或者,另一方面,如果你只是在我們期中考試那天才開(kāi)始復(fù)習(xí),那么你一定會(huì)感到很失落。
You'll come to me and say, 'It's impossible.' I'll tell you to keep working and by week two, you'll find you'll make significant progress."
你將跑過(guò)來(lái)跟我說(shuō)‘這不可能。’我想告訴你們,持續(xù)努力,到了第二周你就會(huì)發(fā)現(xiàn)你將取得重大進(jìn)步。”
We sometimes think of being good at mathematics as an innate ability. You either have it, or you don't.
有些時(shí)候我們將優(yōu)秀的數(shù)學(xué)能力看作一種內(nèi)在的能力?;蛘吣憔邆?,或者你不具備。
But to Schoenfeld, it's not so much ability as attitude. You master mathematics if you are willing to try.
但是對(duì)于肖恩菲爾德來(lái)說(shuō),什么能力都不如態(tài)度重要。如果你有意愿去嘗試,你就會(huì)掌握數(shù)學(xué),
That's what Schoenfeld attempts to teach his students.
這就是他想傳授給學(xué)生的。
Success is a function of persistence and doggedness and the willingness to work hard for twenty-two minutes
成功就是堅(jiān)持不懈地鉆研,
To make sense of something that most people would give up on after thirty seconds.
比如,帶有強(qiáng)烈的意愿花22分鐘去解決一個(gè)大多數(shù)人只花30秒就放棄的問(wèn)題,
Put a bunch of Renees in a classroom, and give them the space and time to explore mathematics with themselves, and you could go a long way.
如果一個(gè)班里都是雷妮這樣的人,只要給她們足夠的空間和時(shí)間讓她們自己解決問(wèn)題,那么一定會(huì)取得很好的成績(jī)。
Or imagine a country where Renee's doggedness is not the exception, but a cultural trait,
或者想象一下,如果在某個(gè)國(guó)家,雷妮的這種堅(jiān)持不是特例,而是一種文化特征,
Embedded as deeply as the culture of honor in the Cumberland Plateau.Now that would be a country good at math.
那么深植在這種文化中的榮譽(yù)感將會(huì)毫無(wú)疑問(wèn)地致使這個(gè)國(guó)家具備卓越的數(shù)學(xué)能力。
Every four years, an international group of educators administers a comprehensive mathematics and science test to elementary and junior high school students around the world.
每四年,一個(gè)由許多學(xué)者組成的國(guó)際組織都會(huì)組織一次高難度的數(shù)學(xué)競(jìng)賽,競(jìng)賽的選手大多都來(lái)自世界各國(guó)的初中生或高中生。
It's called the TIMSS (the same test we discussed earlier when looking at differences between forth grader born near the beginning of a school cutoff date and those born near the end of the date),
這個(gè)數(shù)學(xué)競(jìng)賽就是TIMSS(這與我們?cè)诘谝徽轮杏懻摰母?jìng)賽是同一個(gè)競(jìng)賽)。
And the point of the TIMSS is to allow us to compare the educational achievement of one country with another.
設(shè)立TIMSS競(jìng)賽的目的就在于比較不同國(guó)家之間的教育成果。
When students sit down to TIMSS exam, they also have to fill out a questionnaire.
當(dāng)學(xué)生們坐下來(lái)參加TIMSS競(jìng)賽時(shí),他們同時(shí)還必須填寫(xiě)一份問(wèn)卷。
It asks them all kinds of things, such as what their parent's level of education is, or what their views about math are, or what their friends are like.
這份問(wèn)卷包括很多內(nèi)容,如父母的教育程度,對(duì)數(shù)學(xué)的看法,以及對(duì)朋友的描述。
It's not a trivial exercise. It's about 120 questions long.
這并非是毫無(wú)意義的測(cè)試。這是個(gè)長(zhǎng)達(dá)120道題的問(wèn)卷,
In fact, it is so tedious and demanding that many students leave as many as ten or twenty questions blank.
因此很多學(xué)生都留下了10道到20道題未能填寫(xiě)。