講真，你知道為什么數(shù)學(xué)比語(yǔ)言難學(xué)嗎？.

　　Language is hard. In fact, it’s infinitely harder and more complicated than math. And yet, nearly every small child can learn and master language.

　　學(xué)語(yǔ)言真的很難。老實(shí)講，它比學(xué)數(shù)學(xué)要復(fù)雜得多，也困難得多。不過(guò)，幾乎所有的小孩子都能夠?qū)W習(xí)并且熟練掌握一門(mén)語(yǔ)言。

　　Why is math so overwhelming for so many students? And how high is the price we pay from having so many math-terrified or even math-illiterate people in our society? Too high, especially as the ability to grasp data and pursue advanced work that involves math is becoming increasingly important for both citizens and job applicants.

　　那到底為什么數(shù)學(xué)會(huì)成為許多學(xué)生難以逾越的鴻溝呢?因?yàn)樯鐣?huì)上這些“數(shù)學(xué)恐懼癥患者”，甚至是“數(shù)學(xué)盲”的存在，我們又得付出多大的代價(jià)呢?不用說(shuō)，這代價(jià)簡(jiǎn)直太大了，尤其是在當(dāng)今社會(huì)，獲取數(shù)據(jù)和從事高難度工作越來(lái)越成為普通人和求職者的必備能力。

　　It often starts with the problem of teaching math in the abstract. This misses the remarkable amount of mathematical knowledge that we humans already possess. We know how to solve for unknowns, for example. That’s algebra. We also are able to think in terms of three dimensional spaces—that’s geometry and trigonometry. So this mathematical language is the analytical expression of the way we already think.

　　問(wèn)題一開(kāi)始出在數(shù)學(xué)的抽象教學(xué)上。這就讓我們錯(cuò)失大量數(shù)學(xué)知識(shí)，而這些知識(shí)是我們本身就具有的。我們知道如何去解決未知的東西，那么這就是代數(shù)。我們也知道用三維空間去思考——這就是幾何學(xué)和三角學(xué)。這門(mén)數(shù)學(xué)語(yǔ)言其實(shí)就是我們思維方式的解析式。

　　But how many of us feel incapable, rather than poorly taught, when we are confronted with the rigors of math? How many children who struggled to grasp math concepts, who lacked the necessary tool kit, were led to feel stupid, even demeaned?

　　然而碰到數(shù)學(xué)難題的時(shí)候，我們當(dāng)中有多少人只會(huì)覺(jué)得是自己無(wú)能，而不會(huì)歸因于教育問(wèn)題?又有多少孩子絞盡腦汁地去記憶數(shù)學(xué)概念，卻因?yàn)槿鄙俦匾膶W(xué)習(xí)工具，而覺(jué)得自己愚蠢之極，甚至變得妄自菲薄?

　　Compare it to spoken or written language. When you make a mistake, a teacher corrects the part that is wrong. And then you proceed. With math, if you don’t have the correct result, it is typically treated as wrong. And, as mistake after mistake builds up, too many students simply give up: I can’t do math.

　　相比起來(lái)書(shū)面語(yǔ)或者口語(yǔ)，如果你犯了錯(cuò)誤，老師就會(huì)對(duì)此進(jìn)行更正，然后你可以再繼續(xù)。而數(shù)學(xué)就不一樣了，數(shù)學(xué)是如果你得不到正確答案，老師就會(huì)認(rèn)定你做錯(cuò)了。隨著錯(cuò)誤不斷堆積，很多學(xué)生干脆破罐破摔，直接放棄了：我就是搞不懂?dāng)?shù)學(xué)。

　　But math is not about intelligence. It’s a language that too many people never learn, often because the education process misses the number of ways that a given person can arrive at a given solution.

　　不過(guò)數(shù)學(xué)無(wú)關(guān)智力，而是一種許多人都未曾學(xué)習(xí)過(guò)的語(yǔ)言。很多時(shí)候就是因?yàn)榻逃^(guò)程不注重因材施教的方法，才會(huì)讓數(shù)學(xué)變得那么“難”。

　　That’s not a failure of children to learn. That’s a failure of teaching. It’s a failure of the school. We should not blame the student. (These are children, after all.)

　　這不是孩子學(xué)習(xí)的失敗，而是教育的失敗，學(xué)校的失敗。我們不該責(zé)怪學(xué)生。(畢竟他們只是孩子而已)

　　Part of the challenge is to identify the gaps in knowledge, to clarify that the challenge is not that a student simply doesn’t understand algebra or trigonometry or whatever. There may be a particular basic concept that stands in the way of going forward in math, as well as other fields such as social science or engineering.

　　我們遇到的挑戰(zhàn)一部分是認(rèn)清知識(shí)之間的缺口，以及明白這份挑戰(zhàn)不只是因?yàn)閷W(xué)生不懂代數(shù)或者三角學(xué)。有時(shí)候我們可能會(huì)遇到某一個(gè)基本概念，它不止阻礙我們步入數(shù)學(xué)的大門(mén)，也會(huì)影響我們通往其他領(lǐng)域的步伐，比如社會(huì)科學(xué)或者工程學(xué)。

　　Overcoming this block requires moving beyond broad industrialized education and to individualized, personalized learning that allows students to find their own way in. Show me a thousand students and I’ll show you a thousand different pathways that they might take to achieve math success.

　　要克服這一困難，我們就必須得摒棄產(chǎn)業(yè)化教育，因材施教，這樣有助于學(xué)生找到自己的學(xué)習(xí)方法。給我1000個(gè)學(xué)生，我就能讓你看到拿下數(shù)學(xué)的1000種不同方法。

　　With new digital technologies and a massive amount of data collection and analytics, we have the ability to help students identify the essential concepts they don’t understand. We have data on all the students that solved a particular math problem and those that failed to solve it. We also have data on the problems they were able to solve prior to that.

　　有了新的數(shù)字科技、大量的數(shù)據(jù)收集和分析學(xué)，我們有能力幫學(xué)生記住一些他們?cè)静⒉焕斫獾幕靖拍?。我們收集的?shù)據(jù)包括：對(duì)于某個(gè)特定的數(shù)學(xué)問(wèn)題，能夠解決和不能解決的學(xué)生情況，以及在那之前他們能夠解決的問(wèn)題。

　　So as a student recognizes that they are struggling with, say, negative number concepts, they can go back and master the material—to fill in the gaps that allows them to go forward. And when they hit another tough spot? They can jump to the problems that allow them to master that concept. The hope is that as they progress, their interest and enthusiasm increases.

　　因此，當(dāng)學(xué)生知道他們正在與，比如說(shuō)負(fù)數(shù)概念艱難地做斗爭(zhēng)，可以回過(guò)頭去，掌握一些必須的材料，將知識(shí)的缺口填補(bǔ)完整，這樣就能繼續(xù)往前走。那以后又碰到難題該怎么辦?他們可以直接去解決一些特定問(wèn)題，從中快速掌握該概念。我們希望，學(xué)生在進(jìn)步的過(guò)程中，自己的興趣和熱情也能一起被提高。

　　We are pursuing this approach at the university level. We also are seeking to incorporate this approach at the high school, middle school and elementary levels. This will make it possible for a growing number of students to pursue degrees and careers that they never thought.

　　我們現(xiàn)在正在大學(xué)教育中推行這一方法，也力求將其與小學(xué)、初中和高中教學(xué)結(jié)合起來(lái)。這樣一來(lái)，越來(lái)越多的學(xué)生便有希望獲得以前從未想過(guò)的學(xué)位或者職業(yè)。

　　In the years ahead, that mindset, borne out of the failure of math instruction, should diminish. If we can succeed at breaking down the assumption that there’s something wrong with a 3rd grader who cannot learn math—rather than something wrong with the teaching process—then we can look forward to new generations of math-literate citizens. Whatever career they choose, they will be more confident and more capable to understand and contribute to an increasingly complex, data-driven world.

　　以后的若干年，由于數(shù)學(xué)教育的失敗而生出的自卑心態(tài)應(yīng)該逐漸消失?，F(xiàn)在人們的想法是，如果一個(gè)三年級(jí)的學(xué)生學(xué)不會(huì)數(shù)學(xué)，那就是他有問(wèn)題，跟教育過(guò)程完全沒(méi)關(guān)系，如果我們能夠成功打破人們這種想法，就可以寄希望于新一代的“數(shù)學(xué)盲”。不管他們選擇什么職業(yè)，都一定會(huì)更加自信，且有更強(qiáng)的能力去理解這個(gè)日益復(fù)雜，數(shù)據(jù)驅(qū)動(dòng)的世界，并為之貢獻(xiàn)出自己的一份力量。