BackpropBuff/TED2020.en-ja · Datasets at Hugging Face

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Yet math is more important to the world than at any point in human history.	しかしながら数学は今までにないほど大事なときを迎えています
So at one end we've got falling interest in education in math, and at the other end we've got a more mathematical world, a more quantitative world than we ever have had.	教育現場では数学への関心が下がる一方で世界は未だかつてないほど数学的で定量的になりつつあります
So what's the problem, why has this chasm opened up, and what can we do to fix it?	この隔たりをつくり出す問題とその解決策は何でしょうか
Well actually, I think the answer is staring us right in the face: Use computers.	解決策は明らかにコンピュータを使うことだと私は思います
I believe that correctly using computers is the silver bullet for making math education work.	数学教育を成功させるにはコンピュータを正しく使う事が解決策であるのは間違いないでしょう
So to explain that, let me first talk a bit about what math looks like in the real world and what it looks like in education.	まず実社会や教育の場で数学はどのようなものなのか説明しましょう
See, in the real world math isn't necessarily done by mathematicians.	実社会で数学は必ずしも数学者がやるものではありません
It's done by geologists, engineers, biologists, all sorts of different people -- modeling and simulation.	地質学者であったりエンジニアや生物学者― いろいろな人たちによってモデリングやシミュレーションと
It's actually very popular.	様々な用途に使われています
But in education it looks very different -- dumbed-down problems, lots of calculating, mostly by hand.	でも教育現場では違います簡略化された問題や計算を手作業で行います
Lots of things that seem simple and not difficult like in the real world, except if you're learning it.	数学を勉強中なら別ですがシンプルに見えるものが多く実社会のように難しくありません
And another thing about math: math sometimes looks like math -- like in this example here -- and sometimes it doesn't -- like "Am I drunk?"	もう一つ言えるのは数学はこの例のように数学のように見えることもありますが見えないこともあります例えば “酔ってる？” という質問は
And then you get an answer that's quantitative in the modern world.	現代の世界では定量的な答えが出てきます
You wouldn't have expected that a few years back.	数年前まで予想もしなかったことですが
But now you can find out all about -- unfortunately, my weight is a little higher than that, but -- all about what happens.	全てのことを見つけ出せます私の体重が少し軽めに表示されていますが何事も見つけ出せます
So let's zoom out a bit and ask, why are we teaching people math?	では少しズームアウトしてなぜ数学を教えているのか考えましょう
What's the point of teaching people math?	数学の教育にはどのような意味があるでしょうか
And in particular, why are we teaching them math in general?	とりわけ数学を教えているのはなぜでしょうか
Why is it such an important part of education as a sort of compulsory subject?	必修科目として数学を教育に組み込むのはなぜ重要なのでしょうか
Over the years we've put so much in society into being able to process and think logically. It's part of human society.	ここ何年も私たちは論理的に考えるよう多大な努力をしてきました
It's very important to learn that math is a great way to do that.	数学はそれを学べる― 素晴らしい方法です
So let's ask another question.	では別の質問ですが
What is math?	数学とは何でしょうか
What do we mean when we say we're doing math, or educating people to do math?	数学を教えるというのはどのような意味があるのでしょうか
Well, I think it's about four steps, roughly speaking, starting with posing the right question.	私は４段階に関することだと思いますまずは正しい質問―
What is it that we want to ask? What is it we're trying to find out here?	見つけ出そうとしているのは何なのかということですが
And this is the thing most screwed up in the outside world, beyond virtually any other part of doing math.	これが数学を使う上で最も機能していない部分です
People ask the wrong question, and surprisingly enough, they get the wrong answer, for that reason, if not for others.	的はずれなことを尋ねるから人々は間違った答えを導きだしてしまいます
So the next thing is take that problem and turn it from a real world problem into a math problem.	次はその問題をとらえ本物の世界の問題から数学の問題にかえることです
That's stage two.	これが第二段階です
Once you've done that, then there's the computation step.	それが終わったら計算の段階です
Turn it from that into some answer in a mathematical form.	答えは数学的な形に変えるのですが数学は非常に
And of course, math is very powerful at doing that.	それに優れています
And then finally, turn it back to the real world.	最後に実世界に戻し
Did it answer the question?	問題に答えたかどうか確認します
And also verify it -- crucial step.	また重要なのが実証してみることです
Now here's the crazy thing right now.	現在ひどいことが起きています
In math education, we're spending about perhaps 80 percent of the time teaching people to do step three by hand.	数学教育では第三段階を手作業でやるように約８割の時間を費やして教えていますが
Yet, that's the one step computers can do better than any human after years of practice.	どんなに人間が頑張ってもコンピュータには敵いません
Instead, we ought to be using computers to do step three and using the students to spend much more effort on learning how to do steps one, two and four -- conceptualizing problems, applying them, getting the teacher to run them through how to do that.	ですから第三段階にはコンピュータを使用するべきで学生は第一と第二と第四段階にもっと努力を費やすべきです問題の概念化や応用をして教師はその仕方を全面的に指導するのです
See, crucial point here: math is not equal to calculating.	数学と計算は同じなのではありません
Math is a much broader subject than calculating.	数学はもっと幅の広い分野です
Now it's understandable that this has all got intertwined over hundreds of years.	何百年という間に数学と計算が絡み合ったのは理解できます
There was only one way to do calculating and that was by hand.	計算は唯一手で行うものでしたが
But in the last few decades that has totally changed.	過去数十年の間にがらりと変わりました
We've had the biggest transformation of any ancient subject that I could ever imagine with computers.	コンピュータによって古代から伝わってきた分野が大きな変貌を遂げました
Calculating was typically the limiting step, and now often it isn't.	計算は限定的な段階でしたが今はそうでないことも多いのです
So I think in terms of the fact that math has been liberated from calculating.	数学が計算ではなくなったのにその事実はまだ教育には
But that math liberation didn't get into education yet.	浸透していません
See, I think of calculating, in a sense, as the machinery of math.	計算は数学の可動部分だと私は考えています
It's the chore.	雑仕事なのです
It's the thing you'd like to avoid if you can, like to get a machine to do.	できれば機械にやらせて自分では避けたいものです
It's a means to an end, not an end in itself, and automation allows us to have that machinery.	手段であって目的ではありませんオートメーションはその可動部分を可能にしてくれます
Computers allow us to do that -- and this is not a small problem by any means.	コンピュータがそうしてくれるのですこれは小さな問題ではありません
I estimated that, just today, across the world, we spent about 106 average world lifetimes teaching people how to calculate by hand.	私の推測では現在世界の至る所で約106人分の生涯に相当する時間をかけて手で行う計算の仕方を教えています
That's an amazing amount of human endeavor.	多大な量の努力をしているのです
So we better be damn sure -- and by the way, they didn't even have fun doing it, most of them -- so we better be damn sure that we know why we're doing that and it has a real purpose.	楽しんでやっている人が非常に少ないのですからそれをやる理由と目的をきちんと把握しておくべきです
I think we should be assuming computers for doing the calculating and only doing hand calculations where it really makes sense to teach people that.	計算はコンピュータの仕事だと思った方がいいと思います合理性のあるときだけ自分で計算をするように教えるべきです
And I think there are some cases.	いくつか例をあげてみましょう
For example: mental arithmetic.	例えば暗算です
I still do a lot of that, mainly for estimating.	目算するとき私は今でも暗算をします
People say, "Is such and such true?"	誰かが何かを言ったとき
And I'll say, "Hmm, not sure." I'll think about it roughly.	本当かどうかざっと計算してみるのです
It's still quicker to do that and more practical.	時間がかからず実用的なので
So I think practicality is one case where it's worth teaching people by hand.	実用性の面で見れば教える価値はあると思います
And then there are certain conceptual things that can also benefit from hand calculating, but I think they're relatively small in number.	手で計算することでためにもなるある概念的なものがありますが数は比較的少ないと思います
One thing I often ask about is ancient Greek and how this relates.	私がよく尋ねるのは古代ギリシャ語とその関連性です
See, the thing we're doing right now is we're forcing people to learn mathematics.	現在私たちは数学を強制的に学ばせています
It's a major subject.	主要な科目です
I'm not for one minute suggesting that, if people are interested in hand calculating or in following their own interests in any subject however bizarre -- they should do that.	手で行う計算に興味があったりどんなに変わっている科目でも自らの興味を追求しているならそれはやるべきです
That's absolutely the right thing, for people to follow their self-interest.	自らの興味の追求はまったく正しい行いです
I was somewhat interested in ancient Greek, but I don't think that we should force the entire population to learn a subject like ancient Greek.	私は古代ギリシャ語に興味がありましたが国民全体に古代ギリシャ語のような教科を強制するべきだとは思いません
I don't think it's warranted.	その必要性はありません
So I have this distinction between what we're making people do and the subject that's sort of mainstream and the subject that, in a sense, people might follow with their own interest and perhaps even be spiked into doing that.	私は二種類のものがあると思います主流とも言える科目である数学そして人々が興味を持ち追究しようとする数学です
So what are the issues people bring up with this?	この問題に持ち出される意見の一つに
Well one of them is, they say, you need to get the basics first.	基礎をまず学ぶ必要があると言う人がいます
You shouldn't use the machine until you get the basics of the subject.	基礎を身につけるまで機械は使うべきではないと言うのです
So my usual question is, what do you mean by "basics?"	でも基礎とは何でしょうか
Basics of what?	何の基礎でしょう？
Are the basics of driving a car learning how to service it, or design it for that matter?	車の運転の基礎は点検の仕方？それともデザインの仕方？
Are the basics of writing learning how to sharpen a quill?	執筆の基礎は羽ペンの削り方？
I don't think so.	違うと思います
I think you need to separate the basics of what you're trying to do from how it gets done and the machinery of how it gets done and automation allows you to make that separation.	自分がやろうとする事の基礎はそのからくりから切り離す必要があると思います自動化がその切り離しを可能にしてくれます
A hundred years ago, it's certainly true that to drive a car you kind of needed to know a lot about the mechanics of the car and how the ignition timing worked and all sorts of things.	100年前であれば車を運転するなら車の仕組みやエンジンの点火時期を知る必要もありました
But automation in cars allowed that to separate, so driving is now a quite separate subject, so to speak, from engineering of the car or learning how to service it.	でも車が自動化されたことで車の運転は車のエンジニアリングや点検の仕方を学ぶことから切り離すことができるようになりました
So automation allows this separation and also allows -- in the case of driving, and I believe also in the future case of maths -- a democratized way of doing that.	自動化によって可能になったのですまた運転に関しては数学の将来にも言えると思いますが庶民的にしてくれます
It can be spread across a much larger number of people who can really work with that.	もっと大勢の人たちが使えるようになります
So there's another thing that comes up with basics.	基礎に関してもう一つの話題があがります
People confuse, in my view, the order of the invention of the tools with the order in which they should use them for teaching.	ツールが発明された順番に学習の順番も決められているような気が私にはするのです
So just because paper was invented before computers, it doesn't necessarily mean you get more to the basics of the subject by using paper instead of a computer to teach mathematics.	コンピュータよりも先に紙が発明されたからといって数学の授業でコンピュータの代わりに紙を使わなければいけないというわけではありません
My daughter gave me a rather nice anecdote on this.	私の娘が面白いことを言いました
She enjoys making what she calls "paper laptops."	娘は紙でパソコンを作って楽しんでいるのですが
(Laughter) So I asked her one day, "You know, when I was your age, I didn't make these.	（会場：笑い声）私が子どものときには作らなかったけどそれはなぜかと
Why do you think that was?"	娘に尋ねてみたら
And after a second or two, carefully reflecting, she said, "No paper?"	少し考えてこう言いました “紙がなかったの？”
(Laughter) If you were born after computers and paper, it doesn't really matter which order you're taught with them in, you just want to have the best tool.	（会場：笑い声）両方存在する時代に生まれたらどちらで教わるかなんて関係ありません最高のツールがあればいいのです
So another one that comes up is "Computers dumb math down."	コンピュータが数学のレベルを下げると言う人もいます
That somehow, if you use a computer, it's all mindless button-pushing, but if you do it by hand, it's all intellectual.	コンピュータはボタンを押すだけですが手で計算をすれば頭を使うと言うのです
This one kind of annoys me, I must say.	この考え方はしゃくにさわります
Do we really believe that the math that most people are doing in school practically today is more than applying procedures to problems they don't really understand, for reasons they don't get?	現在学校で学生たちは理解していない問題を解かされその必要性も理解していませんでもこれが本来の状況ではないとでも思いますか？

Yet math is more important to the world than at any point in human history.

しかしながら数学は今までにないほど大事なときを迎えています

So at one end we've got falling interest in education in math, and at the other end we've got a more mathematical world, a more quantitative world than we ever have had.

教育現場では数学への関心が下がる一方で世界は未だかつてないほど数学的で定量的になりつつあります

So what's the problem, why has this chasm opened up, and what can we do to fix it?

この隔たりをつくり出す問題とその解決策は何でしょうか

Well actually, I think the answer is staring us right in the face: Use computers.

解決策は明らかにコンピュータを使うことだと私は思います

I believe that correctly using computers is the silver bullet for making math education work.

数学教育を成功させるにはコンピュータを正しく使う事が解決策であるのは間違いないでしょう

So to explain that, let me first talk a bit about what math looks like in the real world and what it looks like in education.

まず実社会や教育の場で数学はどのようなものなのか説明しましょう

See, in the real world math isn't necessarily done by mathematicians.

実社会で数学は必ずしも数学者がやるものではありません

It's done by geologists, engineers, biologists, all sorts of different people -- modeling and simulation.

地質学者であったりエンジニアや生物学者― いろいろな人たちによってモデリングやシミュレーションと

It's actually very popular.

様々な用途に使われています

But in education it looks very different -- dumbed-down problems, lots of calculating, mostly by hand.

でも教育現場では違います簡略化された問題や計算を手作業で行います

Lots of things that seem simple and not difficult like in the real world, except if you're learning it.

数学を勉強中なら別ですがシンプルに見えるものが多く実社会のように難しくありません

And another thing about math: math sometimes looks like math -- like in this example here -- and sometimes it doesn't -- like "Am I drunk?"

もう一つ言えるのは数学はこの例のように数学のように見えることもありますが見えないこともあります例えば “酔ってる？” という質問は

And then you get an answer that's quantitative in the modern world.

現代の世界では定量的な答えが出てきます

You wouldn't have expected that a few years back.

数年前まで予想もしなかったことですが

But now you can find out all about -- unfortunately, my weight is a little higher than that, but -- all about what happens.

全てのことを見つけ出せます私の体重が少し軽めに表示されていますが何事も見つけ出せます

So let's zoom out a bit and ask, why are we teaching people math?

では少しズームアウトしてなぜ数学を教えているのか考えましょう

What's the point of teaching people math?

数学の教育にはどのような意味があるでしょうか

And in particular, why are we teaching them math in general?

とりわけ数学を教えているのはなぜでしょうか

Why is it such an important part of education as a sort of compulsory subject?

必修科目として数学を教育に組み込むのはなぜ重要なのでしょうか

Over the years we've put so much in society into being able to process and think logically. It's part of human society.

ここ何年も私たちは論理的に考えるよう多大な努力をしてきました

It's very important to learn that math is a great way to do that.

数学はそれを学べる― 素晴らしい方法です

So let's ask another question.

では別の質問ですが

What is math?

数学とは何でしょうか

What do we mean when we say we're doing math, or educating people to do math?

数学を教えるというのはどのような意味があるのでしょうか

Well, I think it's about four steps, roughly speaking, starting with posing the right question.

私は４段階に関することだと思いますまずは正しい質問―

What is it that we want to ask? What is it we're trying to find out here?

見つけ出そうとしているのは何なのかということですが

And this is the thing most screwed up in the outside world, beyond virtually any other part of doing math.

これが数学を使う上で最も機能していない部分です

People ask the wrong question, and surprisingly enough, they get the wrong answer, for that reason, if not for others.

的はずれなことを尋ねるから人々は間違った答えを導きだしてしまいます

So the next thing is take that problem and turn it from a real world problem into a math problem.

次はその問題をとらえ本物の世界の問題から数学の問題にかえることです

That's stage two.

これが第二段階です

Once you've done that, then there's the computation step.

それが終わったら計算の段階です

Turn it from that into some answer in a mathematical form.

答えは数学的な形に変えるのですが数学は非常に

And of course, math is very powerful at doing that.

それに優れています

And then finally, turn it back to the real world.

最後に実世界に戻し

Did it answer the question?

問題に答えたかどうか確認します

And also verify it -- crucial step.

また重要なのが実証してみることです

Now here's the crazy thing right now.

現在ひどいことが起きています

In math education, we're spending about perhaps 80 percent of the time teaching people to do step three by hand.

数学教育では第三段階を手作業でやるように約８割の時間を費やして教えていますが

Yet, that's the one step computers can do better than any human after years of practice.

どんなに人間が頑張ってもコンピュータには敵いません

Instead, we ought to be using computers to do step three and using the students to spend much more effort on learning how to do steps one, two and four -- conceptualizing problems, applying them, getting the teacher to run them through how to do that.

ですから第三段階にはコンピュータを使用するべきで学生は第一と第二と第四段階にもっと努力を費やすべきです問題の概念化や応用をして教師はその仕方を全面的に指導するのです

See, crucial point here: math is not equal to calculating.

数学と計算は同じなのではありません

Math is a much broader subject than calculating.

数学はもっと幅の広い分野です

Now it's understandable that this has all got intertwined over hundreds of years.

何百年という間に数学と計算が絡み合ったのは理解できます

There was only one way to do calculating and that was by hand.

計算は唯一手で行うものでしたが

But in the last few decades that has totally changed.

過去数十年の間にがらりと変わりました

We've had the biggest transformation of any ancient subject that I could ever imagine with computers.

コンピュータによって古代から伝わってきた分野が大きな変貌を遂げました

Calculating was typically the limiting step, and now often it isn't.

計算は限定的な段階でしたが今はそうでないことも多いのです

So I think in terms of the fact that math has been liberated from calculating.

数学が計算ではなくなったのにその事実はまだ教育には

But that math liberation didn't get into education yet.

浸透していません

See, I think of calculating, in a sense, as the machinery of math.

計算は数学の可動部分だと私は考えています

It's the chore.

雑仕事なのです

It's the thing you'd like to avoid if you can, like to get a machine to do.

できれば機械にやらせて自分では避けたいものです

It's a means to an end, not an end in itself, and automation allows us to have that machinery.

手段であって目的ではありませんオートメーションはその可動部分を可能にしてくれます

Computers allow us to do that -- and this is not a small problem by any means.

コンピュータがそうしてくれるのですこれは小さな問題ではありません

I estimated that, just today, across the world, we spent about 106 average world lifetimes teaching people how to calculate by hand.

私の推測では現在世界の至る所で約106人分の生涯に相当する時間をかけて手で行う計算の仕方を教えています

That's an amazing amount of human endeavor.

多大な量の努力をしているのです

So we better be damn sure -- and by the way, they didn't even have fun doing it, most of them -- so we better be damn sure that we know why we're doing that and it has a real purpose.

楽しんでやっている人が非常に少ないのですからそれをやる理由と目的をきちんと把握しておくべきです

I think we should be assuming computers for doing the calculating and only doing hand calculations where it really makes sense to teach people that.

計算はコンピュータの仕事だと思った方がいいと思います合理性のあるときだけ自分で計算をするように教えるべきです

And I think there are some cases.

いくつか例をあげてみましょう

For example: mental arithmetic.

例えば暗算です

I still do a lot of that, mainly for estimating.

目算するとき私は今でも暗算をします

People say, "Is such and such true?"

誰かが何かを言ったとき

And I'll say, "Hmm, not sure." I'll think about it roughly.

本当かどうかざっと計算してみるのです

It's still quicker to do that and more practical.

時間がかからず実用的なので

So I think practicality is one case where it's worth teaching people by hand.

実用性の面で見れば教える価値はあると思います

And then there are certain conceptual things that can also benefit from hand calculating, but I think they're relatively small in number.

手で計算することでためにもなるある概念的なものがありますが数は比較的少ないと思います

One thing I often ask about is ancient Greek and how this relates.

私がよく尋ねるのは古代ギリシャ語とその関連性です

See, the thing we're doing right now is we're forcing people to learn mathematics.

現在私たちは数学を強制的に学ばせています

It's a major subject.

主要な科目です

I'm not for one minute suggesting that, if people are interested in hand calculating or in following their own interests in any subject however bizarre -- they should do that.

手で行う計算に興味があったりどんなに変わっている科目でも自らの興味を追求しているならそれはやるべきです

That's absolutely the right thing, for people to follow their self-interest.

自らの興味の追求はまったく正しい行いです

I was somewhat interested in ancient Greek, but I don't think that we should force the entire population to learn a subject like ancient Greek.

私は古代ギリシャ語に興味がありましたが国民全体に古代ギリシャ語のような教科を強制するべきだとは思いません

I don't think it's warranted.

その必要性はありません

So I have this distinction between what we're making people do and the subject that's sort of mainstream and the subject that, in a sense, people might follow with their own interest and perhaps even be spiked into doing that.

私は二種類のものがあると思います主流とも言える科目である数学そして人々が興味を持ち追究しようとする数学です

So what are the issues people bring up with this?

この問題に持ち出される意見の一つに

Well one of them is, they say, you need to get the basics first.

基礎をまず学ぶ必要があると言う人がいます

You shouldn't use the machine until you get the basics of the subject.

基礎を身につけるまで機械は使うべきではないと言うのです

So my usual question is, what do you mean by "basics?"

でも基礎とは何でしょうか

Basics of what?

何の基礎でしょう？

Are the basics of driving a car learning how to service it, or design it for that matter?

車の運転の基礎は点検の仕方？それともデザインの仕方？

Are the basics of writing learning how to sharpen a quill?

執筆の基礎は羽ペンの削り方？

I don't think so.

違うと思います

I think you need to separate the basics of what you're trying to do from how it gets done and the machinery of how it gets done and automation allows you to make that separation.

自分がやろうとする事の基礎はそのからくりから切り離す必要があると思います自動化がその切り離しを可能にしてくれます

A hundred years ago, it's certainly true that to drive a car you kind of needed to know a lot about the mechanics of the car and how the ignition timing worked and all sorts of things.

100年前であれば車を運転するなら車の仕組みやエンジンの点火時期を知る必要もありました

But automation in cars allowed that to separate, so driving is now a quite separate subject, so to speak, from engineering of the car or learning how to service it.

でも車が自動化されたことで車の運転は車のエンジニアリングや点検の仕方を学ぶことから切り離すことができるようになりました

So automation allows this separation and also allows -- in the case of driving, and I believe also in the future case of maths -- a democratized way of doing that.

自動化によって可能になったのですまた運転に関しては数学の将来にも言えると思いますが庶民的にしてくれます

It can be spread across a much larger number of people who can really work with that.

もっと大勢の人たちが使えるようになります

So there's another thing that comes up with basics.

基礎に関してもう一つの話題があがります

People confuse, in my view, the order of the invention of the tools with the order in which they should use them for teaching.

ツールが発明された順番に学習の順番も決められているような気が私にはするのです

So just because paper was invented before computers, it doesn't necessarily mean you get more to the basics of the subject by using paper instead of a computer to teach mathematics.

コンピュータよりも先に紙が発明されたからといって数学の授業でコンピュータの代わりに紙を使わなければいけないというわけではありません

My daughter gave me a rather nice anecdote on this.

私の娘が面白いことを言いました

She enjoys making what she calls "paper laptops."

娘は紙でパソコンを作って楽しんでいるのですが

(Laughter) So I asked her one day, "You know, when I was your age, I didn't make these.

（会場：笑い声）私が子どものときには作らなかったけどそれはなぜかと

Why do you think that was?"

娘に尋ねてみたら

And after a second or two, carefully reflecting, she said, "No paper?"

少し考えてこう言いました “紙がなかったの？”

(Laughter) If you were born after computers and paper, it doesn't really matter which order you're taught with them in, you just want to have the best tool.

（会場：笑い声）両方存在する時代に生まれたらどちらで教わるかなんて関係ありません最高のツールがあればいいのです

So another one that comes up is "Computers dumb math down."

コンピュータが数学のレベルを下げると言う人もいます

That somehow, if you use a computer, it's all mindless button-pushing, but if you do it by hand, it's all intellectual.

コンピュータはボタンを押すだけですが手で計算をすれば頭を使うと言うのです

This one kind of annoys me, I must say.

この考え方はしゃくにさわります

Do we really believe that the math that most people are doing in school practically today is more than applying procedures to problems they don't really understand, for reasons they don't get?

現在学校で学生たちは理解していない問題を解かされその必要性も理解していませんでもこれが本来の状況ではないとでも思いますか？