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掌握方法,你也能成为数学达人 – 译学馆
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掌握方法,你也能成为数学达人

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

大想法
big think
我认为世界上每个人都可以成为数学达人
I think that everyone in the world could be a math person,
只要他们想
if they wanted to.
注意我说的这个条件 只要他们想
The keyword though, I want to say, is if they wanted to.
也就是说我认为每个美国人
That said, I do think that everyone in America
都能够从基于数学的推理思维中有所收获
could benefit from having that mathematical background in reasoning
这种思维有助于帮助大家做好决策
just to help everyone make very good decisions.
这里我已经把人们
And here I’m distinguishing already between math
一般意义上认为的数学
as people usually conceive of it,
和决策分析区分开了
and decision making and analysis,
我认为后者才是数学精神所在
which is actually what I think math is.
比如我并不认为
So, for example, I don’t think that
成为数学达人意味着
being a math person means that
你能背诵各种公式
you can recite the formulas between
正弦 余弦 正切
sines, cosines, tangents,
并能自如的换算对数和指数
and to use logarithms and exponentials interchangeably.
我并不认为
That’s not necessarily what I think
每个人都需要去试图理解这些内容
everyone should try to concentrate to understand.
最需要去理解的
The main things to concentrate to understand
就是数学的推理原则
are the mathematical principles of reasoning. 
但是我们回来看看这些正弦 余弦和对数
But let me go back to these sines, cosines and logarithms.
实际上他们是有价值的
Well, actually they do have value.
它们的价值在于 它们为你展示了
What they are is that they are ways to show you
这些基本的推理原则
how these basic building blocks of reasoning
是如何被用来解构例外情况或复杂事物的
can be used to deduce surprising things or difficult things.
某种意义上 它们就像种历史范畴
In some sense, they’re like the historical coverages
数学的征服史
of the triumphs of mathematics,
所以一个人不能仅仅抽象的说
so one cannot just talk abstractly about
“好 让我们来谈谈数学逻辑”
“yes, let’s talk about mathematical logic”.
实际上这最好结合案例分析或实例
It’s actually quite useful to have case studies or stories,
也就是说这些著名的定理
which are these famous theorems.
那么我实际上认为每个人都能学会
Now, I actually think that these are accessible to everyone.
我认为之所以数学那么难懂
I think that actually one reason mathematics is difficult to understand
就是因为先决知识网络
is actually because of that network of prerequisites.
你看 数学是一种奇怪的学科
You see, math is one of these strange subjects,
它的各种概念组成了一条条有逻辑先后次序的知识链条
for which the concepts are chained in sequences of dependencies
当你建立起了这种知识链条后
When you have long chains,
需要记忆的要点
there are very few starting points,
和知识点就非常少了
very few things I need to memorize.
比如说我就不用去记忆
I don’t need to memorize, for example,
各种历史事件了
all these things in history such as
例如“1812年战争在什么时候?”
“when was the war of 1812?”
实际上我知道这个答案 因为这是个数学常识
Well, actually I know that one, because that’s a math fact.
就在1812年
It was 1812.
但我没法告诉你其他事
But I can’t tell you a lot of other facts,
其他那些需要纯粹记忆的事儿
which are just purely memorized.
在数学中需要记忆的东西很少
In mathematics, you have very few that you memorize,
其他知识都可以推导出来
and the rest you deduce as you go through,
这个推导的链条很关键
and this chain of deductions is actually what’s critical. 
那么我来和其他学科对比一下
Now, let me contrast that with other subjects,
比如说历史
like, say history.
历史就没有如此长的知识链条
History doesn’t have this long chain.
实际上如果你完全了解1812年战争当然很好
In fact, if you fully understand the war of 1812, that’s great.
而当然这个或许会对
And it is true that that will influence
你理解之后的妇女解放运动有所帮助
perhaps your understanding later of the women’s movement.
但这个并不是绝对的先决条件
But it won’t to be as absolutely prerequisite.
在这个意义上 如果你想想这些概念
In the sense that, if you think about the concepts,
我正认为历史学比数学的概念更多
I actually think that history has more concepts than mathematics.
这些概念涵盖范围更广
It’s just that they’re spread out broader,
并且互相之间的逻辑先后次序没有那么强
and they don’t depend on each other as strongly.
所以 比方说你缺课一周
So, for example, if you miss a week,
你会有一个单元课听不懂
you will miss the understanding of one unit,
但这并不影响
but that won’t…that won’t stop you
你理解其他部分的内容
from understanding all of the rest of the components. 
所以这就是我脑中认为的
So, that’s actually the difference between math
数学与其他学科的不同之处
and other subjects in my head.
数学的基本概念更少但联系更紧密
Math has fewer concepts, but they’re chained deeper.
由于我们通常的学习方法
And because of the way that we usually learn,
当知识链条连接紧密时 它其实非常脆弱
when you had deep chains, it’s very fragile.
因为你只要缺失任何一环
Because you lose any one link,
就是说如果你缺少了知识链条中的一部分概念
meaning if you miss a few concepts along the chain,
你就可能完全搞不明白了
you can actually be completely lost.
例如 如果你请了一周病假
If, for example, you’re sick for a week,
或者如果你这周心不在焉
or if your mind is somewhere else for a week,
你的先决知识体系中就出现了一个漏洞
you might make a hole in your prerequisites.
而教育的原理经常是这样
And the way that education often works,
非常的像
where it’s almost like
从始发站乘坐火车去终点站
riding a train from a beginning to an end.
那么就比如
Well, it’s such that
如果你的轨道上某处有个洞
if you have a hole somewhere in your track,
火车是不可能通过的
the train is not going to pass that hole.
那么我认为一种
Now, I think that the way to
有助于解决此问题的方法
help to address this,
就是找到一种方法 让每人按自己的节奏学习
is to provide a way for everyone to learn at their own pace,
一旦找到知识漏洞 就立马填补好
and in fact to fill in the holes whenever they are sensed.
我实际上觉得
And I actually feel like
如果每个人都能
if everyone was able to
掌握每一个必要的先决知识点
pick up every one of those prerequisites as necessary,
填补知识体系中的空白地带
filling in any gaps they have.
数学就不再是最难的学科
Mathematics would change from being the hardest subject
而是最简单的学科了
to the easiest subject.
我认为每个人都可以成为数学达人
I think everyone’s a math person,
他们所需要做的
and all that one has to do
就是理顺他们的知识链条
is to go through the chain,
填补他们的知识漏洞
and fill in all the gaps.
你将会更好的掌握这门学科
And you’ll understand it easier,
比其他学科都更容易
more better than all the other subjects actually.
bigthink.com
BIGTHINK.COM

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成为数学达人并不难,只要你构建起数学的知识链条,掌握好自己学习的节奏

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红花老七

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