I think that everyone in the world could be a math person if they wanted to.
The keyword though, I want to say, is if they wanted to.
That said, I do think that everyone in America could benefit from having that mathematical
background in reasoning just to help everyone make very good decisions.
And here I’m distinguishing already between math as people usually conceive of it, and
decision making and analysis, which is actually what I think math is.
So, for example, I don’t think that being a math person means that you can recite the
formulas between the sines, cosines, tangents and to use logarithms and exponentials interchangeably.
That’s not necessarily what I think everyone should try to concentrate to understand.
The main things to concentrate to understand are the mathematical principles of reasoning.
But let me go back to these sines, cosines and logarithms.
Well actually they do have value.
What they are is that they are ways to show you how these basic building blocks of reasoning
can be used to deduce surprising things or difficult things.
In some sense they’re like the historical coverages of the triumphs of mathematics,
so one cannot just talk abstractly about “yes let’s talk about mathematical logic”, it’s
actually quite useful to have case studies or stories, which are these famous theorems.
Now, I actually think that these are accessible to everyone.
I think that actually one reason mathematics is difficult to understand is actually because
of that network of prerequisites.
You see, math is one of these strange subjects for which the concepts are chained in sequences
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
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
you a lot of other facts, which are just purely memorized.
In mathematics you have very few that you memorize and the rest you deduce as you go
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.
History doesn’t have this long chain, in fact if you fully understand the war of 1812 that’s
great, and it is true that that will influence perhaps your understanding later of the women’s
movement, but it won’t to be as absolutely prerequisite.
In the sense that if you think about the concepts I actually think that history has more concepts
than mathematics; it’s just that they’re spread out broader and they don’t depend on each
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
won’t stop you from understanding all of the rest of the components.
So that’s actually the difference between math and other subjects in my head.
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
because you lose any one link—meaning if you miss a few concepts along the chain you
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,
you might make a hole in your prerequisites.
And the way that education often works where it’s almost like riding a train from a beginning
to an end, well it’s such that if you have a hole somewhere in your track the train is
not going to pass that hole.
Now, I think that the way to help to address this is to provide a way for everyone to learn
at their own pace and in fact to fill in the holes whenever they are sensed.
And I actually feel like if everyone was able to pick up every one of those prerequisites
as necessary, filling in any gap they have, mathematics would change from being the hardest
subject to the easiest subject.
I think everyone is a math person, and all that one has to do is to go through the chain
and fill in all the gaps, and you will understand it better than all the other subjects actually.