# Annotated captions of Conrad Wolfram: Teaching kids real math with computers in English

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tedtalks |
00:00 00:04 |
We've got a real problem with math education right now. |

tedtalks |
00:04 00:07 |
Basically, no one's very happy. |

tedtalks |
00:07 00:09 |
Those learning it |

tedtalks |
00:09 00:11 |
think it's disconnected, |

tedtalks |
00:11 00:13 |
uninteresting and hard. |

tedtalks |
00:13 00:15 |
Those trying to employ them |

tedtalks |
00:15 00:17 |
think they don't know enough. |

tedtalks |
00:17 00:20 |
Governments realize that it's a big deal for our economies, |

tedtalks |
00:20 00:23 |
but don't know how to fix it. |

tedtalks |
00:23 00:25 |
And teachers are also frustrated. |

tedtalks |
00:25 00:28 |
Yet math is more important to the world |

tedtalks |
00:28 00:30 |
than at any point in human history. |

tedtalks |
00:30 00:32 |
So at one end we've got falling interest |

tedtalks |
00:32 00:34 |
in education in math, |

tedtalks |
00:34 00:37 |
and at the other end we've got a more mathematical world, |

tedtalks |
00:37 00:40 |
a more quantitative world than we ever have had. |

tedtalks |
00:41 00:43 |
So what's the problem, why has this chasm opened up, |

tedtalks |
00:43 00:46 |
and what can we do to fix it? |

tedtalks |
00:46 00:48 |
Well actually, I think the answer |

tedtalks |
00:48 00:50 |
is staring us right in the face: |

tedtalks |
00:50 00:52 |
Use computers. |

tedtalks |
00:52 00:54 |
I believe |

tedtalks |
00:54 00:56 |
that correctly using computers |

tedtalks |
00:56 00:58 |
is the silver bullet |

tedtalks |
00:58 01:01 |
for making math education work. |

tedtalks |
01:01 01:03 |
So to explain that, |

tedtalks |
01:03 01:06 |
let me first talk a bit about what math looks like in the real world |

tedtalks |
01:06 01:08 |
and what it looks like in education. |

tedtalks |
01:08 01:10 |
See, in the real world |

tedtalks |
01:10 01:13 |
math isn't necessarily done by mathematicians. |

tedtalks |
01:13 01:15 |
It's done by geologists, |

tedtalks |
01:15 01:17 |
engineers, biologists, |

tedtalks |
01:17 01:19 |
all sorts of different people -- |

tedtalks |
01:19 01:21 |
modeling and simulation. |

tedtalks |
01:21 01:23 |
It's actually very popular. |

tedtalks |
01:23 01:26 |
But in education it looks very different -- |

tedtalks |
01:26 01:28 |
dumbed-down problems, lots of calculating, |

tedtalks |
01:28 01:30 |
mostly by hand. |

tedtalks |
01:31 01:33 |
Lots of things that seem simple |

tedtalks |
01:33 01:35 |
and not difficult like in the real world, |

tedtalks |
01:35 01:37 |
except if you're learning it. |

tedtalks |
01:38 01:40 |
And another thing about math: |

tedtalks |
01:40 01:42 |
math sometimes looks like math -- |

tedtalks |
01:42 01:45 |
like in this example here -- |

tedtalks |
01:45 01:47 |
and sometimes it doesn't -- |

tedtalks |
01:47 01:50 |
like "Am I drunk?" |

tedtalks |
01:52 01:55 |
And then you get an answer that's quantitative in the modern world. |

tedtalks |
01:55 01:58 |
You wouldn't have expected that a few years back. |

tedtalks |
01:58 02:01 |
But now you can find out all about -- |

tedtalks |
02:01 02:04 |
unfortunately, my weight is a little higher than that, but -- |

tedtalks |
02:04 02:06 |
all about what happens. |

tedtalks |
02:06 02:08 |
So let's zoom out a bit and ask, |

tedtalks |
02:08 02:10 |
why are we teaching people math? |

tedtalks |
02:10 02:13 |
What's the point of teaching people math? |

tedtalks |
02:13 02:16 |
And in particular, why are we teaching them math in general? |

tedtalks |
02:16 02:19 |
Why is it such an important part of education |

tedtalks |
02:19 02:21 |
as a sort of compulsory subject? |

tedtalks |
02:21 02:24 |
Well, I think there are about three reasons: |

tedtalks |
02:24 02:26 |
technical jobs |

tedtalks |
02:26 02:29 |
so critical to the development of our economies, |

tedtalks |
02:29 02:32 |
what I call "everyday living" -- |

tedtalks |
02:33 02:35 |
to function in the world today, |

tedtalks |
02:35 02:37 |
you've got to be pretty quantitative, |

tedtalks |
02:37 02:39 |
much more so than a few years ago: |

tedtalks |
02:39 02:41 |
figure out your mortgages, |

tedtalks |
02:41 02:44 |
being skeptical of government statistics, those kinds of things -- |

tedtalks |
02:45 02:48 |
and thirdly, what I would call something like |

tedtalks |
02:48 02:51 |
logical mind training, logical thinking. |

tedtalks |
02:51 02:53 |
Over the years |

tedtalks |
02:53 02:55 |
we've put so much in society |

tedtalks |
02:55 02:58 |
into being able to process and think logically. It's part of human society. |

tedtalks |
02:58 03:00 |
It's very important to learn that |

tedtalks |
03:00 03:02 |
math is a great way to do that. |

tedtalks |
03:02 03:04 |
So let's ask another question. |

tedtalks |
03:04 03:06 |
What is math? |

tedtalks |
03:06 03:08 |
What do we mean when we say we're doing math, |

tedtalks |
03:08 03:10 |
or educating people to do math? |

tedtalks |
03:10 03:13 |
Well, I think it's about four steps, roughly speaking, |

tedtalks |
03:13 03:15 |
starting with posing the right question. |

tedtalks |
03:15 03:18 |
What is it that we want to ask? What is it we're trying to find out here? |

tedtalks |
03:18 03:20 |
And this is the thing most screwed up in the outside world, |

tedtalks |
03:20 03:23 |
beyond virtually any other part of doing math. |

tedtalks |
03:23 03:25 |
People ask the wrong question, |

tedtalks |
03:25 03:27 |
and surprisingly enough, they get the wrong answer, |

tedtalks |
03:27 03:29 |
for that reason, if not for others. |

tedtalks |
03:29 03:31 |
So the next thing is take that problem |

tedtalks |
03:31 03:33 |
and turn it from a real world problem |

tedtalks |
03:33 03:35 |
into a math problem. |

tedtalks |
03:35 03:37 |
That's stage two. |

tedtalks |
03:37 03:40 |
Once you've done that, then there's the computation step. |

tedtalks |
03:40 03:42 |
Turn it from that into some answer |

tedtalks |
03:42 03:45 |
in a mathematical form. |

tedtalks |
03:45 03:47 |
And of course, math is very powerful at doing that. |

tedtalks |
03:47 03:49 |
And then finally, turn it back to the real world. |

tedtalks |
03:49 03:51 |
Did it answer the question? |

tedtalks |
03:51 03:54 |
And also verify it -- crucial step. |

tedtalks |
03:55 03:57 |
Now here's the crazy thing right now. |

tedtalks |
03:57 03:59 |
In math education, |

tedtalks |
03:59 04:02 |
we're spending about perhaps 80 percent of the time |

tedtalks |
04:02 04:05 |
teaching people to do step three by hand. |

tedtalks |
04:05 04:07 |
Yet, that's the one step computers can do |

tedtalks |
04:07 04:10 |
better than any human after years of practice. |

tedtalks |
04:10 04:13 |
Instead, we ought to be using computers |

tedtalks |
04:13 04:15 |
to do step three |

tedtalks |
04:15 04:18 |
and using the students to spend much more effort |

tedtalks |
04:18 04:20 |
on learning how to do steps one, two and four -- |

tedtalks |
04:20 04:23 |
conceptualizing problems, applying them, |

tedtalks |
04:23 04:26 |
getting the teacher to run them through how to do that. |

tedtalks |
04:26 04:28 |
See, crucial point here: |

tedtalks |
04:28 04:30 |
math is not equal to calculating. |

tedtalks |
04:30 04:33 |
Math is a much broader subject than calculating. |

tedtalks |
04:33 04:36 |
Now it's understandable that this has all got intertwined |

tedtalks |
04:36 04:38 |
over hundreds of years. |

tedtalks |
04:38 04:41 |
There was only one way to do calculating and that was by hand. |

tedtalks |
04:41 04:43 |
But in the last few decades |

tedtalks |
04:43 04:45 |
that has totally changed. |

tedtalks |
04:45 04:48 |
We've had the biggest transformation of any ancient subject |

tedtalks |
04:48 04:51 |
that I could ever imagine with computers. |

tedtalks |
04:52 04:54 |
Calculating was typically the limiting step, |

tedtalks |
04:54 04:56 |
and now often it isn't. |

tedtalks |
04:56 04:58 |
So I think in terms of the fact that math |

tedtalks |
04:58 05:01 |
has been liberated from calculating. |

tedtalks |
05:01 05:04 |
But that math liberation didn't get into education yet. |

tedtalks |
05:04 05:06 |
See, I think of calculating, in a sense, |

tedtalks |
05:06 05:08 |
as the machinery of math. |

tedtalks |
05:08 05:10 |
It's the chore. |

tedtalks |
05:10 05:13 |
It's the thing you'd like to avoid if you can, like to get a machine to do. |

tedtalks |
05:14 05:17 |
It's a means to an end, not an end in itself, |

tedtalks |
05:19 05:21 |
and automation allows us |

tedtalks |
05:21 05:23 |
to have that machinery. |

tedtalks |
05:23 05:25 |
Computers allow us to do that -- |

tedtalks |
05:25 05:28 |
and this is not a small problem by any means. |

tedtalks |
05:28 05:31 |
I estimated that, just today, across the world, |

tedtalks |
05:31 05:34 |
we spent about 106 average world lifetimes |

tedtalks |
05:34 05:37 |
teaching people how to calculate by hand. |

tedtalks |
05:37 05:40 |
That's an amazing amount of human endeavor. |

tedtalks |
05:40 05:42 |
So we better be damn sure -- |

tedtalks |
05:42 05:45 |
and by the way, they didn't even have fun doing it, most of them -- |

tedtalks |
05:45 05:47 |
so we better be damn sure |

tedtalks |
05:47 05:49 |
that we know why we're doing that |

tedtalks |
05:49 05:51 |
and it has a real purpose. |

tedtalks |
05:51 05:53 |
I think we should be assuming computers |

tedtalks |
05:53 05:55 |
for doing the calculating |

tedtalks |
05:55 05:58 |
and only doing hand calculations where it really makes sense to teach people that. |

tedtalks |
05:58 06:00 |
And I think there are some cases. |

tedtalks |
06:00 06:02 |
For example: mental arithmetic. |

tedtalks |
06:02 06:05 |
I still do a lot of that, mainly for estimating. |

tedtalks |
06:05 06:07 |
People say, "Is such and such true?" |

tedtalks |
06:07 06:09 |
And I'll say, "Hmm, not sure." I'll think about it roughly. |

tedtalks |
06:09 06:11 |
It's still quicker to do that and more practical. |

tedtalks |
06:11 06:13 |
So I think practicality is one case |

tedtalks |
06:13 06:15 |
where it's worth teaching people by hand. |

tedtalks |
06:15 06:17 |
And then there are certain conceptual things |

tedtalks |
06:17 06:19 |
that can also benefit from hand calculating, |

tedtalks |
06:19 06:21 |
but I think they're relatively small in number. |

tedtalks |
06:21 06:23 |
One thing I often ask about |

tedtalks |
06:23 06:26 |
is ancient Greek and how this relates. |

tedtalks |
06:26 06:28 |
See, the thing we're doing right now |

tedtalks |
06:28 06:30 |
is we're forcing people to learn mathematics. |

tedtalks |
06:30 06:32 |
It's a major subject. |

tedtalks |
06:32 06:35 |
I'm not for one minute suggesting that, if people are interested in hand calculating |

tedtalks |
06:35 06:37 |
or in following their own interests |

tedtalks |
06:37 06:39 |
in any subject however bizarre -- |

tedtalks |
06:39 06:41 |
they should do that. |

tedtalks |
06:41 06:43 |
That's absolutely the right thing, |

tedtalks |
06:43 06:45 |
for people to follow their self-interest. |

tedtalks |
06:45 06:47 |
I was somewhat interested in ancient Greek, |

tedtalks |
06:47 06:50 |
but I don't think that we should force the entire population |

tedtalks |
06:50 06:52 |
to learn a subject like ancient Greek. |

tedtalks |
06:52 06:54 |
I don't think it's warranted. |

tedtalks |
06:54 06:57 |
So I have this distinction between what we're making people do |

tedtalks |
06:57 06:59 |
and the subject that's sort of mainstream |

tedtalks |
06:59 07:02 |
and the subject that, in a sense, people might follow with their own interest |

tedtalks |
07:02 07:04 |
and perhaps even be spiked into doing that. |

tedtalks |
07:04 07:07 |
So what are the issues people bring up with this? |

tedtalks |
07:07 07:10 |
Well one of them is, they say, you need to get the basics first. |

tedtalks |
07:10 07:12 |
You shouldn't use the machine |

tedtalks |
07:12 07:14 |
until you get the basics of the subject. |

tedtalks |
07:14 07:17 |
So my usual question is, what do you mean by "basics?" |

tedtalks |
07:17 07:19 |
Basics of what? |

tedtalks |
07:19 07:21 |
Are the basics of driving a car |

tedtalks |
07:21 07:24 |
learning how to service it, or design it for that matter? |

tedtalks |
07:24 07:27 |
Are the basics of writing learning how to sharpen a quill? |

tedtalks |
07:28 07:30 |
I don't think so. |

tedtalks |
07:30 07:33 |
I think you need to separate the basics of what you're trying to do |

tedtalks |
07:33 07:35 |
from how it gets done |

tedtalks |
07:35 07:38 |
and the machinery of how it gets done |

tedtalks |
07:39 07:42 |
and automation allows you to make that separation. |

tedtalks |
07:42 07:45 |
A hundred years ago, it's certainly true that to drive a car |

tedtalks |
07:45 07:47 |
you kind of needed to know a lot about the mechanics of the car |

tedtalks |
07:47 07:50 |
and how the ignition timing worked and all sorts of things. |

tedtalks |
07:51 07:53 |
But automation in cars |

tedtalks |
07:53 07:55 |
allowed that to separate, |

tedtalks |
07:55 07:58 |
so driving is now a quite separate subject, so to speak, |

tedtalks |
07:58 08:01 |
from engineering of the car |

tedtalks |
08:01 08:04 |
or learning how to service it. |

tedtalks |
08:05 08:07 |
So automation allows this separation |

tedtalks |
08:07 08:09 |
and also allows -- in the case of driving, |

tedtalks |
08:09 08:11 |
and I believe also in the future case of maths -- |

tedtalks |
08:11 08:13 |
a democratized way of doing that. |

tedtalks |
08:13 08:15 |
It can be spread across a much larger number of people |

tedtalks |
08:15 08:18 |
who can really work with that. |

tedtalks |
08:18 08:20 |
So there's another thing that comes up with basics. |

tedtalks |
08:20 08:22 |
People confuse, in my view, |

tedtalks |
08:22 08:25 |
the order of the invention of the tools |

tedtalks |
08:25 08:28 |
with the order in which they should use them for teaching. |

tedtalks |
08:28 08:31 |
So just because paper was invented before computers, |

tedtalks |
08:31 08:34 |
it doesn't necessarily mean you get more to the basics of the subject |

tedtalks |
08:34 08:36 |
by using paper instead of a computer |

tedtalks |
08:36 08:38 |
to teach mathematics. |

tedtalks |
08:40 08:43 |
My daughter gave me a rather nice anecdote on this. |

tedtalks |
08:43 08:46 |
She enjoys making what she calls "paper laptops." |

tedtalks |
08:46 08:48 |
(Laughter) |

tedtalks |
08:48 08:50 |
So I asked her one day, "You know, when I was your age, |

tedtalks |
08:50 08:52 |
I didn't make these. |

tedtalks |
08:52 08:54 |
Why do you think that was?" |

tedtalks |
08:54 08:56 |
And after a second or two, carefully reflecting, |

tedtalks |
08:56 08:58 |
she said, "No paper?" |

tedtalks |
08:58 09:03 |
(Laughter) |

tedtalks |
09:04 09:06 |
If you were born after computers and paper, |

tedtalks |
09:06 09:09 |
it doesn't really matter which order you're taught with them in, |

tedtalks |
09:09 09:11 |
you just want to have the best tool. |

tedtalks |
09:11 09:14 |
So another one that comes up is "Computers dumb math down." |

tedtalks |
09:14 09:16 |
That somehow, if you use a computer, |

tedtalks |
09:16 09:18 |
it's all mindless button-pushing, |

tedtalks |
09:18 09:20 |
but if you do it by hand, |

tedtalks |
09:20 09:22 |
it's all intellectual. |

tedtalks |
09:22 09:25 |
This one kind of annoys me, I must say. |

tedtalks |
09:25 09:27 |
Do we really believe |

tedtalks |
09:27 09:29 |
that the math that most people are doing in school |

tedtalks |
09:29 09:31 |
practically today |

tedtalks |
09:31 09:33 |
is more than applying procedures |

tedtalks |
09:33 09:36 |
to problems they don't really understand, for reasons they don't get? |

tedtalks |
09:36 09:38 |
I don't think so. |

tedtalks |
09:38 09:41 |
And what's worse, what they're learning there isn't even practically useful anymore. |

tedtalks |
09:41 09:44 |
Might have been 50 years ago, but it isn't anymore. |

tedtalks |
09:44 09:47 |
When they're out of education, they do it on a computer. |

tedtalks |
09:47 09:50 |
Just to be clear, I think computers can really help with this problem, |

tedtalks |
09:50 09:52 |
actually make it more conceptual. |

tedtalks |
09:52 09:54 |
Now, of course, like any great tool, |

tedtalks |
09:54 09:56 |
they can be used completely mindlessly, |

tedtalks |
09:56 09:59 |
like turning everything into a multimedia show, |

tedtalks |
09:59 10:02 |
like the example I was shown of solving an equation by hand, |

tedtalks |
10:02 10:04 |
where the computer was the teacher -- |

tedtalks |
10:04 10:07 |
show the student how to manipulate and solve it by hand. |

tedtalks |
10:07 10:09 |
This is just nuts. |

tedtalks |
10:09 10:12 |
Why are we using computers to show a student how to solve a problem by hand |

tedtalks |
10:12 10:14 |
that the computer should be doing anyway? |

tedtalks |
10:14 10:16 |
All backwards. |

tedtalks |
10:16 10:18 |
Let me show you |

tedtalks |
10:18 10:21 |
that you can also make problems harder to calculate. |

tedtalks |
10:21 10:23 |
See, normally in school, |

tedtalks |
10:23 10:26 |
you do things like solve quadratic equations. |

tedtalks |
10:26 10:29 |
But you see, when you're using a computer, |

tedtalks |
10:29 10:33 |
you can just substitute. |

tedtalks |
10:33 10:35 |
You can make it a quartic equation. Make it kind of harder, calculating-wise. |

tedtalks |
10:35 10:37 |
Same principles applied -- |

tedtalks |
10:37 10:39 |
calculations, harder. |

tedtalks |
10:39 10:41 |
And problems in the real world |

tedtalks |
10:41 10:43 |
look nutty and horrible like this. |

tedtalks |
10:43 10:45 |
They've got hair all over them. |

tedtalks |
10:45 10:48 |
They're not just simple, dumbed-down things that we see in school math. |

tedtalks |
10:49 10:51 |
And think of the outside world. |

tedtalks |
10:51 10:53 |
Do we really believe that engineering and biology |

tedtalks |
10:53 10:55 |
and all of these other things |

tedtalks |
10:55 10:57 |
that have so benefited from computers and maths |

tedtalks |
10:57 11:00 |
have somehow conceptually gotten reduced by using computers? |

tedtalks |
11:00 11:03 |
I don't think so -- quite the opposite. |

tedtalks |
11:03 11:06 |
So the problem we've really got in math education |

tedtalks |
11:06 11:09 |
is not that computers might dumb it down, |

tedtalks |
11:09 11:12 |
but that we have dumbed-down problems right now. |

tedtalks |
11:12 11:14 |
Well, another issue people bring up |

tedtalks |
11:14 11:16 |
is somehow that hand calculating procedures |

tedtalks |
11:16 11:18 |
teach understanding. |

tedtalks |
11:18 11:20 |
So if you go through lots of examples, |

tedtalks |
11:20 11:22 |
you can get the answer, |

tedtalks |
11:22 11:25 |
you can understand how the basics of the system work better. |

tedtalks |
11:25 11:28 |
I think there is one thing that I think very valid here, |

tedtalks |
11:28 11:31 |
which is that I think understanding procedures and processes is important. |

tedtalks |
11:32 11:35 |
But there's a fantastic way to do that in the modern world. |

tedtalks |
11:35 11:38 |
It's called programming. |

tedtalks |
11:38 11:40 |
Programming is how most procedures and processes |

tedtalks |
11:40 11:42 |
get written down these days, |

tedtalks |
11:42 11:44 |
and it's also a great way |

tedtalks |
11:44 11:46 |
to engage students much more |

tedtalks |
11:46 11:48 |
and to check they really understand. |

tedtalks |
11:48 11:50 |
If you really want to check you understand math |

tedtalks |
11:50 11:53 |
then write a program to do it. |

tedtalks |
11:53 11:56 |
So programming is the way I think we should be doing that. |

tedtalks |
11:56 11:58 |
So to be clear, what I really am suggesting here |

tedtalks |
11:58 12:00 |
is we have a unique opportunity |

tedtalks |
12:00 12:02 |
to make maths both more practical |

tedtalks |
12:02 12:05 |
and more conceptual, simultaneously. |

tedtalks |
12:05 12:08 |
I can't think of any other subject where that's recently been possible. |

tedtalks |
12:08 12:10 |
It's usually some kind of choice |

tedtalks |
12:10 12:12 |
between the vocational and the intellectual. |

tedtalks |
12:12 12:15 |
But I think we can do both at the same time here. |

tedtalks |
12:17 12:20 |
And we open up so many more possibilities. |

tedtalks |
12:20 12:22 |
You can do so many more problems. |

tedtalks |
12:22 12:24 |
What I really think we gain from this |

tedtalks |
12:24 12:27 |
is students getting intuition and experience |

tedtalks |
12:27 12:30 |
in far greater quantities than they've ever got before. |

tedtalks |
12:30 12:32 |
And experience of harder problems -- |

tedtalks |
12:32 12:34 |
being able to play with the math, interact with it, |

tedtalks |
12:34 12:36 |
feel it. |

tedtalks |
12:36 12:39 |
We want people who can feel the math instinctively. |

tedtalks |
12:39 12:42 |
That's what computers allow us to do. |

tedtalks |
12:42 12:45 |
Another thing it allows us to do is reorder the curriculum. |

tedtalks |
12:45 12:47 |
Traditionally it's been by how difficult it is to calculate, |

tedtalks |
12:47 12:49 |
but now we can reorder it |

tedtalks |
12:49 12:51 |
by how difficult it is to understand the concepts, |

tedtalks |
12:51 12:53 |
however hard the calculating. |

tedtalks |
12:53 12:56 |
So calculus has traditionally been taught very late. |

tedtalks |
12:56 12:58 |
Why is this? |

tedtalks |
12:58 13:01 |
Well, it's damn hard doing the calculations, that's the problem. |

tedtalks |
13:02 13:04 |
But actually many of the concepts |

tedtalks |
13:04 13:07 |
are amenable to a much younger age group. |

tedtalks |
13:07 13:10 |
This was an example I built for my daughter. |

tedtalks |
13:10 13:12 |
And very, very simple. |

tedtalks |
13:13 13:15 |
We were talking about what happens |

tedtalks |
13:15 13:17 |
when you increase the number of sides of a polygon |

tedtalks |
13:17 13:19 |
to a very large number. |

tedtalks |
13:21 13:23 |
And of course, it turns into a circle. |

tedtalks |
13:23 13:25 |
And by the way, she was also very insistent |

tedtalks |
13:25 13:27 |
on being able to change the color, |

tedtalks |
13:27 13:30 |
an important feature for this demonstration. |

tedtalks |
13:31 13:34 |
You can see that this is a very early step |

tedtalks |
13:34 13:36 |
into limits and differential calculus |

tedtalks |
13:36 13:39 |
and what happens when you take things to an extreme -- |

tedtalks |
13:39 13:41 |
and very small sides and a very large number of sides. |

tedtalks |
13:41 13:43 |
Very simple example. |

tedtalks |
13:43 13:45 |
That's a view of the world |

tedtalks |
13:45 13:48 |
that we don't usually give people for many, many years after this. |

tedtalks |
13:48 13:51 |
And yet, that's a really important practical view of the world. |

tedtalks |
13:51 13:54 |
So one of the roadblocks we have |

tedtalks |
13:54 13:57 |
in moving this agenda forward |

tedtalks |
13:57 13:59 |
is exams. |

tedtalks |
13:59 14:02 |
In the end, if we test everyone by hand in exams, |

tedtalks |
14:02 14:05 |
it's kind of hard to get the curricula changed |

tedtalks |
14:05 14:07 |
to a point where they can use computers |

tedtalks |
14:07 14:10 |
during the semesters. |

tedtalks |
14:10 14:12 |
And one of the reasons it's so important -- |

tedtalks |
14:12 14:15 |
so it's very important to get computers in exams. |

tedtalks |
14:15 14:18 |
And then we can ask questions, real questions, |

tedtalks |
14:18 14:21 |
questions like, what's the best life insurance policy to get? -- |

tedtalks |
14:21 14:24 |
real questions that people have in their everyday lives. |

tedtalks |
14:25 14:27 |
And you see, this isn't some dumbed-down model here. |

tedtalks |
14:27 14:30 |
This is an actual model where we can be asked to optimize what happens. |

tedtalks |
14:30 14:32 |
How many years of protection do I need? |

tedtalks |
14:32 14:34 |
What does that do to the payments |

tedtalks |
14:34 14:37 |
and to the interest rates and so forth? |

tedtalks |
14:37 14:40 |
Now I'm not for one minute suggesting it's the only kind of question |

tedtalks |
14:40 14:42 |
that should be asked in exams, |

tedtalks |
14:42 14:44 |
but I think it's a very important type |

tedtalks |
14:44 14:47 |
that right now just gets completely ignored |

tedtalks |
14:47 14:50 |
and is critical for people's real understanding. |

tedtalks |
14:50 14:53 |
So I believe [there is] critical reform |

tedtalks |
14:53 14:55 |
we have to do in computer-based math. |

tedtalks |
14:55 14:57 |
We have got to make sure |

tedtalks |
14:57 15:00 |
that we can move our economies forward, |

tedtalks |
15:00 15:02 |
and also our societies, |

tedtalks |
15:02 15:05 |
based on the idea that people can really feel mathematics. |

tedtalks |
15:07 15:10 |
This isn't some optional extra. |

tedtalks |
15:10 15:12 |
And the country that does this first |

tedtalks |
15:12 15:15 |
will, in my view, leapfrog others |

tedtalks |
15:15 15:18 |
in achieving a new economy even, |

tedtalks |
15:18 15:20 |
an improved economy, |

tedtalks |
15:20 15:22 |
an improved outlook. |

tedtalks |
15:22 15:24 |
In fact, I even talk about us moving |

tedtalks |
15:24 15:27 |
from what we often call now the "knowledge economy" |

tedtalks |
15:27 15:30 |
to what we might call a "computational knowledge economy," |

tedtalks |
15:30 15:33 |
where high-level math is integral to what everyone does |

tedtalks |
15:33 15:35 |
in the way that knowledge currently is. |

tedtalks |
15:35 15:38 |
We can engage so many more students with this, |

tedtalks |
15:38 15:41 |
and they can have a better time doing it. |

tedtalks |
15:41 15:43 |
And let's understand: |

tedtalks |
15:43 15:46 |
this is not an incremental sort of change. |

tedtalks |
15:47 15:49 |
We're trying to cross the chasm here |

tedtalks |
15:49 15:51 |
between school math and the real-world math. |

tedtalks |
15:51 15:53 |
And you know if you walk across a chasm, |

tedtalks |
15:53 15:56 |
you end up making it worse than if you didn't start at all -- |

tedtalks |
15:56 15:58 |
bigger disaster. |

tedtalks |
15:58 16:00 |
No, what I'm suggesting |

tedtalks |
16:00 16:02 |
is that we should leap off, |

tedtalks |
16:02 16:04 |
we should increase our velocity |

tedtalks |
16:04 16:06 |
so it's high, |

tedtalks |
16:06 16:09 |
and we should leap off one side and go the other -- |

tedtalks |
16:09 16:12 |
of course, having calculated our differential equation very carefully. |

tedtalks |
16:12 16:14 |
(Laughter) |

tedtalks |
16:14 16:16 |
So I want to see |

tedtalks |
16:16 16:18 |
a completely renewed, changed math curriculum |

tedtalks |
16:18 16:20 |
built from the ground up, |

tedtalks |
16:20 16:22 |
based on computers being there, |

tedtalks |
16:22 16:24 |
computers that are now ubiquitous almost. |

tedtalks |
16:24 16:26 |
Calculating machines are everywhere |

tedtalks |
16:26 16:29 |
and will be completely everywhere in a small number of years. |

tedtalks |
16:29 16:33 |
Now I'm not even sure if we should brand the subject as math, |

tedtalks |
16:33 16:35 |
but what I am sure is |

tedtalks |
16:35 16:37 |
it's the mainstream subject of the future. |

tedtalks |
16:38 16:41 |
Let's go for it, |

tedtalks |
16:41 16:43 |
and while we're about it, |

tedtalks |
16:43 16:45 |
let's have a bit of fun, |

tedtalks |
16:45 16:48 |
for us, for the students and for TED here. |

tedtalks |
16:48 16:50 |
Thanks. |

tedtalks |
16:50 16:57 |
(Applause) |