告訴你讓你覺得數學那麼難學的真正原因大綱

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.
語言真的很難。老實講，它比數學要複雜得多，也困難得多。不過，幾乎所有的小孩子都能夠學習並且熟練掌握一門語言。

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.
那到底爲什麼數學會讓許多學生覺得無所適從呢？而因社會上這些“數學恐懼症患者”，甚至是“數學盲”的存在，我們又得付出多大的代價呢？這代價簡直太大了，尤其是在當今社會，獲取數據和從事高難度工作越來越成爲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.
問題一開始出在數學的抽象教學上。這就讓我們錯過了大量我們本身就具有的數學知識。我們知道如何去解決未知的東西，那麼這就是代數。我們也知道用三維空間去思考--這就是幾何學和三角學。這門數學語言其實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?
然而碰到數學難題的時候，我們當中有多少人只會覺得是自己無能，而不會歸因於教育問題？又有多少孩子絞盡腦汁地去記憶數學概念，卻因爲缺少必要的學習工具，而覺得自己愚蠢之極，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.
相比起來書面語或者口語，如果你犯了錯誤，老師就會對此進行更正，然後你可以再繼續。而數學就不一樣了，數學是如果你得不到正確答案，老師就會認定你做錯了。隨着錯誤不斷堆積，很多學生直接放棄了：我就是搞不懂數學。

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.
不過數學無關智力，而是一種許多人都未曾學習過的語言。很多時候就是因爲教育過程不注重因材施教的方法，纔會讓數學變得那麼“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.)
這不是孩子學習的失敗，而是教育的失敗，學校的失敗。我們不該責怪學生。（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.
我們遇到的挑戰一部分是認清知識之間的缺口，以及明白這份挑戰不只是因爲學生不懂代數或者三角學。有時候我們可能會遇到某一個基本概念，它不止阻礙我們步入數學的大門，也會影響我們通往其他領域的步伐，比如社會科學或者工程學。

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業化教育，因材施教，這樣有助於學生找到自己的學習方法。給我1000個學生，我就能讓你看到拿下數學的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.
有了新的數字科技、大量的數據收集和分析學，我們有能力幫學生記住一些他們原本並不理解的基本概念。我們收集的數據包括：對於某個特定的數學問題，能夠解決和不能解決的學生情況，以及在那之前他們能夠解決的問題。

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，當學生知道他們正在與，比如說負數概念艱難地做鬥爭，可以回過頭去，掌握一些必須的材料，將知識的缺口填補完整，這樣就能繼續往前走。那以後又碰到難題該怎麼辦？他們可以直接去解決一些特定問題，從中快速掌握該概念。我們希望，學生在進步的過程中，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.
我們現在正在大學教育中推行這一方法，也力求將其與小學、初中和高中教學結合起來。這樣一來，越來越多的學生便有希望獲得以前從未想過的學位或者職業。

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.
以後的若干年，由於數學教育的失敗而生出的自卑心態應該逐漸消失。現在人們的想法是，如果一個三年級的學生學不會數學，那就是他有問題，跟教育過程完全沒關係，如果我們能夠成功打破人們這種想法，就可以寄希望於新一代的“數學盲”。不管他們選擇什麼職業，都一定會更加自信，且有更強的能力去理解這個日益複雜，數據驅動的世界，併爲之貢獻出自己的一份力量。