年来，这项政策发生了一些变化，但擅长数学仍然有助于大学入学。
The problems that students need to solve in such competitions are very challenging. Such competitions also help to select the national team of IMO. At the same time, students who are good at physics, chemistry, biology, computer science and have won awards in similar competitions have the opportunity to be admitted to top universities.
学生在此类比赛中需要解决的问题非常具有挑战性，此类比赛也有助于选拔IMO（奥数竞赛）的国家队。同时，擅长物理、化学、生物、计算机科学并在类似比赛中获奖的学生也有机会获得顶级大学录取。
This opportunity to enter a top university without other exams once again encourages "smart" students to concentrate on mathematics or other four courses in high school. In the first two years of high school, they may spend more than half of their time studying a subject. If they do not win the corresponding competition, they can study other courses in the third year.
这种在没有其他考试的情况下进入顶尖大学的机会再次激励“聪明”的学生在高中集中学习数学或其他4门课程。在高中的前两年，他们可能会投入一半以上的时间学习一门学科，如果在相应的比赛中没有获奖，他们可以在第三年学习其他课程。
In order to help students win prizes in math competitions, most of the top high schools (the first or second high schools in major cities in China) have offered math learning courses for students. These courses are usually taught by the best teachers in the school, and even by professors from local universities. In addition to lectures, students majoring in mathematics will often gather together to discuss mathematical problems and solutions. Such discussion has obviously improved students' logical thinking, deepened their understanding of definitions and theorems, and improved their ability to solve problems.
为了帮助学生在数学竞赛中获奖，大多数排名靠前的高中（中国主要城市排名第1或第2的高中）都为学生开设了数学学习课程。这些课程通常由学校最好的老师教授，甚至由当地的大学教授教授。除了讲座，数学专业的学生将经常聚集在一起讨论数学问题和解决方案。这样的讨论明显提高了学生的逻辑思维，加深了他们对定义、定理的理解，提高了他们解决问题的能力。
In fact, most of the top students (yes, we rank high school students according to their monthly exam results) choose to participate in at least one competition course. If they don't win any first prize and have to take the college entrance examination, they may feel ashamed.
事实上，大多数排名靠前的学生（是的，我们根据每个月的考试成绩对高中学生进行排名）选择参加至少一门比赛课程。如果他们没有获得任何一门一等奖，并且不得不参加高考，他们可能会感到羞愧。
Of course, I think the most important reason is that because of the large population, we have enough talent in mathematics. They have the ability to solve IMO problems through appropriate learning and training.
当然，我认为最重要的原因是，由于人口众多，我们在数学方面有足够的人有足够的天赋。他们有能力通过适当的学习和培训解决IMO问题。
Of course, I agree that many Chinese students spend time memorizing theorems, even the past test questions and answers, but I don't think the students who participate in IMO are such students. They may have a good memory, but the difference between them and others is more logical thinking and a good sense of "mathematical thinking".
当然，我同意许多中国学生花时间记忆定理，甚至过去的试题和答案，但我不认为参加IMO的学生就是这样的学生。他们可能有很好的记忆力，但他们与其他人的区别更多的是逻辑思维和良好的“数学思维”意识。
In short, the main reasons for the excellent performance of Chinese students in IMO are:
总之，中国学生在IMO表现出色的主要原因是：
• Schools, universities and the whole society encourage "smart" students to learn mathematics (as well as the other four courses in IPhO, IChO, IBO and IOI), even at the expense of other courses.
•学校、大学和整个社会鼓励“聪明”学生学习数学（以及IPhO、IChO、IBO和IOI中的其他4门课程），甚至牺牲其他课程的学习。
• Students have enough motivation to learn mathematics, because good mathematics is the highest honor.
•学生有足够的动力学习数学，因为数学好是最高的荣誉。
• China has many mathematical talents.
•中国有很多数学天才。
I think this is a good question. I spent a little time thinking about it. In short, there has always been a subtle confusion between mathematics and mathematics education, that is, the confusion between repetition and rote memorization.
我认为这是一个很好的问题，我花了一点时间来思考这个问题。简而言之，数学和数学教育中一直存在着一种微妙的混淆，那就是重复不等同于死记硬背。
Of course, rote learning is not conducive to healthy learning. However, repetition is essential for good learning.
当然，死记硬背不利于健康的学习。然而，重复对于良好的学习至关重要。
Chinese educators have found a way to use repetition without worsening it into rote memorization, while American educators tend to give up most of the value of repetition because they pay too much attention to rote memorization in learning mathematics, and underestimate the value of repetition (because it is confused with rote memorization).
中国的教育工作者已经找到了一种方法来利用重复而不使其恶化为死记硬背，而美国的教育工作者则倾向于放弃重复的大部分价值，因为他们过度关注学习数学的死记硬写方面，而低估了重复的价值（因为它与死记硬记混为一谈）。
If you are curious, you can find the following references:
如果你很好奇，你可以找到以下参考文献：
Dahlin, B, Watkins, D (2000) The Role of Repetition in the Process of Memory and Understanding: A Comparison of the Viewpoints of Chinese and German Middle School Students in Hong Kong. British Journal of Educational Psychology 70: 65-84
Dahlin，B，Watkins，D（2000）《重复在记忆和理解过程中的作用：香港中德中学生观点的比较》。英国教育心理学杂志70：第65-84页
Marton, F, Wen, Q, Wong, KC (2005) "After reading 100 times, the meaning will appear..." The view of Chinese college students on learning time structure has changed. Higher education 49: 291-318
Marton，F，Wen，Q，Wong，KC（2005）“读一百遍，意义就会显现……”中国大学生对学习时间结构的看法发生了变化。高等教育49：第291-318页
Handa，Yuichi（2012）。 Get rid of repetition from corruption: two versions of papers on will, research on mathematics education, v79 n2 p263-272
Handa，Yuichi（2012）。从腐朽中摆脱重复：关于意志的两种版本的论文，数学教育研究，v79 n2 p263-272
In some areas of mathematics education, repetition and rote memorization are confused to some extent in terms of their teaching purposes and consequences. In this paper, I propose to separate the two based on the framework proposed by Martin Buber's "I you" ontology. When introducing Buber's idea, I emphasized the concept of "the combination of will and elegance", in contrast with the common "will". As I said, the advantage of repetitive teaching is not in automaticity - this is the common theoretical basis - but in cultivating and supporting a deeper sense of connection and/or intimacy with the research object.
在数学教育的某些领域中，重复和死记硬背在其教学用途和后果方面被某种程度上混为一谈。在本文中，我依据马丁·布伯的“我-你”本体论提出的框架，主张将两者分开。在介绍布伯的想法时，我强调了“意志与优雅结合”的概念，与普通的“意志”形成对比。正如我所说的，重复教学的优点不在于自动性——这是共同的理论基础——而是在于培养和支持与研究对象加深的联系感和/或亲密感。
Chinese education does not emphasize rote learning, but lacks an environment that encourages creative thinking and social skills. I think this is the root cause you see.
中国教育不强调死记硬背，但缺乏鼓励创造性思维和社会技能的环境。我认为这是你所看到的根本原因。
Statistical reasons: more of us study mathematics than the rest of you. We account for almost half of the world's population. We will have "math champions" more often than other "races".
统计原因：我们中学习数学的人比你们中的其他人多，我们几乎占了世界人口的一半。我们将比其他“种族”更经常出现“数学冠军”。
Social reasons: For centuries, our culture has been emphasizing education and learning. Education is more important than owning property, while "white culture" is the opposite.
社会原因：几个世纪以来，我们的文化一直强调教育和学术。受教育比拥有财产更重要，而“白人文化”则相反。
Social management: Because immigrants are usually "better qualified" immigrants, that is, smarter, richer or with some advantages, immigrants need a lot of courage and motivation, otherwise they can't migrate there at the beginning, especially in China and India, where there is huge demand, and immigration officials can nitpick who is allowed to enter. With the unfair advantages of smarter, richer, more ambitious and better parents (compared with other former or new compatriots), children are more likely to perform well.
社会管理：因为移民通常是“条件更好”的移民，即更聪明、更富有或有一些优势，移民需要很大的勇气和动力，否则他们一开始就无法移民到那里，特别是中国和印度，那里有巨大的需求，移民官员可以挑剔允许谁入境。而拥有更聪明、更富有、更有抱负、更优秀的父母（相对于其他前同胞或新同胞），孩子们更有可能表现出色。
By the way, some studies have "proved" that Asians are "smarter" than other "races". They are controversial, to say the least.
顺便说一句，有研究“证明”亚洲人比其他“种族”更“聪明”。至少可以说，它们是有争议的。
According to this study, the IQ range of different races is obviously different. For reference only, this racial classification is the standard of the United States Census.
根据这项研究，不同种族的智商范围显然不同。仅供参考，这个种族分类是美国人口普查标准。
Personally, there are two reasons why Chinese and Indian immigrants have achieved such excellent academic achievements. This is a non-academic hypothesis
就个人而言，中国和印度移民在学术上取得如此优异的成绩有两个原因，这是非学术假设：
1. If they are ethnic minorities: because they are socially isolated in the community. As new neighbors, they are faced with the challenge of making new friends. If they are not outgoing, this may be a bigger challenge. Most importantly, they are culturally different from others, which exacerbates social isolation. If you don't have friends to play ball games (or video games), you will spend more time studying. The result shows that because you have recorded enough experience.
1.如果他们是少数民族：因为他们在社区中处于社会孤立状态。作为初来乍到者，他们面临着结交新朋友的挑战，如果他们不外向，这可能是一个更大的挑战。最重要的是，他们在文化上与其他人不同，这加剧了社会孤立。如果你没有朋友一起打球（或玩电子游戏），那么你会花更多的时间学习。结果表明，因为你积累了足够多的经验。
2. They are forced to meet expectations in society.
2.他们被迫在社会上符合预期。
First of all, due to the traditional emphasis on education, cultural expectations from their own communities, parents or families. Second, because the wider society expects "Asians" to become model minorities, blacks to become criminals, Latinos to become slaves, and so on... Yes, this is racism, yes, unreasonable, but unfortunately, this is a social expectation. Perhaps you are not very interested in learning: you are "forced" to maintain the lowest feasible academic level (this is me), so that you can meet your expectations. Maybe you are not good at learning: you are forced to smoke and mirror to cover up your learning defects, or you may take part in extracurricular activities or volunteer to make excuses for your poor academic performance.
首先，由于传统上对教育的重视，来自自己社区、父母或家庭的文化期望。第二，因为更广泛的社会，期望“亚洲人”成为模范少数民族，黑人成为罪犯，拉美裔成为奴隶等等……是的，这是种族主义，是的，不合理，但不幸的是，这是一种社会期望。也许你对学习不太感兴趣：你“被迫”保持最低可行的学术水平（这就是我），这样你才能满足期望。也许你不太擅长学习：你被迫吸烟和镜子来掩饰你的学习缺陷，也许是通过参加课外活动或自愿为你的学习成绩不佳找借口。
I think this is mainly due to a choice effect in the process of immigration. Both China and India have large populations (about 1.2 billion in India and about 1.35 billion in China). It is not easy to immigrate to the United States. Those who succeed are often willing to make great efforts to improve not only their own lives, but also their children's lives. At least, most Chinese people I know immigrate mainly for their children and future generations. They are willing to stay away from friends and family, the security of social networks, learn a second language, and endure prejudice and racial prejudice in some cases. Although I dare not say that these are the "best and smartest" of India and China, they are certainly not common goods of any country.
我认为，这主要是由于移民过程中的一种选择效应。中国和印度都是人口大国（印度约12亿，中国约13.5亿），移民到美国绝非易事。那些成功的人往往愿意付出巨大的努力，不仅改善自己的生活，也改善孩子的生活。至少，我认识的大多数中国人移民主要是为了他们的孩子和后代。他们愿意远离朋友和家人，远离社交网络的安全保障，学习第二语言，在某些情况下忍受偏见和种族偏见。虽然我不敢说这些是印度和中国“最好的、最聪明的”，但它们肯定不是任何一个国家的普通货。
Educational, professional or artistic achievements, or success in business (read: wealth) have greatly improved a person's chances of obtaining immigration status. Among them, education is almost certainly the biggest factor.
教育、专业或艺术成就，或在商业上的成功（读：财富）都大大提高了一个人获得移民身份的机会。其中，教育几乎可以肯定是最大的因素。
In recent decades, a large number of Chinese and Indian immigrants to the United States are for graduate education, usually in the STEM field.
近几十年来，大量移民到美国的中国人和印度人都是为了研究生教育，通常是在STEM领域。
After studying graduate students in the United States (in some cases), these parents will tend to find jobs in technology companies, finance, academic research or other fields, which will not only put them in a socio-economic position, but also geographically close to the upper middle class of the United States, sometimes even further away. These are demographics with high property taxes, which means good (read: competitive) schools. These schools will only emphasize the possibility of certain children participating in math, science and spelling competitions.
在美国读过研究生（在某些情况下）后，这些父母会倾向于在科技公司、金融、学术研究或其他领域找到工作，这些领域不仅会使他们处于社会经济地位，而且会在地理上接近美国中上阶层，有时甚至更远。这些都是缴纳高额财产税的人口统计学，这意味着好的（读：有竞争力的）学校。这些学校只会强调特定孩子参加数学、科学和拼写比赛的可能性。
To sum up, up to now, Chinese and Indian students are highly represented in the best schools in the United States, because the barriers to immigration and immigration often choose certain types of success from populous Asian countries, and immigrants from these countries will seek to replicate the same advantages they think can be immigration and immigration in their children.
综上所述，到目前为止，中国和印度学生在美国最好的学校中的代表性很大，因为移民和移民的障碍往往会从人口众多的亚洲国家选择某些类型的成功，来自这些国家的移民将寻求在他们的孩子身上复制他们认为能够移民和移民的相同优势。
I am quite confident in this respect. But I believe there are more. I don't know much about the teaching tradition in India. I hope someone can describe it in detail here, but I know that in China's educational norms, people attach great importance to rote learning. In fact, since written Chinese only provides some pronunciation clues (different from alphabetic or syllabic language), even basic literacy requires a lot of memory.
在这方面我相当有信心。但我相信还有更多。我不太了解印度的教学传统，希望有人能在这里详加描述，但我知道，在中国的教育规范中，人们非常强调死记硬背。事实上，由于书面汉语只提供了部分的发音线索（不同于字母或音节语言），即使是基本的识字也需要大量的记忆。
Anyway, watching my own children go to primary school in Beijing, I was shocked by the number of memories: multiplication tables, squares and square roots, long lists of prime numbers, and poems with more than 100 lines (yes, they are very short, only three lines, but they did so when they were 4 years old!).
无论如何，看着我自己的孩子在北京上小学，我对记忆的数量感到震惊：20年代的乘法表、正方形和平方根、长长的素数列表、超过100行的诗歌（是的，它们很短，只有三行字，但他们在4岁时就这样做了！）。
Although I have no statistics in front of me, I clearly remember that studies have shown that the academic advantages of the second-generation immigrant families from the United States, East and South Asian countries, have declined sharply in the following generations, which shows that the really prominent factor here is the influence of immigrant parents.
虽然我面前没有统计数据，但我清楚地记得，有研究表明，来自美国东亚和南亚国家的第二代移民家庭所表现出的学业优势在随后几代人中急剧下降，这表明这里真正突出的因素是移民父母的影响。