Conrad Wolfram: Teaching kids real math with computers

Translator: rozana reffit Reviewer: Helena Bedalli

We've got a real problem with math education right now.

Ne jemi ballafaquar me nje problem mese te vertete ne edukimin matematikor ne kohet e sotme.

Basically, no one's very happy.

Me nje fjale, asnje nuk eshte i kenaqur.

Those learning it

Ata qe mundohen te mesojne matematike

think it's disconnected,

jane te mendimit qe nuk ka lidhje fare me shkencat e tjera,

uninteresting and hard.

e pa interesueshme dhe teper e veshtire.

Those trying to employ them

Ata qe mundohen te punesojne matematicientet

think they don't know enough.

jane te mendimit qe nuk kane mjaft njohuri te vlershme ne matematike.

Governments realize that it's a big deal for our economies,

Te gjitha strukturate tona qeveritare po e nenkuptojne qe kjo eshte nje ceshtje thelbesore per ekonomine,

but don't know how to fix it.

por nuk jane ne dije se si mund te japin nje rrugezgjithje.

And teachers are also frustrated.

Mbi te gjitha, dhe profesoret jane teper te lodhur me kete problem.

Yet math is more important to the world

Akoma me teper, matematika eshte lenda me e rendesishme ne te gjithe boten

than at any point in human history.

me e rrendesishmja nga te gjitha ne historine e njerrezimit.

So at one end we've got falling interest

Keshtu pra, nga njerra ane ne jemi ballafaquar me nje interes te deshtuar

in education in math,

ne dhenjen e lendes te matematikes,

and at the other end we've got a more mathematical world,

dhe nga ana tjeter, ne jetojme ne nje kohe nga me te nderlikuarat me matematiken.

a more quantitative world than we ever have had.

ne nje kohe ne llogarine financiare qe nuk e kemi hasur asnjehere me perpara.

So what's the problem, why has this chasm opened up,

Atehere, cili eshte problemi, pse na ka lindur kjo pengese e madhe,

and what can we do to fix it?

dhe cfare mund te paraqitim, ne menyre qe ti japim nje rrugezgjithje?

Well actually, I think the answer

Mire atehere aktualisht, Une mendoj qe pergjigja

is staring us right in the face:

eshte perpara fytyres tone:

Use computers.

Le te perdorim kompjuterat.

I believe

Une jam i vendosur

that correctly using computers

qe ne qofte se ne perdorim kompjuterat korektesisht

is the silver bullet

do te jete me pa tjeter fisheku jone i argjente

for making math education work.

per ti dhene rrugezgjidhje problemit tone ne shkencen e matematikes.

So to explain that,

Atehere pra, per te shpjeguar kete,

let me first talk a bit about what math looks like in the real world

me lejoni te flas pak rreth lendes te matematikes, se si paraqitet tek ne, ne kete kohe

and what it looks like in education.

dhe ne te njejten gje se si paraqitet ne ambjentet akademike.

See, in the real world

Shikoni pra, ne kohet e sotme

math isn't necessarily done by mathematicians.

matematika nuk behet nga matematicientet.

It's done by geologists,

Ajo behet nga gjeologet,

engineers, biologists,

ingjinieret, biologet,

all sorts of different people --

dhe shume njerrez te ndryeshm-

modeling and simulation.

duke krijuar modele dhe duke paraqitur faktore te lidhur me matematiken.

It's actually very popular.

Eshte faktikisht shume e perhapur.

But in education it looks very different --

Por ne shkencat akademike duke komplet ndryshe--

dumbed-down problems, lots of calculating,

probleme te mbytura per dhenie te sakta ne pergjigje, duke perfshire shume llogaritje,

mostly by hand.

me dore.

Lots of things that seem simple

Shume gjera qe duken dhe jane te thjeshta

and not difficult like in the real world,

ne tregun e sotem financiar, nuk jane te veshtira pasi

except if you're learning it.

e kane mesuar.

And another thing about math:

Dhe nje gje tjeter rreth matematikes:

math sometimes looks like math --

matematika nganjehere duket si matematike--

like in this example here --

si ky shembulli ketu--

and sometimes it doesn't --

dhe nga njehere nuk krahasohet fare me matematiken--

like "Am I drunk?"

per shembull," A jam une i dehur?"

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

Dhe pas kesaj ju merrni nje pergjigje qe eshte llogaritare ne kohet e sotme.

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

Ju as mund te prisni nje gje te tille fite me perpara.

But now you can find out all about --

Por tani juve keni te gjitha pergjigjet rreth kesaj pyetje--

unfortunately, my weight is a little higher than that, but --

Fatkeqesisht, pesha ime eshte pak me e madhe sesa kjo,

all about what happens.

une jam me interesuar se cfare do te ndodhe pas kesaj.

So let's zoom out a bit and ask,

Atehere pra, let te fillojme te zgjerojme ceshtjen dhe te pyesim veten,

why are we teaching people math?

pse u shpjegojme njerzve matematike?

What's the point of teaching people math?

Cila eshte arsyeja qe ne u shpjegojme njerzve matematike?

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

Dhe ne vecanerisht, pse ne vashdojme tju shpegojme matematike ne pergjithesi?

Why is it such an important part of education

Pse eshte nje aspekt shume i rendesishem ne akademite shkollore

as a sort of compulsory subject?

sidomos nje lende qe ne kembengulim kaq shume?

Well, I think there are about three reasons:

E pra, une mendoj qe ne shikojme tre arsye te pergjithshme:

technical jobs

punesimet teknike

so critical to the development of our economies,

jane me patjeter kritike ne zhvillimin e ekonomise tone

what I call "everyday living" --

ate qe une e quaj, " jetesa e perditshme"--

to function in the world today,

te funksionosh ne diten e perditshme ne kohet e sotme,

you've got to be pretty quantitative,

juve duhet te jeni shume llogaritare,

much more so than a few years ago:

akoma me shume ne krahasim me disa vite me pare:

figure out your mortgages,

se pari, llogaritja e pageses te shtepise,

being skeptical of government statistics, those kinds of things --

se dyti, dyshimi i datave statistike, gjera te kesaj natyre--

and thirdly, what I would call something like

dhe se treti, te cilin une e quaj

logical mind training, logical thinking.

trajnimin e logjikes mendore, mendimin logjik.

Over the years

Nder vitet

we've put so much in society

ne i jemi nenshtruar shume gjerave ne njerezimin tone shoqeror

into being able to process and think logically. It's part of human society.

duke u perpjekur ne procedurimin dhe menduar logjikisht. Eshte pjese e njerezimit.

It's very important to learn that

Eshte shume e rendesishme te mesojme qe

math is a great way to do that.

matematika eshte nje menyre shume e mire per te zgjeruar hapesirat e mendimeve logjike.

So let's ask another question.

Keshtu pra, le te paraqitim nje pyetje tjeter.

What is math?

C'fare eshte matematika?

What do we mean when we say we're doing math,

C'fare do te thote kur ne pergjigjemi qe po bejme matematike,

or educating people to do math?

ose te edukojme njerzit te mesojne matematike?

Well, I think it's about four steps, roughly speaking,

Pra, Une mendoj qe gjenden kater hapa ne kete moment, ndersa po bisedojme,

starting with posing the right question.

le te fillojme te paraqitim nje pyetje me te sakte.

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

Cila eshte arsyeja qe ne duam te pyesim per dicka? Perse po perpiqemi kaq shume qe te zbulojme c'fare?

And this is the thing most screwed up in the outside world,

Dhe po ketu, ne kete moment, gjendet problemi kryesor shume i ngaterruar ne boten e jashtme,

beyond virtually any other part of doing math.

me thellesisht, virtualiteti i shpjegimit te matematikes.

People ask the wrong question,

Pra, njerezit bejne pyetjen e gabuar,

and surprisingly enough, they get the wrong answer,

dhe me habitese, njerezit marrin pergjigje te gabuar,

for that reason, if not for others.

per kete arsye, jo per te tjera.

So the next thing is take that problem

Atehere, ceshtja tjeter eshte marrja e problemit

and turn it from a real world problem

kthimi i saj ne nje problem real

into a math problem.

te lidhur me matematike.

That's stage two.

Kjo eshte faza e dyte.

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

Pasi ke mbaruar me kete faze, atehere vazhdon me faktoret llogaritse ne kompjuter.

Turn it from that into some answer

Po ne kete moment, juve mund te arrini te gjeni disa pergjigje

in a mathematical form.

formale matematikore.

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

Dhe sigurisht, matematike eshte shume e fuqishme ne kete gje.

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

Dhe me se fundi,le te kthehemi te bota reale.

Did it answer the question?

Ne moment, pyet veten nese gjithcka qe bere, a more pergjogje te sakta qe kane kuptim ne situaten perkatse?

And also verify it -- crucial step.

Dhe perpiqu te verifikosh keto pergjigje me faktoret e dhene-- e cila eshte nje hap shume kritik dhe i rendesishem.

Now here's the crazy thing right now.

Tani, ketu eshte nje gje absurde, po tani ne kete moment.

In math education,

Ne akademite matematikore,

we're spending about perhaps 80 percent of the time

ne kalojme afersisht 80 perqind te kohes

teaching people to do step three by hand.

duke dhene mesim, berrja e llogarise me dore, e cila eshte dhe hape i trete qe nefolem pak me pare.

Yet, that's the one step computers can do

Kompjuterat mund te bejne te njejten gje ne po kete menyre, cfare bejme ne me dore

better than any human after years of practice.

dhe kompjuterat kane mundesine te bejne te njejtat llogari, me me saktesi sesa te gjithe njerzit qe kane vite te shumta eksperience ne matematike.

Instead, we ought to be using computers

Ne vend te dores, ne duhet te perdorim kompjuterat

to do step three

per te zgjithur hapin e trete te problemit

and using the students to spend much more effort

ne kete menyre studentet e zvendesojne kete kohe

on learning how to do steps one, two and four --

per te mesuar si te bejne fazen e pare; fazen e dyte, dhe fazen e kater--

conceptualizing problems, applying them,

duke dhene koncepte problematike, duke i applikuar keto,

getting the teacher to run them through how to do that.

dhe duke e pyetur mesuesin se si mund te vene keto probleme ne aplikime me praktike.

See, crucial point here:

E pra, pike kryesore ketu:

math is not equal to calculating.

matematika nuke eshte e njejte dhe e barabarte me faktoret llogaritse.

Math is a much broader subject than calculating.

Matematika eshte nje lende me e thelle sesa mbledhje dhe shumezime apo ceshtje llogaritare.

Now it's understandable that this has all got intertwined

Tani eshte mese e kuptushme qe keshte ehste mese e bashkangjitur

over hundreds of years.

me qindra vitesh.

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

Gjendej vetem nje menyre te beje matematike dhe ajo menyre eshte berrja me dore.

But in the last few decades

Por ne disa dekadat e fundit

that has totally changed.

kjo lloj ceshtje ka ndryshur komplet.

We've had the biggest transformation of any ancient subject

Ky eshte transformimi me i madh nga te gjitha lendet e tjere te lashtesise

that I could ever imagine with computers.

imagjinata me kompjuterrat dhe cfare mund te bejme me ta.

Calculating was typically the limiting step,

Llogaria ishte tipikisht nje faze e matur,

and now often it isn't.

dhe me pas, tani asqe nuk sihet ne fjale.

So I think in terms of the fact that math

E pra, Une mendoj ne fakte me baza qe matematika

has been liberated from calculating.

ka dale si rrjedhoje e fakteve llogaritare.

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

Por, liberalizimi i matematikes nuk u shfaq menjehere ne akademite edukative.

See, I think of calculating, in a sense,

E shikoni pra, Une e paramendoj faktet llogaritse ne nje kuptim

as the machinery of math.

te makinerise matematike.

It's the chore.

Pra mund te them qe eshte nje detyre e pergjithshme.

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

Eshte nje gje e tille qe ne shumice e rrasteve do ti shmangesh, po pate mundesine, per shembull perdor nje makine llogaritse ne vend qe ti besh me dore.

It's a means to an end, not an end in itself,

Eshte nje ceshtje qe i erdhi fundi perfundimisht, jo nje ceshtje e pazgjithshme,

and automation allows us

makinat automatike na japin mundesine te bejme nje gje te tille

to have that machinery.

nepermjet perdorimit te tyre.

Computers allow us to do that --

Kompjuterat na lejojne te bejme nje gje te tille--

and this is not a small problem by any means.

dhe ky nuk eshte nje problem absolutisht i vogel.

I estimated that, just today, across the world,

Une mendova per afersisht qe sot, ne te gjithe boten,

we spent about 106 average world lifetimes

ne kalojme 106 mesatarisht kohen e jetes tone

teaching people how to calculate by hand.

duke mesuar dhe edukuar njerzit si te bejne matematike me dore.

That's an amazing amount of human endeavor.

Kjo eshte nje kohe shume e madhe dhe e perkushtueshme e njerezimit.

So we better be damn sure --

Keshtu pra ne duhet te jemi te sigurte--

and by the way, they didn't even have fun doing it, most of them --

dhe me qe ra fjala, ata nuk e kishin shume me qef te benin pune te tille, shume prej tyre--

so we better be damn sure

pra te jemi te sigurte

that we know why we're doing that

qe ne duhet te jemi ne dijeni pse po bejme nje gje te tille

and it has a real purpose.

dhe me patjeter qe ka nje qellim teper real.

I think we should be assuming computers

Une mendoj qe ne duhet te paramendojme qe kompjuterat

for doing the calculating

te cilat bejne keto llogari te tilla

and only doing hand calculations where it really makes sense to teach people that.

fakte llogaritare qe beheshin me dore, tani duhet ti shpjegohen njerzve dhe te kene kuptim qe ata mund ti perdorin ne jeten e perditshme.

And I think there are some cases.

Une mendoj qe ka disa raste.

For example: mental arithmetic.

Per shembull: aritmetika mendore.

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

akoma e perdor aritmetiken, kryesisht per raste qe dua te gje dicka perafersisht.

People say, "Is such and such true?"

Shume njerez me thone, " A eshte e vertete kjo apo ajo pergjigje?"

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

Dhe une pergjigjem, "Hmmm, nuk jam i sigurte." Duhet te mendohem nje cike me shume.

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

Eshte me shpejt dhe me praktike te japish nje pergjigje te tille.

So I think practicality is one case

Pra ne disa raste praktikisht

where it's worth teaching people by hand.

eshte me mire te mesosh disa menyra matematikore se si behen me dore.

And then there are certain conceptual things

Dhe po ashtu, ka disa raste konceptuale

that can also benefit from hand calculating,

qe behen me mire dhe me me hollesi me dore,

but I think they're relatively small in number.

por ato raste jane shume te rralla.

One thing I often ask about

Nje gje qe une pyes zakonisht

is ancient Greek and how this relates.

eshte greqishtja e lashte dhe menyra se si lidhet me te.

See, the thing we're doing right now

E pra, ajo qe po bejme ne tani eshte

is we're forcing people to learn mathematics.

shtyrja e njerezve te mesojne matematike.

It's a major subject.

Eshte nje lende kryesore.

I'm not for one minute suggesting that, if people are interested in hand calculating

Jo vetem per nje minute nuk po sugjeroj qe njerzit duhet te bejne matematike me dore me shume tani

or in following their own interests

ose ne raste qe ata kane interes te vecante

in any subject however bizarre --

megjithate, edhe pse duket e cuditshme

they should do that.

ata duhet te nenshtrohen zgjithjes te problemeve matematikore me dore, po te duan.

That's absolutely the right thing,

Eshte apsolutisht nje gje e drejte,

for people to follow their self-interest.

per ata njerez qe ndekin interesin e tyre.

I was somewhat interested in ancient Greek,

Une isha pak a shume i interesuar ne Greqishten e lashte,

but I don't think that we should force the entire population

por nuk mendoj qe ne duhet te sforcarim te gjithe popullaten

to learn a subject like ancient Greek.

te filloje te mesoje lenden e greqishtes te lashte.

I don't think it's warranted.

Asnjeher nuk mund te garantohet nje gje e tille.

So I have this distinction between what we're making people do

Pra, une kam kete lloj dallimi ne mes te dy gjerrave, ne po i sforcarim njerzit

and the subject that's sort of mainstream

ti nenshtrohen lendeve qe jane njera pas tjetres ne shkencen perkatse

and the subject that, in a sense, people might follow with their own interest

dhe nje lende, qe ne nje lloj kuptimi, njerzit mund te ndjekin per interesat e veta

and perhaps even be spiked into doing that.

dhe ndoshta mund te jene te frymezuar per te mesuar nje lende te tille.

So what are the issues people bring up with this?

Pra, cilat jane pengesat te cilat njerzit mund te gjejne gjate kesaj situate?

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

Nje nga pengesat, mesa thuhet, ne duhet te kemi parasysh bazat kryesore fillimisht.

You shouldn't use the machine

Nuk duhet te perdorim makinat llogaritse

until you get the basics of the subject.

deri sa i kemi profesionuar basat fillestare dhe themelore te lendes te matematikes.

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

Atehere pra, ketu lind pyetja perseri, cilat jane bazat themelore te matematikes?

Basics of what?

Cilat jane bazat?

Are the basics of driving a car

A jane bazat kryesore per te ngare nje makine?

learning how to service it, or design it for that matter?

apo per ti bere sherbim? apo ndertimi i ingjinierise te makines?

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

Si jane bazat e shkruajtjes se si mund te mprehesh nje maje gjilpere?

I don't think so.

Nuk e mendoj nje gje te tille.

I think you need to separate the basics of what you're trying to do

Une mendoj se ju duhet te veconi basamentet kryesore se cfare kerkoni te beni

from how it gets done

dhe se si mund te filloje te behet

and the machinery of how it gets done

dhe makinerite se si mund te vazhdosh te perfundosh nje gje te tille

and automation allows you to make that separation.

dhe keshtu pra makinat automatike ju lejon you te ndani bazat nga njera tjetra.

A hundred years ago, it's certainly true that to drive a car

Njeqind vjet me perpara, sigurisht qe ishte e vertete te ngisje makinen

you kind of needed to know a lot about the mechanics of the car

dhe duhej te dije shume gjerra nga ana mekanike para se ta ngisje

and how the ignition timing worked and all sorts of things.

si punonte barometri dhe shume gjera te tjera.

But automation in cars

Por tani, makinat automatike

allowed that to separate,

bejne te mundur nje gje te tille qe nuk eshte nevoja te dish shume hollesira,

so driving is now a quite separate subject, so to speak,

pra, ngarrja e makines eshte jashtezakonisht nje ceshtje e ndryshme, me qe ra fjala,

from engineering of the car

nga ingjinieria e makines

or learning how to service it.

deri nga te mesuarit se si mund ti sherbesh makines per jete me te gjate.

So automation allows this separation

E pra, fakti qe eshte automatike na lejon kete vecori

and also allows -- in the case of driving,

dhe mbi te gjitha na ndihmon ne grajen e makines,

and I believe also in the future case of maths --

dhe jam mese i sigurte qe ne te ardhmen, ne disa raste te matematikes--

a democratized way of doing that.

me patjeter qe do te gjendet nje lloj me demokratik per te zgjithur raste me te ndryshme te ngarjes te makines.

It can be spread across a much larger number of people

Ajo menyre mund te perhapet nepermjet shume njerzve

who can really work with that.

te cilet mund te punojne me nje menyre te tille.

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

Atehere pra, ketu na lind dhe nje gje tjeter bashke me bazat kryesore.

People confuse, in my view,

Nga pikpamja ime, ketu njerzit ngaterrohen,

the order of the invention of the tools

me ceshtjet e zbulimeve te veglave

with the order in which they should use them for teaching.

dhe rradha ne te cilat ata duhet ti perdorin per qellime akademike.

So just because paper was invented before computers,

Keshtu pra, edhe pse letra ishte zbuluar me perpara se kompjuteri,

it doesn't necessarily mean you get more to the basics of the subject

nuk do te thote qe ju jeni me te perkushtuar

by using paper instead of a computer

ne perdorimin e letres sesa ne perdorimin e kompjuterit

to teach mathematics.

per te shpjeguar lenden e matematikes.

My daughter gave me a rather nice anecdote on this.

Vajza ime me tregoi nje anektode ne kete rast te tille.

She enjoys making what she calls "paper laptops."

Ajo ka shume kenaqesi te madhe kurr merret me ndertimin e te cilave ajo i quan "kompjuter portative prej letre".

(Laughter)

(te qeshura)

So I asked her one day, "You know, when I was your age,

Nje dite une e pyeta, " Degjo, kur une isha mosha jote,

I didn't make these.

une nuk dija te beja nje gje te tille.

Why do you think that was?"

Si thua ti, pse nuk mundesha?"

And after a second or two, carefully reflecting,

Dhe pas ndertimit te te parit dhe te te dytit, me shume kujdes duke reflektuar,

she said, "No paper?"

ajo u pergjigj, " Nuk kishte leter?"

(Laughter)

(te qeshura)

If you were born after computers and paper,

Ne qoftese do te ishe lindur pas zbulimit te kompjuterave dhe letres,

it doesn't really matter which order you're taught with them in,

nuk ka rendesi se ne c'fare rradhe ikeni mesuar,

you just want to have the best tool.

ju deshironi te keni veglat e punimit me te mira.

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

Keshtu pra, dhe nje gje tjeter qe lind eshte, " Kompjuterat e hedhin poshte fare matematiken."

That somehow, if you use a computer,

Ne nje fare menyre, ne qofte se ju perdorni nje kompjuter,

it's all mindless button-pushing,

eshte apsolutisht vetem shtypje butonash,

but if you do it by hand,

per ne qofte se ti zgjedh menyren per te berre matematike me dore (ne mend),

it's all intellectual.

eshte me patjeter teper intelektuale.

This one kind of annoys me, I must say.

Por duhet te dhem qe kjo looj menyre eshte teper e bezdishme.

Do we really believe

A jemi ne te vendosur qe

that the math that most people are doing in school

matematika qe po bejne njerzit tone ne shkolle

practically today

sot

is more than applying procedures

eshte praktikisht me shume sesa aplikimi i nje procedure

to problems they don't really understand, for reasons they don't get?

te problemeve te cilat ata nuke e kane idene fare, per arsy the fakte qe ata nuk mund te jene ne dijeni?

I don't think so.

Nuk e besoj.

And what's worse, what they're learning there isn't even practically useful anymore.

Dhe akoma me keq, ato qe ata po mesojne nuk jane me praktikisht te nevojshme ne kohen e sotme.

Might have been 50 years ago, but it isn't anymore.

Mund te kene qene te nevojshme 50 vjet me perpara, por jo me tani.

When they're out of education, they do it on a computer.

Kur ata nuk merren me me shkencat akademike, ata do te perdorin kompjuterat per cfare do lloj gjeje.

Just to be clear, I think computers can really help with this problem,

Per te qene me i qarte, Une mendoj qe kompjuterat mund te na ndihmojne shume me kete problem,

actually make it more conceptual.

e paraqitin me konceptuale.

Now, of course, like any great tool,

Tani, sigurisht, ashtu si te gjitha veglat e tjera,

they can be used completely mindlessly,

kompjuterat mund te perdoren pa u menduar,

like turning everything into a multimedia show,

tamam sikur shikon nje shfaqje ne television,

like the example I was shown of solving an equation by hand,

ashtu si shembulli qe ju tregova kur po zgjithnim ekuacionet me dore,

where the computer was the teacher --

kompjuteri po zvendesonte mesuesin--

show the student how to manipulate and solve it by hand.

gjithashtu, dhe mund te shpjegonte studenteve se si mund te manipulonin dhe gjenin zgjidhjen e problemeve dhe me dore.

This is just nuts.

Kjo eshte jashte mase e pa mendushme.

Why are we using computers to show a student how to solve a problem by hand

Pse ne jemi ne kete situate qe po perdorim kompjuterat ne menyre qe tju shpjegojme studenteve se si mund te zgjithin problemat me dore?

that the computer should be doing anyway?

mbi te gjitha pse te mos e lejojme kompjuterin te zvendesoje zgjithjen e problemeve me dore?

All backwards.

Te gjitha mbrapsh.

Let me show you

Le te shikojme

that you can also make problems harder to calculate.

se si mund te bejme nje problem akoma me te veshtire per te zgjidhur.

See, normally in school,

E pra, normalisht ne shkolle,

you do things like solve quadratic equations.

ne zgjidhim per shembull ekuacione te shkalles te dyte, me rrenje katrore.

But you see, when you're using a computer,

Por, ne kemi mundesi te shikojme te njejten menyre zgjedhje, duke perdor nje kompjuter,

you can just substitute.

duke bere zvendesime.

You can make it a quartic equation. Make it kind of harder, calculating-wise.

Ne mund ta bejme ekuacion te shkalles te kater. E pra duke e veshtirresuar me shume per ti dhene zgjidhje.

Same principles applied --

Disa Teori te cilat jane vene ne aplikim--

calculations, harder.

llogaritje matematikore me te veshtira.

And problems in the real world

Dhe disa probleme ne jeten e perditshme praktikore

look nutty and horrible like this.

duken sikur jane jashte normave reale.

They've got hair all over them.

Kane pengesa te medha ne cdo drejtim

They're not just simple, dumbed-down things that we see in school math.

Ato nuk jane dhjesht problema elementare, problema matematike qe ne hasim gjate shkolles ne lenden e matematikes.

And think of the outside world.

Aq me teper po te mendosh dhe jashte normave, te jetes te perditshme.

Do we really believe that engineering and biology

A jemi te sigurte qe ingjinieria dhe bilogjia

and all of these other things

dhe te gjitha lendet e tjera

that have so benefited from computers and maths

te cilat kane perfituar nga perdorimi i kompjuterave dhe matematika

have somehow conceptually gotten reduced by using computers?

jane pak a shume konceptualisht zvogeluar nga perdorimi i shumte i kompjuterave?

I don't think so -- quite the opposite.

Nuk besoj-- me tej, eshte komplet e kunderta.

So the problem we've really got in math education

Pra, problemi qe ne hasim tani ne shkencat akademike te matematikes

is not that computers might dumb it down,

nuk mendoj qe perdorimi i kompjuterave ndikon ne zvogelimin apo zvendesimin e lendes

but that we have dumbed-down problems right now.

por me konkretisht eshte nje problem qe ne hasim tani per tani

Well, another issue people bring up

Gjithashtu, nje tjeter pengese qe njerzit po hasin

is somehow that hand calculating procedures

eshte pak a shume procedura(metoda) e hapave te llogaritjes me dore

teach understanding.

dhe shpjegimi i tyre per ti bere me te kuptushme.

So if you go through lots of examples,

Atehere pra, n.q.s. merresh me zgjidhjen e shume shembujve,

you can get the answer,

ju arrini perfundimisht ne nje pergjigje te sakte,

you can understand how the basics of the system work better.

gjithashtu, ju mund te kuptoni dhe pervetesoni dhe bazat e menyrave matematike.

I think there is one thing that I think very valid here,

Une besoj qe nje gje eshte mese e vertete ketu,

which is that I think understanding procedures and processes is important.

kuptimi i procesit dhe procedurave te matematikes eshte jashtezakonisht e rendesishme.

But there's a fantastic way to do that in the modern world.

Por, nje menyre fantastike gjendet per te zgjithur kete problem ne kohen e modernizimit te sotem.

It's called programming.

Kjo lloj menyre quhet dega e programimit.

Programming is how most procedures and processes

Programimi eshte perkatesisht i specializuar per te gjitha keto procese dhe procedura

get written down these days,

te cilat jane zhvilluar mjaft ne ditet e sotme,

and it's also a great way

gjithashtu eshte dhe nje menyre maft e mire

to engage students much more

te interesosh studentet akoma me teper

and to check they really understand.

ne kete menure, te jepet mundesia dhe te kontrollsh cdhe nivelin e kuptimit(nese e kuptuan te gjithe apo jo)

If you really want to check you understand math

N.q.s. deshiron me patjeter te kontrollosh nese te gjithe e kuptuan

then write a program to do it.

matematiken(temen pe te cilen flet), atehere zhvillo nje aplikim programimi qe te beje punen per ty(kontrolloje nivelin e kuptimit te nivelit te matematikes)

So programming is the way I think we should be doing that.

Pra, programimi eshte nje nga menyrat me perkatse per ne ne kete ceshtje

So to be clear, what I really am suggesting here

Qartesisht, Ate qe dua te sugjeroj ketu

is we have a unique opportunity

eshte nje krijim mundesi teper e vecante

to make maths both more practical

per te bere matematiken me terheqse dhe praktike

and more conceptual, simultaneously.

dhe praktikisht, me konceptuale,

I can't think of any other subject where that's recently been possible.

Nuk e mendoj qe kjo mund te jete e mundur ne ndonje lende tjeter

It's usually some kind of choice

Zakonisht eshte me teper rrugezgjithja jote

between the vocational and the intellectual.

ndermjet menyres intelektuale dhe teknike.

But I think we can do both at the same time here.

Por ne kemi mundesi te bejme te dyja teknikat.

And we open up so many more possibilities.

Ne kete menyre ne hapim mundesi me te shumta.

You can do so many more problems.

Mundesira per te zgjithur probleme te tjera.

What I really think we gain from this

Dhe dicka tjeter qe une besoj, eshte perfitimi

is students getting intuition and experience

qe studentet fitojne prirje dhe pervoje

in far greater quantities than they've ever got before.

me teper sesa kishin.

And experience of harder problems --

Dhe po qe se pate pervoje me probleme me te veshtira--

being able to play with the math, interact with it,

bashkepunimi nepermjet lendes te matematikes,

feel it.

drejt per drejt.

We want people who can feel the math instinctively.

ne duam qe njerzit te ndiejne matematiken dhe duan lenden naturalisht, pa sforcarie.

That's what computers allow us to do.

Dhe nje gje te tille na lejojne kompjuterat.

Another thing it allows us to do is reorder the curriculum.

Dicka tjeter qe ne jemi te mundur te bejme eshte ristrukturimi i lendeve te pergjithshme matematikore.

Traditionally it's been by how difficult it is to calculate,

Zakonisht, ka qene e matur se sa e veshtire eshte te besh llogari matematikore,

but now we can reorder it

por tani ne mund to perseritim ato

by how difficult it is to understand the concepts,

nepermejt nivelit te konceptiti dhe shkalles te veshtiresise,

however hard the calculating.

dhe perllogaritjes.

So calculus has traditionally been taught very late.

Keto lende zakonisht jane dhene ne vitet e mevonshme shkollore.

Why is this?

Pse keshtu?

Well, it's damn hard doing the calculations, that's the problem.

Sepse eshte apsolutisht e veshtire te merresh me faktore dhe llogaritje financiare ne moshe te vogel.

But actually many of the concepts

Por, aktualisht shumica e koncepteve

are amenable to a much younger age group.

jane me terheqese nga grupe moshatare me te vogla.

This was an example I built for my daughter.

Ky vlen dhe si shembull per vajzen time.

And very, very simple.

i cila eshte shume e thjesht.

We were talking about what happens

Ne po bisedojme se cfare do te ndodhe

when you increase the number of sides of a polygon

kur numri i poligoneve shtohet

to a very large number.

dhe nenkuptimi i numrave ne shkalle masive.

And of course, it turns into a circle.

Dhe sigurisht, qe po kjo lloj menyre kthehet perseri.

And by the way, she was also very insistent

Dhe me qe ra fjala, vajsa ime ishte shume kembengulse

on being able to change the color,

dhe arriti te ndryshonte dhe ngjyren e poligonit,

an important feature for this demonstration.

nje cilesi teper e rendesishme per kete lloj shembulli qe ne po flasim tani.

You can see that this is a very early step

E pra, ju e shikoni qe ky eshte nje hap mjaft fillestar

into limits and differential calculus

dhe duke hyre ne limitet dhe ekuacionet diferenciale

and what happens when you take things to an extreme --

dhe c'fare ndodh kur ne i marrim gjerrat me lart--

and very small sides and a very large number of sides.

duke i zmadhuar dhe zvogeluar pjeset e poligonit ashtu si te deshirosh

Very simple example.

Shume shembull i thjeshte, pra.

That's a view of the world

Keshtu eshte dhe pikpamja e vendeve te tjerra

that we don't usually give people for many, many years after this.

qe ne nuk ju afrojme keto gjerra njerzve per shume vite.

And yet, that's a really important practical view of the world.

Akoma me teper, kjo eshte nje pikpamje praktike dhe e rendesishme per te gjithe boten.

So one of the roadblocks we have

Nje nga urrat ndertuese qe ne kemi

in moving this agenda forward

per te vazhduar me tej me kete agjende

is exams.

eshte dhenia e provimeve.

In the end, if we test everyone by hand in exams,

Me ne fund, n.q.s ne u japim te behen provime me dore per te gjithe,

it's kind of hard to get the curricula changed

na krijon veshtiresi ne ndryshimin e lendeve te tjera te pergjithshme

to a point where they can use computers

ne nje shkalle ne te cilen ne mund te veme ne perdorim kompjuterat

during the semesters.

gjate kohes te simestrave shkollore.

And one of the reasons it's so important --

Dhe nje nga arsyet qe eshte kaq e rrendesishme--

so it's very important to get computers in exams.

eshte veshtiresia e provimeve te vihen ne programe kompjutersha.

And then we can ask questions, real questions,

Me pas ne na jepet mundesi te bejme pyetje me te shumta,

questions like, what's the best life insurance policy to get? --

si per shembull, cila eshte inshuranca me ekonomike dhe me e pershtatshme per mua?--

real questions that people have in their everyday lives.

pyetje me te nevojshme te cilet njerzit perdorin ne jeten e perditshme.

And you see, this isn't some dumbed-down model here.

E pra, e shikoni qe ky model nuk eshte fare i pavlefshem.

This is an actual model where we can be asked to optimize what happens.

Ky eshte nje model ku ne mund te bejme pyetje se c'fare mund te ndodhe gjate optimizimit.

How many years of protection do I need?

Per sa vjet mbrojtje kemi nevoje?

What does that do to the payments

Si ndikon kjo ne pagesat

and to the interest rates and so forth?

interesat e perqindjeve dhe me rradhe?

Now I'm not for one minute suggesting it's the only kind of question

Mos me keqkuptoni qe ne asnje menyre, une nuk sugjeroj qe kjo eshte e vetmja rruge

that should be asked in exams,

qe ne duhet te ndjekim per te dhene provime,

but I think it's a very important type

por mendoj qe eshte shume e rrendesishme

that right now just gets completely ignored

qe ne mos harrojme dhe kete ceshtje

and is critical for people's real understanding.

sepse eshte teper kritike per nenkuptimin e njerzve ne jeten e perditshme.

So I believe [there is] critical reform

Jam plot i bindur qe gjendet nje reforme kritike

we have to do in computer-based math.

qe ne duhet te bejme me patjeter matematike qe eshte ne mardhenie me programet kompjuterike

We have got to make sure

Ne duhet te jemi mese te sigurte

that we can move our economies forward,

qe ne duhet te zhvillojme dhe te ecim perpara me ekonomine,

and also our societies,

dhe me zhvillimin e njerezimit,

based on the idea that people can really feel mathematics.

nepermjet idese qe njerzit e duan dhe jane te frymezuar per te mesuar matematike.

This isn't some optional extra.

Kjo nuk eshte nje rruge e humbur.

And the country that does this first

Dhe vendi qe ka fillaur se pari me kete

will, in my view, leapfrog others

do te ece me shume nga te tjeret, me sa besoj une,

in achieving a new economy even,

duke avantazhuar dhe ne zhvillimin e nje ekonomie te re,

an improved economy,

nje ekonomi me te permiresuar,

an improved outlook.

me pikpamje me te qarta.

In fact, I even talk about us moving

Faktikisht, une mendoj

from what we often call now the "knowledge economy"

dhe qe ne e quajme tani " Njohuria ekonomike"

to what we might call a "computational knowledge economy,"

ne iden qe une gjithashtu mund ta quaj " Njohurite Ekonomike nepermjet Kompjuterit,"

where high-level math is integral to what everyone does

e cila matematika e nje shkalle te larte eshte integrale me ate qe secili nga ne

in the way that knowledge currently is.

gjenden ne njohurine e sotme.

We can engage so many more students with this,

Ne mund te jemi ne gjendje te angazhojme shume studente

and they can have a better time doing it.

me kete lloj njohurie dhe jam mese i bindur qe ata do te kene kenaqesi me te madhe ne krahasim me mendimin qe eshte matematike dhe eshte e merzitshme.

And let's understand:

Dhe ndersa ne e kuptojme:

this is not an incremental sort of change.

kjo nuk eshte nje lloj zvogelues i ketij ndryshimi qe ne po flasim.

We're trying to cross the chasm here

Ne po perpiqemi te kalojme kete pengese

between school math and the real-world math.

midis matematikes akademike dhe matematikes ne jeten e perditshme praktike.

And you know if you walk across a chasm,

Dhe ju e dini me teper qe n.q.s. ju hidhni hapin ne nje pengese te tille,

you end up making it worse than if you didn't start at all --

ju do te perfundoni ne nje situate me te veshtire ne krahasim me fillimin,

bigger disaster.

veshtiresi me e madhe.

No, what I'm suggesting

No, c'fare une jam duke sugjeruar

is that we should leap off,

eshte kaperzimi i kesaj veshtiresie,

we should increase our velocity

ne duhet te shtojme shpejtesine e ketij ndryshimi ne ceshtjen e matematikes akademike

so it's high,

neduhet te pershpejtojme, qe shpejtesie e ndryshimit te jete e madhe,

and we should leap off one side and go the other --

dhe ne duhet te kaperzejme nje ane dhe duhet te hidhemi ne anene tjeter--

of course, having calculated our differential equation very carefully.

sigurisht, duke parallogaritur ekuacionin diferencial me shume kujdes.

(Laughter)

(spektatoret qeshin)

So I want to see

Atehere, Une dua te shikoj

a completely renewed, changed math curriculum

kethimin e lendeve te matematikes qe jane te ndryshuar, komplet te reja mbi ato basa qe ne permendem pak me pare

built from the ground up,

duke filluar ndryshimet qe nga basat me elementare,

based on computers being there,

nepermejt perdorimit te kompjuterave,

computers that are now ubiquitous almost.

kompjuterate te cilet pothuajse gjenden ne cdo lloj ambienti.

Calculating machines are everywhere

makinat llogaritse gjenden kudo

and will be completely everywhere in a small number of years.

dhe keto makina llogaritse do te jene kudo dhe per disa vite te tjera

Now I'm not even sure if we should brand the subject as math,

Tani, une nuk jame i bindur nese ne duhet te cilesojme kete ceshtje si matematike,

but what I am sure is

por, per c'fare jam i bindur

it's the mainstream subject of the future.

eshte shtrirja e kesaj ceshtje ne te ardhmen.

Let's go for it,

Le te fillojme,

and while we're about it,

dhe ne te njejten kohe,

let's have a bit of fun,

ne duhet te ndjejme kenaqesine,

for us, for the students and for TED here.

midis nesh, midis studenteve qe merren me matematike, dhe per kete komunitet ketu ne TED.

Thanks.

Faleminderit.

(Applause)

(Duartrokitje)