So, this is my grandfather,

薩爾曼‧蕭肯

Salman Schocken,

他出生時家裡很窮 父母都沒上過學

who was born into a poor and uneducated family

還要養六個小孩

with six children to feed,

14歲的時候

and when he was 14 years old, he was forced to

他被迫輟學,幫忙賺錢養家

drop out of school in order to help put bread on the table.

後來都沒有回過學校

He never went back to school.

但他的事業成就輝煌

Instead, he went on to build a glittering empire

建立了百貨帝國

of department stores.

我爺爺凡事要求盡善盡美

Salman was the consummate perfectionist,

他開的每家百貨公司

and every one of his stores was a jewel

都堪稱包浩斯風格建築的極品

of Bauhaus architecture.

他熱中自學到了極點

He was also the ultimate self-learner,

和其他事情一樣 他自學得有聲有色

and like everything else, he did it in grand style.

他的身邊總圍繞著一群

He surrounded himself with an entourage

當時年輕,默默無聞的學者

of young, unknown scholars like Martin Buber

像布伯,阿格農,卡夫卡等

and Shai Agnon and Franz Kafka,

爺爺每個月付他們薪水

and he paid each one of them a monthly salary

讓他們能安心寫作

so that they could write in peace.

但30年代末,納粹迫害猶太人 爺爺知道大禍要臨頭了

And yet, in the late '30s, Salman saw what's coming.

他帶著家人逃出德國

He fled Germany, together with his family,

沒有帶走任何財產

leaving everything else behind.

他的百貨公司被沒收

His department stores confiscated,

從此以後,他窮畢生之力

he spent the rest of his life in a relentless pursuit

追求文化與藝術

of art and culture.

中學沒念完的爺爺

This high school dropout

享壽82歲

died at the age of 82,

他是傑出的知識份子 創辦耶路撒冷希伯來大學

a formidable intellectual, cofounder and first CEO

並擔任第一屆董事長

of the Hebrew University of Jerusalem,

他還創立蕭肯出版社 (Schocken Books)

and founder of Schocken Books,

當時廣受好評

an acclaimed imprint that was later acquired

後來被藍燈書屋 (Random House) 買下

by Random House.

這就是自學的力量

Such is the power of self-study.

這是我的父母

And these are my parents.

他們沒有接受大學教育

They too did not enjoy the privilege of college education.

因為他們忙著成家 忙著建立以色列

They were too busy building a family and a country.

但就像我爺爺,他們終其一生

And yet, just like Salman, they were lifelong,

都自學不輟,我的家裡

tenacious self-learners, and our home was stacked

堆了上千本書,唱片,藝術品

with thousands of books, records and artwork.

我清楚記得父親說過

I remember quite vividly my father telling me

等左鄰右舍都買電視機了

that when everyone in the neighborhood will have a TV set,

我們再去買收音機吧

then we'll buy a normal F.M. radio. (Laughter)

這是我

And that's me,

我拿的是我的第一個算盤

I was going to say holding my first abacus,

但我父親會說

but actually holding what my father would consider

我拿著山寨版的 iPad

an ample substitute to an iPad. (Laughter)

我在家裡學到了一件事

So one thing that I took from home is this notion

就是教育家不見得要教書

that educators don't necessarily have to teach.

而是給你環境和資源

Instead, they can provide an environment and resources

激發你自學的本能

that tease out your natural ability to learn on your own.

自主學習,自我探索 做自己的主人

Self-study, self-exploration, self-empowerment:

都是良好教育下養成的美德

these are the virtues of a great education.

我現在要和大家分享一個故事

So I'd like to share with you a story about a self-study,

關於一門注重自主學習 的電腦課程

self-empowering computer science course

是我和我的好同事 諾姆‧尼森共同創立的

that I built, together with my brilliant colleague Noam Nisan.

照片裡是我和諾姆

As you can see from the pictures, both Noam and I

我們小時候都很迷 基本的科學原理

had an early fascination with first principles,

多年以後,我們的知識更豐富了

and over the years, as our knowledge of

科學和科技的素養愈來愈高

science and technology became more sophisticated,

從小對基本原理的崇敬之情

this early awe with the basics

只有愈變愈強烈

has only intensified.

所以毫無意外,12 年前

So it's not surprising that, about 12 years ago, when

我和諾姆都當上教授 在教計算機科學了

Noam and I were already computer science professors,

我們卻覺得沮喪

we were equally frustrated by the same phenomenon.

因為電腦愈做愈精密

As computers became increasingly more complex,

我們的學生卻見樹不見林

our students were losing the forest for the trees,

事實上,如果想了解

and indeed, it is impossible to connect

計算機科學的精髓

with the soul of the machine if you interact

你不能只會操作電腦裡

with a black box P.C. or a Mac which is shrouded

各式各樣的專利授權軟體

by numerous layers of closed, proprietary software.

我和諾姆體認到 如果我們希望學生

So Noam and I had this insight that if we want our students

了解電腦如何運作

to understand how computers work,

而且是徹底了解

and understand it in the marrow of their bones,

也許最好的辦法

then perhaps the best way to go about it

就是讓學生完成一臺

is to have them build a complete, working,

功能齊全,堪用且好用的電腦

general-purpose, useful computer, hardware and software,

而且要從最基本的 原理開始學習

from the ground up, from first principles.

於是我們開始著手進行 我和諾姆認為

Now, we had to start somewhere, and so Noam and I

要蓋萬丈高樓

decided to base our cathedral, so to speak,

就要從平地開始

on the simplest possible building block,

我們從基本的 NAND 邏輯運算開始

which is something called NAND.

NAND 是最普通的一種邏輯閘

It is nothing more than a trivial logic gate

有四組輸入輸出的數據

with four input-output states.

我們一開始這麼告訴學生

So we now start this journey by telling our students

上帝給我們 NAND

that God gave us NAND — (Laughter) —

要我們組一台電腦

and told us to build a computer, and when we asked how,

怎麼做呢? 上帝說,"一次一個步驟就好"

God said, "One step at a time."

於是乎,我們就開始了

And then, following this advice, we start

從低階,普通的NAND邏輯閘起手

with this lowly, humble NAND gate,

我們以精心設計的 學習進度帶領學生

and we walk our students through an elaborate sequence

他們先做出了晶片組

of projects in which they gradually build a chip set,

到硬體平台,組合語言,虛擬機器

a hardware platform, an assembler, a virtual machine,

再到基本款的作業系統 和編譯程序

a basic operating system and a compiler

最後完成了一種類似 JAVA 的程式語言,我們稱之為 "JACK"

for a simple, Java-like language that we call "JACK."

我們學生慶祝這項成果的方式

The students celebrate the end of this tour de force

是利用 JACK 寫了很多有趣的遊戲

by using JACK to write all sorts of cool games

如彈珠台,貪食蛇,俄羅斯方塊等

like Pong, Snake and Tetris.

各位應該能想像他們有多高興

You can imagine the tremendous joy of playing

因為他們玩的俄羅斯方塊 是用 JACK 語言編寫

with a Tetris game that you wrote in JACK

再使用自己寫的編譯程序 轉為機器語言

and then compiled into machine language in a compiler

接著看轉譯出來的結果

that you wrote also, and then seeing the result

用來跑程式的機器還是 自己做出來的

running on a machine that you built starting

是由幾千組 NAND 邏輯閘 累積起來的

with nothing more than a few thousand NAND gates.

這種成就感非同小可

It's a tremendous personal triumph of going

因為他們從基本原理開始 最後做出了非常精密

from first principles all the way to a fantastically complex

而且可以用的機器

and useful system.

我和諾姆用了五年時間

Noam and I worked five years to facilitate

簡化課程,製作教材和設備

this ascent and to create the tools and infrastructure

讓學生用一學期 就可以組一台電腦

that will enable students to build it in one semester.

這是我們偉大的團隊 幫助我們做到了

And this is the great team that helped us make it happen.

作法是解構電腦

The trick was to decompose the computer's construction

分出許多獨立單元

into numerous stand-alone modules,

各單元都可以分別開課

each of which could be individually specified,

分別完成組裝與測試

built and unit-tested in isolation from the rest of the project.

一開始我和諾姆就決定

And from day one, Noam and I decided to put

基本課程都免費

all these building blocks freely available in open source

上網就看得到

on the Web.

所以晶片規格 應用程式介面 (API), 專案說明

So chip specifications, APIs, project descriptions,

軟體工具,硬體模擬器 模擬 CPU

software tools, hardware simulators, CPU emulators,

很多的幻燈片,演講等等

stacks of hundreds of slides, lectures --

我們都放上網路

we laid out everything on the Web

歡迎大家來瀏覽

and invited the world to come over,

找他們需要的資源

take whatever they need,

並自行運用

and do whatever they want with it.

後來神奇的事情發生了

And then something fascinating happened.

大家都來了

The world came.

沒過多久,許多人

And in short order, thousands of people

都照我們的課程組電腦

were building our machine.

"從 NAND 到俄羅斯方塊"

And NAND2Tetris became one of the first

更是史上第一門 線上開放式課程

massive, open, online courses,

儘管 7 年前我們還不知道

although seven years ago we had no idea that what

線上開放式課程的概念

we were doing is called MOOCs.

我們發現自修課程

We just observed how self-organized courses

好像愈來愈多了

were kind of spontaneously spawning

很多都用我們的教材

out of our materials.

例如這位普勒蒙德先生

For example, Pramode C.E.,

是印度喀拉拉邦的工程師

an engineer from Kerala, India,

他帶領一群人自學

has organized groups of self-learners

用我們的教材組裝電腦 他教得很好

who build our computer under his good guidance.

這位帕爾克 · 沙阿先生 是孟買的工程師

And Parag Shah, another engineer, from Mumbai,

他把我們的課程分得更細

has unbundled our projects into smaller,

也更好教,並把課程

more manageable bites that he now serves

用於他首創的 "電腦DIY" 課程

in his pioneering do-it-yourself computer science program.

這些被我們課程吸引的人

The people who are attracted to these courses

通常有一顆愛電腦的心

typically have a hacker mentality.

他們想知道電腦如何運作

They want to figure out how things work,

他們想一起研究

and they want to do it in groups,

這個電腦迷俱樂部 在華盛頓特區

like this hackers club in Washington, D.C.,

就使用我們的教材開課

that uses our materials to offer community courses.

我們的教材容易取得

And because these materials are widely available

大家都可以用 所以不同的人運用

and open-source, different people take them

就會有非常不同 出乎意料的結果

to very different and unpredictable directions.

例如這位中國廣州的 余芳明 (音譯) 先生

For example, Yu Fangmin, from Guangzhou,

使用現場可程式邏輯閘陣列 ( FPGA) 技術

has used FPGA technology

組裝我們教材中的電腦

to build our computer and show others how to do the same

並透過視訊短片教給其他人

using a video clip, and Ben Craddock developed

這位班‧克萊杜克先生 設計了一個很棒的遊戲

a very nice computer game that unfolds

可以在我們的電腦裡玩

inside our CPU architecture, which is quite a complex

班設計的是一個 很複雜的 3D 迷宮

3D maze that Ben developed

他使用"當個創世神" (Minecraft) 搭載的 3D 模擬引擎

using the Minecraft 3D simulator engine.

Minecraft 玩家為之瘋狂

The Minecraft community went bananas over this project,

班也一夕之間爆紅

and Ben became an instant media celebrity.

事實上,對不少人來說

And indeed, for quite a few people,

這趟 "從 NAND 到俄羅斯方塊" 之旅

taking this NAND2Tetris pilgrimage, if you will,

改變了他們的一生

has turned into a life-changing experience.

例如這位丹‧朗茲先生

For example, take Dan Rounds, who is a music

他在密西根東蘭辛大學 主修音樂和數學

and math major from East Lansing, Michigan.

幾個星期前,丹發表一篇文章

A few weeks ago, Dan posted a victorious post

在我們的網站上 我想念給你們聽聽

on our website, and I'd like to read it to you.

丹是這麼說的

So here's what Dan said.

"我來這裡學電腦, 因為懂電腦很重要"

"I did the coursework because understanding computers

"跟識字和算術一樣"

is important to me, just like literacy and numeracy,

"而我完成了課程, 我從來沒這麼認真過"

and I made it through. I never worked harder on anything,

"從來沒碰過這麼大的挑戰"

never been challenged to this degree.

"但看看我學到了什麼東西"

But given what I now feel capable of doing,

"這個課程上再多次都值得"

I would certainly do it again.

"各位還在考慮的朋友"

To anyone considering NAND2Tetris,

"這趟路很難走, 但走完你會脫胎換骨"

it's a tough journey, but you'll be profoundly changed."

丹代表了許多自學的人

So Dan demonstrates the many self-learners

他們被我們的課程吸引

who take this course off the Web, on their own traction,

他們主動學習 而且有件事相當驚人

on their own initiative, and it's quite amazing because

這些人根本不計較

these people cannot care less about

成績的事

grades.

他們這樣做只有一個動機

They are doing it because of one motivation only.

他們有極大的學習熱情

They have a tremendous passion to learn.

講到這點

And with that in mind,

我想提一下傳統的大學評分制度

I'd like to say a few words about traditional college grading.

我很討厭

I'm sick of it.

我們都太迷信分數

We are obsessed with grades

對數據資料深信不疑

because we are obsessed with data,

但光靠分數就 決定了是否及格

and yet grading takes away all the fun from failing,

受教育最重要的事

and a huge part of education

就是不要被當掉

is about failing.

邱吉爾說,所謂勇氣

Courage, according to Churchill,

是能夠一而再,再而三失敗

is the ability to go from one defeat to another

還不喪失熱情

without losing enthusiasm. (Laughter)

(喬艾斯說) 錯誤就是

And [Joyce] said that mistakes

通往發現之門

are the portals of discovery.

但我們不能容忍錯誤

And yet we don't tolerate mistakes,

我們只著重分數

and we worship grades.

所以我們把學生的成績加總

So we collect your B pluses and your A minuses

算出總分,再劃分等第

and we aggregate them into a number like 3.4,

好像在額頭上蓋章一樣

which is stamped on your forehead

這就是你的程度

and sums up who you are.

在我看來,這種亂象非常嚴重

Well, in my opinion, we went too far with this nonsense,

打分數讓教育制度更退步

and grading became degrading.

既然說到退步 我就講講如何進步

So with that, I'd like to say a few words about upgrading,

我要和各位分享 我最近的一項計畫

and share with you a glimpse from my current project,

不是剛剛講的電腦課

which is different from the previous one,

但有完全一樣的特色

but it shares exactly the same characteristics

就是自學,做中學

of self-learning, learning by doing,

自我探索和團體學習

self-exploration and community-building,

這個計畫涵蓋 幼稚園到中學的數學教育

and this project deals with K-12 math education,

從幼稚園數學開始

beginning with early age math,

而且用平板電腦來教 因為我們認為

and we do it on tablets because we believe that

學數學也應該動手做

math, like anything else, should be taught hands on.

我們是這麼做的 基本上,我們開發了

So here's what we do. Basically, we developed

很多應用程式 每個都解釋

numerous mobile apps, every one of them explaining

一個特定的數學概念

a particular concept in math.

以面積的概念為例

So for example, let's take area.

處理面積問題的時候

When you deal with a concept like area --

程式裡提供一套工具

well, we also provide a set of tools that the child

讓孩子操作,並從中學習

is invited to experiment with in order to learn.

如果要計算面積

So if area is what interests us, then one thing

最直接的方法是填滿法

which is natural to do is to tile the area

用這種特定形狀的磁磚來填

of this particular shape and simply count

再數數要用多少磁磚 才能填滿

how many tiles it takes to cover it completely.

這樣的小活動可以幫孩子

And this little exercise here gives you a first

建立初步的面積概念

good insight of the notion of area.

那平行四邊形的面積呢?

Moving along, what about the area of this figure?

用填滿法的話算不出來,對吧?

Well, if you try to tile it, it doesn't work too well, does it.

所以可以試試看

So instead, you can experiment

這裡其他的工具

with these different tools here by some process

經過幾次嘗試和錯誤

of guided trial and error,

也許某一次就會發現

and at some point you will discover that one thing

好幾種方法當中

that you can do among several legitimate transformations

這一種可以用 用美工刀切

is the following one. You can cut the figure,

重新排列圖形,再黏起來

you can rearrange the parts, you can glue them

然後就是剛才的填滿法了

and then proceed to tile just like we did before.

(掌聲)

(Applause)

這個變換形狀的方法

Now this particular transformation

沒有改變原圖的面積

did not change the area of the original figure,