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掌握这个技巧任何人都能成为数学达人 – 译学馆
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掌握这个技巧任何人都能成为数学达人

Anyone Can Be a Math Person Once They Know the Best Learning Techniques | Po-Shen Loh

我觉得只要他们愿意 任何人都能成为数学达人
I think that everyone in the world could be a math person if they wanted to.
我想说的是关键在于他们是否有这个意愿
The keyword though, I want to say, is if they wanted to.
简言之 我真的认为美国的每个人都能因有一定的数学背景而受益匪浅
That said, I do think that everyone in America could benefit from having that mathematical
理由仅仅是它可以帮助人们做出更好地选择
background in reasoning just to help everyone make very good decisions.
在此我已经区分了人们通常构想的数学和我认为的数学
And here I’m distinguishing already between math as people usually conceive of it, and
我认为数学就是用来决策和分析的
decision making and analysis, which is actually what I think math is.
比如我不认为作为一个数学达人就意味着你可以列举出
So, for example, I don’t think that being a math person means that you can recite the
正弦余弦正切公式完成对数和指数的互相互换
formulas between the sines, cosines, tangents and to use logarithms and exponentials interchangeably.
我认为没必要每个人都去尝试集中精力获悉那些
That’s not necessarily what I think everyone should try to concentrate to understand.
最需要集中精力去明白的是数学的推理原则
The main things to concentrate to understand are the mathematical principles of reasoning.
但让我们回到正弦余弦和对数
But let me go back to these sines, cosines and logarithms.
它们确实对我们很重要
Well actually they do have value.
它们之所以很重要在于它们在向我们演示基本的推理模块
What they are is that they are ways to show you how these basic building blocks of reasoning
是如何推理出令人惊讶的或复杂事物的方法
can be used to deduce surprising things or difficult things.
从某些方面而言它们就像是数学成功的历史保障
In some sense they’re like the historical coverages of the triumphs of mathematics,
所以人们不能仅仅是抽象地说 好让我们来谈论一下数学逻辑
so one cannot just talk abstractly about “yes let’s talk about mathematical logic”, it’s
这些著名的定理真的是非常有用的研究案例或故事
actually quite useful to have case studies or stories, which are these famous theorems.
现在 我觉得这对大家来说是可以理解的
Now, I actually think that these are accessible to everyone.
我认为实际上数学很难理解的原因是
I think that actually one reason mathematics is difficult to understand is actually because
网状的预备知识
of that network of prerequisites.
数学是按概念相关性顺序被连接起来的
You see, math is one of these strange subjects for which the concepts are chained in sequences
奇怪学科之一
of dependencies.
当你有很长的网链时出发点就会很少 需要记住的东西也会非常少
When you have long chains, there are very few starting points—very few things I need to memorize.
我不需要记忆 举个例子 所有这些东西从历史的角度来说就好比
I don’t need to memorize, for example, all these things in history such as “when was
1812年的战争是什么时候发生的
the war of 1812?”
我当然知道 因为这是一个数学事实 就是1812年啊 但我不能告诉你
Well actually I know that one, because that’s a math fact—it was 1812—but I can’t tell
一些别的什么事实 这只是单纯的被记住了
you a lot of other facts, which are just purely memorized.
在数学运算中你要记住的东西真的很少 其余的都是你通过推理得出的
In mathematics you have very few that you memorize and the rest you deduce as you go
这个学习链的简化实际上是至关重要的
through, and this chain of deductions is actually what’s critical.
现在 让我来将数学和其它学科对比一下 譬如历史
Now, let me contrast that with other subjects like say history.
历史没有很长的网链关联 事实上如果你完全了解1812年的战争当然很好
History doesn’t have this long chain, in fact if you fully understand the war of 1812 that’s
也许你后来才了解到它确实影响了女权运动
great, and it is true that that will influence perhaps your understanding later of the women’s
但这并不是绝对的先决条件
movement, but it won’t to be as absolutely prerequisite.
在这个意义上如果你考虑概念 事实上我觉得历史的概念多于数学
In the sense that if you think about the concepts I actually think that history has more concepts
仅仅只是历史传播更广泛 并且它们不像数学依耐性
than mathematics; it’s just that they’re spread out broader and they don’t depend on each
那么强
other as strongly.
所以 打个比方 如果你翘了一周的课你这个单元都听不懂了 但是
So, for example, if you miss a week you will miss the understanding of one unit, but that
这并不会阻断你理解历史的其它组成部分
won’t stop you from understanding all of the rest of the components.
所以在我看来这才是数学和其他学科的差别
So that’s actually the difference between math and other subjects in my head.
数学的概念比较少但关联更深
Math has fewer concepts but they’re chained deeper.
由于我们通常的学习方法的问题 当你对数学的学习进入到深层次的关联理解时 这个环节是很脆弱的
And because of the way that we usually learn when you had deep chains it’s very fragile
因为你可能漏掉其中任何一个环节 意味着如果你漏掉了这个链中很小的一个概念
because you lose any one link—meaning if you miss a few concepts along the chain you
你就完全跟不上进度了
can actually be completely lost.
如果 打个比方 你感冒了一个星期 或者你思想开小差了一个星期
If, for example, you’re sick for a week, or if your mind is somewhere else for a week,
你的预备知识就可能有一个大漏洞了
you might make a hole in your prerequisites.
通常教育的运行模式就像一辆火车从起始点
And the way that education often works where it’s almost like riding a train from a beginning
到达终点 就好比如果你的轨道中有了一个窟窿
to an end, well it’s such that if you have a hole somewhere in your track the train is
火车就无法通过这个窟窿了
not going to pass that hole.
现在 我认为处理这个问题的方法就是
Now, I think that the way to help to address this is to provide a way for everyone to learn
每个人以自己的速度学习 一旦他们发现哪儿有漏洞就要及时填补上
at their own pace and in fact to fill in the holes whenever they are sensed.
我想如果每个人都能捡起每一个必需的预备知识
And I actually feel like if everyone was able to pick up every one of those prerequisites
填补他们有的每一个漏洞 数学将会从最难的学科
as necessary, filling in any gap they have, mathematics would change from being the hardest
变成最简单的学科
subject to the easiest subject.
我认为每个人都是数学达人 大家需要做的就是把数学的这个链给建起来
I think everyone is a math person, and all that one has to do is to go through the chain
并且查漏补缺 你会了解到实际上你对数学的理解比其它所有的学科都要更好
and fill in all the gaps, and you will understand it better than all the other subjects actually.

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成为数学达人,你只是需要建立好预备知识链

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