中國人真的很擅長數(shù)學(xué)嗎？

Is it true that Chinese are pretty good at maths?

2024-06-24 Phelps 9798 53 12 收藏糾錯&舉報

譯文簡介

網(wǎng)友：根據(jù)我的經(jīng)驗(yàn),中國孩子在數(shù)學(xué)方面很出色。我見過中國中學(xué)生在完成的那種作業(yè),按加拿大的標(biāo)準(zhǔn),基本相當(dāng)于高中前期的微積分水平。

正文翻譯

研究顯示，中國人在算術(shù)方面確實(shí)更勝一籌。

評論翻譯

Jaret Neilson
In my experience, Chinese children are very good at math. I've seen the kind of homework Chinese middle school students are zipping through and it was basically high school pre-calculus by Canadian standards.

根據(jù)我的經(jīng)驗(yàn),中國孩子在數(shù)學(xué)方面很出色。我見過中國中學(xué)生在完成的那種作業(yè),按加拿大的標(biāo)準(zhǔn),基本相當(dāng)于高中前期的微積分水平。

Another poster interestingly pointed out that it's because of the language, and I think so too, but actually another facet which I think is more responsible for Chinese students' ability to learn math more quickly than others. Some people feel that Chinese people are less creative than others, (which in some ways can be true in my experience) and I would say that this is for the same reason.

另一位網(wǎng)友有趣地指出,這是因?yàn)檎Z言的原因,我也這樣認(rèn)為,但我認(rèn)為還有另一個方面更能解釋為什么中國學(xué)生比其他人更快掌握數(shù)學(xué)。一些人覺得中國人不如其他人富有創(chuàng)造力(在某些方面根據(jù)我的經(jīng)驗(yàn)來看是真的),我想這也是出于同樣的原因。
原創(chuàng)翻譯：龍騰網(wǎng) http://www.flyercoupe.com 轉(zhuǎn)載請注明出處

Please allow me to point out here that I'm not an expert in this field. The following is my understanding based on first-hand observation. I'm definitely not trying to say any race or nationality is smarter or more capable than any other or that any culture is right or wrong.

請允許我指出,我并非這一領(lǐng)域的專家。以下是我根據(jù)第一手觀察所得出的理解。我絕不是想說任何種族或國籍比其他種族或國籍更聰明或更能干,或任何文化就是正確或錯誤的。

The Chinese language is taught by memorization. Endless repetition until success is achieved, especially when it comes to reading. A Chinese word has 4 components to remember: the meaning, the pronunciation, the character and the tone. The character specifically causes problems.

漢語是通過記憶來學(xué)習(xí)的。尤其是閱讀時,需要不斷重復(fù)直到成功。一個漢語單詞有4個部分需要記住:意義、發(fā)音、字形和聲調(diào)。字形尤其會導(dǎo)致問題。
Many people think of Chinese characters as being something like pictograms describing their meaning. That's only true of some very basic characters: 日 sun 山 mountain 月 moon. There's a fair amount of characters that fall into this category, but even though the shapes of these characters remind us of the meanings, they don't tell us any thing about the sounds or the tone. Most written languages have been broken down into letters, which allow us, once we understand the code of what sound each letter makes to read basically any word in that language, and if we know what that word means, we're set. Chinese doesn't do this. Not much, anyway.
許多人認(rèn)為漢字就像是表義符號,描繪著它們的意義。這只對一些最基本的字是對的:日(太陽)、山(山)、月(月亮)。確實(shí)有相當(dāng)一部分字屬于這一類,但即使這些字的形狀讓我們聯(lián)想到它們的意義,它們也沒有告訴我們發(fā)音或聲調(diào)。大多數(shù)書面語言都被分解成字母,只要我們理解每個字母代表什么發(fā)音,就能讀出該語言中的任何單詞,如果我們知道單詞的意思,我們就沒問題了。漢語并非如此,反正大體上不是這樣。
馬嗎媽罵碼瑪螞 these characters are ALL pronounced the same way! Ma. Their meanings are completely unrelated! You may notice that they all share the integral component 馬. This one means horse, the next is a question mark, the next is mother… It doesn't get any easier from here. We can at least look at this and say ok 'ma = 馬' so if I see 馬 I know to say 'ma,' and if I want to write 'ma' I need to use that component. NOT. SO. FAST. 嘛孖蟆犘 ma, ma, ma, ma. It also goes the other way: 骉驢 biao, lv. In all fairness, the second one means donkey, and my Chinese wife doesn't know what the first one means, (neither did google translate!) but the pronunciation isn't ma.
馬、嗎、媽、罵、碼、瑪、螞這些字全部讀音相同!都是ma。它們的意思完全不相關(guān)!你可能會注意到它們都包含一個"馬"的部件。第一個意思是馬,下一個是問號,再下一個是母親...從這里開始并不會變得更容易。我們至少可以這樣說"好吧,'ma=馬',所以如果我看到'馬'就知道讀作'ma',如果我要寫'ma',我需要使用這個部件"。別著急,嘛、孖、蟆、犘,ma、ma、ma、ma。反過來也一樣:骉、驢,biao、lv。說句公道話,第二個意思是驢,我中國太太也不知道第一個是什么意思(連谷歌翻譯也不知道!),但發(fā)音并不是ma。
Sometimes, the meaning of a character can be intuitive: 林 means forest. It's simply the short form of tree written twice. Less obvious, but still easy to remember, 男 a male (person). The top is a field, the bottom is strength. True for farmers at least, the man uses his strength in the field. Other times, things aren't as logical.
有時一個字的意思是很直觀的:林意為森林。它只是"木"的兩個簡體字并列。稍微不那么明顯,但仍然容易記住的是男,指男性(人)。上邊是"田",下邊是"力"。對農(nóng)民來說是真實(shí)的,男人在田里用力干活。有時事物并不那么符合邏輯。
There are also 4 tones, which are used in spoken Chinese so that ma doesn't sound like ma or ma or ma. Often times even if you get the pronunciation right, and there's an obvious context to what you're saying, a mistake in tone will make it very difficult for people to understand you. 豬柳 this is zhu liu, 1st tone then 3rd tone. It's what McDonald's in China calls the pork sausage in a sausage mcmuffin, which I was craving one morning. What I said was 豬六 zhu liu, 1st tone then 4th. It means "pig six," which is nonsense and doesn't mean anything. I got a grilled chicken mcmuffin, even though I'd said the pig part right and it's the only thing on the menu made from pork. So tones are pretty important.
漢語還有4種聲調(diào),用于口語中,以便ma不會發(fā)音像ma或ma或ma。有時即使你的發(fā)音是正確的,語境也很明顯,但一個聲調(diào)的錯誤就會讓人極難理解你在說什么。豬柳,朱留,第一聲后第三聲。這是中國麥當(dāng)勞對香腸麥滿分中的豬肉香腸的稱呼,一天早上我正渴望吃這個。但我說成了豬六,朱留,第一聲后第四聲。意思是"豬六",這是無稽之談,沒有任何意義。盡管我把"豬"這部分說對了,而且這也是菜單上唯一一個豬肉產(chǎn)品,但我得到的是一個烤雞麥滿分。所以聲調(diào)相當(dāng)重要。

Considering how important tones are, you might be surprised to know that there is nothing in Chinese characters to tell you the tone. You just have to remember. And that's basically the point of all of this. When you look at a Chinese character, you aren't told the meaning, the phonetic pronunciation or which tone to use to say it. You might get some hints from your knowledge of other Chinese characters about the sound or the meaning, but they're only hints. When you hear a Chinese word, you only have 4 tones (or the lack of a tone) and context to differentiate which of the dozens of different meanings it might have.

考慮到聲調(diào)如此重要,你可能會感到驚訝的是,漢字本身并沒有任何標(biāo)記來告訴你讀什么聲調(diào)。你只能靠記憶。這基本就是重點(diǎn)所在。當(dāng)你看到一個漢字時,它不會告訴你意思、拼音發(fā)音或者該用哪個聲調(diào)讀它。你可能從你對其他漢字的了解中獲得一些關(guān)于讀音或意思的線索,但它們只是線索而已。當(dāng)你聽到一個漢語單詞時,你只有4種聲調(diào)(或者沒有聲調(diào))和語境來區(qū)分它可能有的數(shù)十種不同意義。

To learn Chinese, you have to memorize: how to read/write a character, how to say it, which tone to say it in AND what it means. A person learning Chinese as their first language has their brain hard-wired to remember.

要學(xué)習(xí)漢語,你必須記住:如何讀寫一個字、如何說它、用哪個聲調(diào)說它,還有它的意思。一個把漢語作為母語學(xué)習(xí)的人,他們的大腦就是為了記憶而生的。

Other languages which use letters to represent the sounds a word is made up of are much more intuitive. In English for example, we simply learn 26 letters and the sounds they make when combined in different ways, and we should in theory be able to pronounce any word we see. We haven't developed this power of memorization because it hasn't been required of us. We do, however learn the relationships between the letters and how they can interact with each other.

使用字母表示單詞發(fā)音的其他語言要直觀得多。例如在英語中,我們只需學(xué)習(xí)26個字母及它們組合成不同方式時的發(fā)音,理論上我們就能發(fā)音任何看到的單詞。我們之所以沒有發(fā)展出這種記憶力,是因?yàn)槲覀儧]有這方面的要求。不過,我們確實(shí)學(xué)會了字母之間的關(guān)系以及它們?nèi)绾蜗嗷ビ绊憽?/b>

I believe these differences carry on through out the learning process and cause a Chinese person's natural learning process to lean toward "what is," whereas others will more naturally turn to "why and how."

我相信這些差異貫穿了整個學(xué)習(xí)過程,導(dǎo)致了中國人天生的學(xué)習(xí)過程更傾向于"是什么",而其他人則會更自然地去追問"為什么和怎么樣"。

These are stereotypes, which are never beneficial, but they're interesting to note. Chinese people are often considered to be good at math, science, history, and playing instruments (specifically classical music). These are all things in which memorization and repetition lead to success. Chinese people are often considered to be awful at driving, learning foreign languages, creating original music, inventing things and playing team sports. These are things which are considered creative, though they often can be thought of as understanding relationships between two or more things. What is vs. how and why.

這些都是陳詞濫調(diào),從未有過什么好處,但觀察到它們還是很有趣的。中國人常被認(rèn)為擅長數(shù)學(xué)、科學(xué)、歷史和彈奏樂器(特別是古典音樂)。這些都是通過記憶和重復(fù)練習(xí)才能獲得成功的領(lǐng)域。而中國人常被認(rèn)為很差勁的方面包括開車、學(xué)外語、創(chuàng)作原創(chuàng)音樂、發(fā)明創(chuàng)新和打團(tuán)隊運(yùn)動。這些都被視為有創(chuàng)意的事物,盡管它們往往可以被認(rèn)為是理解兩者或多者之間關(guān)系的能力。是什么,與怎么做和為什么形成對比。

Jian Heng
Chinese is superior at arithmetic, according to study.
Yes, according to certain research. "the Chinese numeral system is relatively straightforward, making at least mathematics very easy to master." Early childhood education researchers have shown that how a language explains numbers may impact how soon youngsters learn add and subtract. Sticks must be properly positioned and crossed in order to multiply using the Chinese Technique, often known as the stick method. Simply arrange the sticks according to the place values of the multiplicands. The sticks' intersections are then counted.

研究顯示，中國人在算術(shù)方面確實(shí)更勝一籌。
是的，根據(jù)某些研究，“中國的數(shù)字系統(tǒng)相對簡單，因此數(shù)學(xué)運(yùn)算很容易掌握。”兒童早期教育研究人員已經(jīng)表明，一門語言闡釋數(shù)字的方式可能會影響兒童學(xué)習(xí)加減法的速度。正確放置和交叉擺放小棍，用中國的運(yùn)算方式就可以進(jìn)行乘法運(yùn)算，這個方法通常被稱為棍棒運(yùn)算法。我們只需根據(jù)乘數(shù)的位置值來排列這些小棍，然后統(tǒng)計這些棍子的交叉點(diǎn)數(shù)目。

Frog Kelly
First of all, I’m a student to Beiing, bdfz(the Chinese abbreviation of my school)
Yes, it is partly true, in big cities like Beiing, Shanghai, students r really good at math, and hard maths problems are used by top mid schools to sext top students.
For myself, in primary school time, I had like about 4 maths classes weekly besides school, parents pay lots of attention to it..
But in other places, children stop school at a very young age(like 14 or 15) for work, they are not good at maths.

首先，我是來自北京bdfz（學(xué)校的拼音首字母縮寫）的學(xué)生。
是的，這個說法在一定程度上是對的，在北京、上海這樣的大城市，學(xué)生的數(shù)學(xué)真的學(xué)得很不錯，頂尖中學(xué)也會用數(shù)學(xué)難題來選拔優(yōu)秀的學(xué)生。
對我自己而言，小學(xué)期間我每周會在校外學(xué)習(xí)大約4節(jié)數(shù)學(xué)課，父母很關(guān)注我的數(shù)學(xué)學(xué)習(xí)情況。
但在某些地區(qū)，孩子們很小的時候(比如14或15歲)就會輟學(xué)，開始打工，他們就不太擅長數(shù)學(xué)了。

Tom Kitta
No. They are far weaker at computer science as well based on small sample of around 30–50 people.
This should be all individual based through not based on particular race.
Main thing I see with Chinese students that is a problem is a brute force attack on a problem with simply trying to memorise stuff that is related. There should be less emphasis on pure memorisation and more emphasis on… why.
This is for college upper level and post grad studies. Everyone that wants to succeed memorises a lot but also balances it with a “why”.

并不是。而且從大約30-50人的小型樣本來分析，他們在計算機(jī)科學(xué)方面也很弱。
這應(yīng)該是個體差異，不是某個族群的特征。
我在中國學(xué)生身上看到的主要問題是，他們會死記硬背一些相關(guān)內(nèi)容，然后暴力破解某個問題。但我們應(yīng)該減少單純的記憶，多想想為什么。
這是我想對大學(xué)高年級和研究生階段的學(xué)習(xí)建議。每個想獲得成功的人都會記住很多東西，但也會關(guān)注“為什么”。

Weijia Deng
No for the educated ones who conduct math-dependent jobs, yes for the rest, comparing to the corresponding class in the western world.
The education system of China has a defect that it does not appreciate proof highly enough as it should be, and proof is the key component of higher-level math.

與西方擁有相同學(xué)位的人相比，中國人的數(shù)學(xué)水平并沒有比從事和數(shù)學(xué)相關(guān)工作的受過教育的人高，但確實(shí)會比剩下的人高。
中國的教育體系存在一個缺陷，即對證明的重視程度不夠，但證明是高等數(shù)學(xué)的重要組成部分。

James Anabo
Yes. It’s in their genes. Chinese people are good in Mathematics in the same way as black people are good in sports.

是的。這是他們的優(yōu)勢基因。中國人擅長數(shù)學(xué)，就像黑人擅長體育一樣。
原創(chuàng)翻譯：龍騰網(wǎng) http://www.flyercoupe.com 轉(zhuǎn)載請注明出處

Anya
No. In China, there are two people, one is called XUEBA, the other is called XUEZHA. The former always have excellent grades, but the latter only can pray tomorrow there will be a earthquake.
If you think the basic math knowledge like add, substrat,multiply,devide meaning good at maths, then I think yes, we are good at maths.

不。在中國有兩種人，一種是學(xué)霸，一種是學(xué)渣。學(xué)霸總是成績優(yōu)異，而學(xué)渣只能祈禱明天會有地震。
如果你認(rèn)為掌握基礎(chǔ)的數(shù)學(xué)知識像加、底、乘、除就意味著擅長數(shù)學(xué)，那么我覺得可以這么說，我們確實(shí)擅長數(shù)學(xué)。

Fu Gui
That's for sure
I think it's probably a Chinese talent, not entirely about education.
You will find a common vegetables rural women, even if she is not high culture, but her mental arithmetic level may be more than American College students.

這是肯定的。
我覺得這可能是中國人的天分，并不完全跟教育水平有關(guān)。
比如一個在菜市場賣菜的普通農(nóng)村婦女，就算她沒有很高的文化水平，但她的心算水平有可能比美國大學(xué)生還要高。

Ariel Lin-Graybill
Not me.
I failed my college entrance math exam.
I like math but I am just very slow and lack of logic when it comes to solving math problem.
I would say Chinese people are a bit better in quick calculation. Practiced that a lot in elementary school.

我就不擅長。
我高考的時候數(shù)學(xué)還不及格呢。
我喜歡數(shù)學(xué)，但在解決數(shù)學(xué)問題時，我的反應(yīng)很慢，邏輯也很混亂。
我想說中國人在計算速度方面確實(shí)很有優(yōu)勢。我們在小學(xué)階段就進(jìn)行了大量訓(xùn)練。

Gloryseeker Huang
I’m from China, born and study in China.
When I see this, I was shocked because I don't understand why someone would ask this question. No offence, but this is really easy even for a 7 grade student in China.
it's true that Chinese students are mostly good at math. but the ability is not inborn. We will spend much time on learning math since we are very young.
Of course, we learn math not just because it's useful, we need to learn it well for the College Entrance Examination. The consequence is that many students gave up learning math in college. But still we are capable of solving many math problems.

我來自中國，在中國出生，在中國接受教育。
當(dāng)我看到這個題目時，我很震驚，因?yàn)槲蚁氩煌槭裁从腥藭堰@個題目發(fā)出來。我無意冒犯，但這個題目對中國7年級的學(xué)生來說都是小意思了。
沒錯，很多中國學(xué)生都很擅長數(shù)學(xué)。但這種能力并非與生俱來的。我們從小就花了很多時間來學(xué)習(xí)數(shù)學(xué)。
當(dāng)然，我們學(xué)習(xí)數(shù)學(xué)不僅僅是因?yàn)樗杏?，我們也是為了高考考出好成績而學(xué)。結(jié)果，很多學(xué)生考入大學(xué)后就放棄了數(shù)學(xué)學(xué)習(xí)。但我們還是能夠解出許多數(shù)學(xué)題。

Alex Chill
Yes.
In fact, the Chinese are religiously obsessed with math.
Back when I was in Secondary School in Australia, we learnt Math that was supposed to be superior compared local schools. The front cover of the book said ‘Advanced Math for Year 10’. A year later when I moved to China for an international IB school, I found that the local schools were studying an advanced version of the advanced version that I was learning back in Australia. Then when I sat in the IB math class, I found that myMath book was again the advanced version of the local advanced version which was the advanced version of the Australian advanced version of Australian local school.

是的。
事實(shí)上，中國人非常推崇數(shù)學(xué)。
我在澳大利亞上中學(xué)的時候，我們學(xué)校的數(shù)學(xué)水平應(yīng)該比當(dāng)?shù)貙W(xué)校略好一些。數(shù)學(xué)書的封面上寫著“10年級高等數(shù)學(xué)”。
一年后，我來到中國就讀國際學(xué)校的IB課程，我發(fā)現(xiàn)當(dāng)?shù)氐膶W(xué)校使用的課本是我在澳大利亞的教材的進(jìn)階版。
當(dāng)我坐在IB課程的數(shù)學(xué)教室里時，我發(fā)現(xiàn)我們的數(shù)學(xué)課本又是比當(dāng)?shù)剡M(jìn)階版教材的更高級版本，是澳大利亞本地學(xué)校使用教材的進(jìn)階版的進(jìn)階版

What shocked me was, all my fellow Chinese classmates were always able to score more than 85 percent!
I never really liked math, and the reality literally said screw you in front of my face. That sucked!
This is just my personal opinion about learning math, if you like math, don’t take me serious.

更令我震驚的是，所有的中國同學(xué)都能拿到85%以上的成績！
我從來都不喜歡數(shù)學(xué)，我被現(xiàn)實(shí)深深打擊到了。太煩人了！
這只是我個人對數(shù)學(xué)學(xué)習(xí)的一點(diǎn)看法，如果你喜歡數(shù)學(xué)，就別把我的話當(dāng)真哈。

Lu Yueti
i am Chinese and i was a senor high
and i think i was preety good at math and i was studying Olympic math.
but that doesn't mean that we all good at math

我是中國人，是個高中老師。
我覺得我自己數(shù)學(xué)是挺好的，我以前一直在學(xué)奧數(shù)。
但這并不意味著我們中國人都擅長數(shù)學(xué)

here is some exercise i did……..

這是我做的一些習(xí)題........

Piyush
You want to listen something good I think. But, unfortunately your neighbouring country is doing good in mathematics and even got a nobel prize in mathematics. Guess which neighbor?

我覺得你肯定是想聽點(diǎn)好聽的。但很遺憾，你們的鄰國在數(shù)學(xué)方面非常出色，甚至獲得了數(shù)學(xué)諾貝爾獎。猜猜看是哪個鄰國呢？

Cornelius Goh
Yes and No.
Chinese are good in counting, like abacus, and all kinds of math tricks, but lack the real “math thinking” in abstractness which is the forté of the French Bourbaki Math. If you name the number of world-class mathematicians by counting the Fields Medals, Wolf, Abel Prizes, the French mathematicians dominate the Math World. However, the Chinese kids beat the French kids in tricky IMO Math by 3 decades of IMO Championships.
The best Math education should combine both the strength of Chinese and French, ie Chinese “Applied” and French “Abstract” pedagogies.

也對，也不對。
中國人擅長計算，比如算盤，各種數(shù)學(xué)游戲，但缺乏真正的抽象的“數(shù)學(xué)思維”，這就是法國布爾巴基數(shù)學(xué)學(xué)派的強(qiáng)項(xiàng)。如果只計算菲爾茲獎、沃爾夫獎、阿貝爾獎等世界級數(shù)學(xué)家的數(shù)量，你會發(fā)現(xiàn)法國數(shù)學(xué)家才是數(shù)學(xué)界的霸主。但中國孩子在復(fù)雜的國際數(shù)學(xué)奧林匹克競賽中擊敗了法國孩子，在冠軍寶座上領(lǐng)先了30年。
最好的數(shù)學(xué)教育應(yīng)該結(jié)合中國和法國的優(yōu)勢，即中國的“應(yīng)用”教學(xué)法和法國的“抽象”教學(xué)法。

Yanshi iong
Math teacher in China is a nightmare, almost for everyone, that's why my math is not bad. I think that fits most Chinese students.
You can ask a Chinese student to imagine his or her math teacher, horrible could be used to describe that image and moment.
Just kidding.

幾乎對每個人而言，中國的數(shù)學(xué)老師都是上學(xué)時的噩夢，這就是我的數(shù)學(xué)還算不賴的原因。我認(rèn)為大多數(shù)中國學(xué)生都是如此。
你可以讓一個中國學(xué)生回憶一下他或她的數(shù)學(xué)老師，大概可以用“可怕”二字來描述老師的形象和場面。
開個玩笑哈。
原創(chuàng)翻譯：龍騰網(wǎng) http://www.flyercoupe.com 轉(zhuǎn)載請注明出處

Bak Chee
Chinese students are pretty good at Math, and in general perform better than Western students.
Because the education system in Asia train their students pretty intensive at Math since a young age. Therefore most of us will outperform the western students when we go study in western schools.

中國學(xué)生很擅長數(shù)學(xué)，總體上的表現(xiàn)好過西方學(xué)生。
因?yàn)閬喼薜慕逃w系會從學(xué)生很小的時候就對他們進(jìn)行密集的數(shù)學(xué)訓(xùn)練。所以當(dāng)我們?nèi)ノ鞣綄W(xué)校學(xué)習(xí)時，我們中的大多數(shù)人在數(shù)學(xué)學(xué)科的表現(xiàn)都會優(yōu)于西方學(xué)生的表現(xiàn)。

However, when it comes to high level Math, those really abstract things, those that need intense imagination or creativity, such as in later years of university, the western students start to catch up, and then surpass many Asian students.
I guess it’s the result of different education systems.

但涉及到高水平的數(shù)學(xué)學(xué)習(xí)，比如真正抽象的東西，比如需要強(qiáng)烈的想象力或創(chuàng)造力的東西，比如在大學(xué)高年級，西方學(xué)生就開始趕超許多亞洲學(xué)生了。
我想這是不同教育體系造成的結(jié)果。

John Richard Jones
Is it down to the way they are taught in school?
I have seen a variation in the UK and am convinced that some of the poorer performing students could be better if they were taught in a better way.

這取決于他們在學(xué)校接受的教育方式嗎？
我在英國看到了這種變化，我相信，如果用更好的方式教育一些表現(xiàn)不佳的學(xué)生，他們也會變得更加優(yōu)秀。

If the capacity of a jug is the full potential of the student and the contents of the jug is how much investment in time and support went into the student, then the more put into the student the more you could get from the student (up to a point).
Don't judge a student by its contents as there could be plenty of unused space for more use. See the student by their capacity and give the necessary contents to maxmise their use.

如果用一個罐子的容量來形容學(xué)生的全部潛力，罐子里裝的是對學(xué)生投入的時間和支持的多少，那么對學(xué)生投入的越多，你從學(xué)生那里得到的就越多(在一定程度上)。
不要根據(jù)學(xué)生現(xiàn)有的能力來判斷一個學(xué)生，因?yàn)樗麄兛赡軗碛泻芏嗌形撮_發(fā)的潛力。我們要關(guān)注學(xué)生的能力，給予必要的教導(dǎo)，最大限度地挖掘他們的潛力。

中國人 數(shù)學(xué)

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