TEDxNYED
Dan Meyer: Math class needs a makeover
Dan Meyer: Nastava matematike treba temeljitu promjenu
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Današnji program nastave matematike poučava učenike da se pripremaju -- i napreduju kroz -- šablonske zadatke, oduzimajući im mogućnost razvoja vještine koja je važnija od rješavanja zadataka, a to je formuliranje problema. Na TEDxNYED, Dan Meyer pokazuje vježbe koje su provjerene u učionici, a koje zahtijevaju od učenika da stanu i razmisle.
Double-click the English transcript below to play the video.
00:15
Can I ask you to please recall a time
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Mogu li vas zamoliti da se prisjetite vremena
00:18
when you really loved something --
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kada ste uistinu nešto voljeli,
00:20
a movie, an album, a song or a book --
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film, album, pjesmu ili knjigu,
00:22
and you recommended it wholeheartedly
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i preporučili ste to iskreno
00:25
to someone you also really liked,
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nekome do koga vam je stalo,
00:27
and you anticipated that reaction, you waited for it,
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i očekivali ste tu reakciju, čekali ste na nju,
00:29
and it came back, and the person hated it?
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i ona je došla; osoba je mrzila vašu preporuku.
00:32
So, by way of introduction,
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Čisto uvoda radi
00:34
that is the exact same state
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ovo je upravo stanje
00:36
in which I spent every working day of the last six years. (Laughter)
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u kojem provodim gotovo svaki dan u posljednjih šest godina.
00:39
I teach high school math.
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Naime, predajem matematiku u srednjoj školi.
00:41
I sell a product to a market
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Prodajem proizvod tržištu
00:44
that doesn't want it, but is forced by law to buy it.
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koje ga ne želi, ali ga je zakonom prisiljeno kupiti.
00:47
I mean, it's just a losing proposition.
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To je unaprijed izgubljen slučaj.
00:50
So there's a useful stereotype about students that I see,
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Postoji koristan stereotip o učenicima koji ja vidim,
00:53
a useful stereotype about you all.
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koristan stereotip o svima vama.
00:55
I could give you guys
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Mogao bih vam dati
00:57
an algebra-two final exam,
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završni ispit iz algebre dva
00:59
and I would expect no higher
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i ne bih očekivao
01:01
than a 25 percent pass rate.
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veću prolaznost od 25%.
01:03
And both of these facts say less about you or my students
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Obje ove činjenice govore manje o vama ili mojim učenicima
01:06
than they do about what we call math education
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nego o onome što nazivamo matematičko obrazovanje
01:08
in the U.S. today.
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u današnjoj Americi.
01:10
To start with, I'd like to break math down into two categories.
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Krenuo bih s time da podijelim matematiku na dvije kategorije.
01:13
One is computation; this is the stuff you've forgotten.
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Jedna je računanje. To su stvari koje ste zaboravili.
01:16
For example, factoring quadratics with
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Na primjer, rastavljanje kvadrata s
01:18
leading coefficients greater than one.
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vodećim koeficijentima koji su veći od jedan.
01:20
This stuff is also really easy to relearn,
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Te je stvari također jako jednostavno ponovno naučiti,
01:22
provided you have a really strong grounding
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pod uvjetom da imate stvarno jako razvijeno
01:24
in reasoning. Math reasoning --
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racionalno razmišljanje, matematičko promišljanje.
01:26
we'll call it the application
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Nazvati ćemo to primjenom
01:28
of math processes to the world around us --
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matematičkih procesa na svijet oko nas.
01:30
this is hard to teach.
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To je teško za naučiti nekoga.
01:32
This is what we would love students to retain,
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To je ono što bismo voljeli da naši učenici dobiju i zadrže,
01:34
even if they don't go into mathematical fields.
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čak i ako ne nastave obrazovanje u matematičkom području.
01:36
This is also something that, the way we teach it in the U.S.
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To je također nešto, s obzirom na način na koji poučavamo u Americi
01:38
all but ensures they won't retain it.
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što oni vrlo vjerojatno neće zadržati.
01:41
So, I'd like to talk about why that is,
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Tako da ću ja govoriti o tome zašto je to tako,
01:42
why that's such a calamity for society, what we can do about it
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zašto je to nesreća za društvo, što možemo po tom pitanju učiniti,
01:45
and, to close with, why this is an amazing time
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i, za kraj, zašto je ovo tako nevjerojatno vrijeme
01:47
to be a math teacher.
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biti nastavnikom matematike.
01:49
So first, five symptoms
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Prije svega, pet simptoma
01:51
that you're doing math reasoning wrong
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koji pokazuju da krivo poučavate matematiku
01:53
in your classroom.
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u svom razredu.
01:55
One is a lack of initiative; your students don't self-start.
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Prvi je manjak inicijative; vaši studenti ne započinju sami.
01:58
You finish your lecture block
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Nakon što završite sa svojim blokom predavanja
02:00
and immediately you have five hands going up
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imate po pravilu barem pet ruku u zraku
02:02
asking you to re-explain the entire thing at their desks.
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koje od vas traže da ponovno objasnite cijelu stvar.
02:04
Students lack perseverance.
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Učenicima nedostaje upornosti.
02:06
They lack retention; you find yourself
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Njima nedostaje sposobnosti da zapamte; često smo
02:08
re-explaining concepts three months later, wholesale.
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u situaciji da moram ponovno objašnjavati koncepte tri mjeseca kasnije.
02:10
There's an aversion to word problems,
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Ne vole problemske zadatke, one s riječima
02:12
which describes 99 percent of my students.
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a takvih je 99% mojih učenika.
02:14
And then the other one percent
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A onih 1%
02:16
is eagerly looking for the formula
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nestrpljivo traži formulu
02:18
to apply in that situation.
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koja se može primijeniti na zadatak.
02:20
This is really destructive.
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To je stvarno destruktivno.
02:22
David Milch, creator of "Deadwood" and other amazing TV shows,
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David Milch, autor serije "Deadwood" i drugih čudesnih TV emisija,
02:25
has a really good description for this.
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ima stvarno dobar opis ovoga.
02:28
He swore off creating
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Zarekao se da će stvoriti
02:30
contemporary drama,
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suvremenu dramu,
02:32
shows set in the present day,
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koja će se prikazivati u sadašnjosti,
02:34
because he saw that when people fill their mind
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jer je shvatio da kada ljudi ispune um
02:36
with four hours a day of, for example, "Two and a Half Men," no disrespect,
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s četiri sada dnevno, na primjer serije "Dva i pol muškarca", uz dužno poštovanje,
02:39
it shapes the neural pathways, he said,
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oblikuju im se veze u mozgu, kaže,
02:41
in such a way that they expect simple problems.
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na takav način da očekuju samo jednostavne probleme.
02:44
He called it, "an impatience with irresolution."
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On je to nazvao, "nestrpljivost za rješenje".
02:47
You're impatient with things that don't resolve quickly.
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Nestrpljivi ste sa stvarima koje se ne razriješe brzo.
02:50
You expect sitcom-sized problems that wrap up in 22 minutes,
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Očekujete jednostavne probleme kao u serijama koje stanu u 22 minute,
02:53
three commercial breaks and a laugh track.
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uključujuće tri pauze za reklame i vrijeme za smijeh.
02:56
And I'll put it to all of you,
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I neću vam otkriti novost ako vam kažem
02:59
what you already know, that no problem worth solving is that simple.
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da niti jedan problem vrijedan rješavanja nije jednostavan.
03:02
I am very concerned about this
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Jako sam zabrinut zbog svega toga,
03:04
because I'm going to retire in a world that my students will run.
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jer ja ću otići u mirovinu u svijetu koji će voditi moji učenici.
03:07
I'm doing bad things
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Činim loše stvari
03:09
to my own future and well-being
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vlastitoj budućnosti i blagostanju
03:11
when I teach this way.
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kada poučavam na taj način.
03:13
I'm here to tell you that the way our textbooks -- particularly
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Ovdje sam da vam kažem kako je način na koji naši udžbenici, posebno
03:16
mass-adopted textbooks -- teach math reasoning
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općeprihvaćeni udžbenici, podučavaju matematičko promišljanje
03:19
and patient problem solving,
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i strpljivo rješavanje problema,
03:21
it's functionally equivalent to turning on "Two and a Half Men" and calling it a day.
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funkcionalno jednak kao kada upalite "sapunicu" i mislite da ste riješili problem.
03:24
(Laughter)
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(Smijeh)
03:26
In all seriousness. Here's an example from a physics textbook.
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Za ozbiljno, ovdje je primjer iz udžbenika iz fizike.
03:29
It applies equally to math.
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Jednako je primjenjiv i na matematiku.
03:31
Notice, first of all here,
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Primjetiti ćete prije svega
03:33
that you have exactly three pieces of information there,
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kako su dane točno tri informacije ovdje,
03:35
each of which will figure into a formula
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od kojih će se svaka preobličiti u formulu
03:37
somewhere, eventually,
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negdje, na kraju,
03:39
which the student will then compute.
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koju će učenici onda izračunati.
03:41
I believe in real life.
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Mislim kako u stvarnom životu to ne postoji.
03:43
And ask yourself, what problem have you solved, ever,
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Zapitajte se: koji ste problem ikada riješili,
03:45
that was worth solving
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a koji je bio vrijedan rješavanja,
03:47
where you knew all of the given information in advance;
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gdje ste znali sve ključne informacije unaprijed,
03:49
where you didn't have a surplus of information and you had to filter it out,
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ili niste imali višak informacija od kojih ste trebali izabrati ključne,
03:52
or you didn't have sufficient information
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ili niste imali manjak informacija
03:54
and had to go find some.
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i trebali ste ih pronaći negdje.
03:56
I'm sure we all agree that no problem worth solving is like that.
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Siguran sam da ćemo se svi složiti kako niti jedan problem vrijedan rješavanja nije takav.
03:59
And the textbook, I think, knows how it's hamstringing students
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Udžbenik, mislim, zna kako sakati učenike.
04:02
because, watch this, this is the practice problem set.
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Jer, pogledajte ovo, ovo je praktični zadatak.
04:05
When it comes time to do the actual problem set,
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Kada dođe vrijeme za rješavanje stvarnih zadataka,
04:07
we have problems like this right here
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zadaju se zadaci poput ovoga ovdje
04:09
where we're just swapping out numbers and tweaking the context a little bit.
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gdje samo izmjenimo brojeve i malo promjenimo kontekst.
04:12
And if the student still doesn't recognize the stamp this was molded from,
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Ako učenik još uvijek ne prepozna po kojoj se šabloni zadatak rješava
04:15
it helpfully explains to you
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prijateljski vam objasni
04:17
what sample problem you can return to to find the formula.
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u kojem ranijem primjeru možete pronaći pravu formulu za rješenje.
04:20
You could literally, I mean this,
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Mogli bi doslovno, to stvarno mislim,
04:22
pass this particular unit without knowing any physics,
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proći ovo poglavlje bez imalo razumijevanja fizike,
04:25
just knowing how to decode a textbook. That's a shame.
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samo treba znati kako dešifrirati udžbenik. To je velika šteta.
04:28
So I can diagnose the problem a little more specifically in math.
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Problem mogu još bolje dijagnosticirati u matematici.
04:31
Here's a really cool problem. I like this.
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Ovdje je stvarno zgodan zadatak.
04:33
It's about defining steepness and slope
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Odnosi se na definiranje kosine i nagiba
04:35
using a ski lift.
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koristeći ski lift.
04:37
But what you have here is actually four separate layers,
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Ali ono što imate ovdje jesu u stvari četiri odvojene razine.
04:39
and I'm curious which of you can see the four separate layers
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I baš me zanima tko od vas može vidjeti četiri odvojene razine
04:42
and, particularly, how when they're compressed together
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i, posebno, kako to što su pomiješane zajedno
04:45
and presented to the student all at once,
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i predstavljeni učenicima svi odjednom,
04:47
how that creates this impatient problem solving.
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kako to uzrokuje taj proces nestrpljivog rješavanja problema.
04:50
I'll define them here: You have the visual.
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Definirati ću ih ovdje. Imate sliku.
04:52
You also have the mathematical structure,
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Imate i matematičku strukturu
04:54
talking about grids, measurements, labels,
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govorim o mrežama, mjerama, oznakama,
04:56
points, axes, that sort of thing.
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točkama, osima, i tako dalje.
04:58
You have substeps, which all lead to what we really want to talk about:
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Imate međukorake, koji vas vode do onoga o čemu uistinu želimo razgovarati,
05:01
which section is the steepest.
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koja dio skijaške staze je najstrmiji.
05:03
So I hope you can see.
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Nadam se da možete vidjeti.
05:05
I really hope you can see how what we're doing here
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Stvarno se nadam da možete vidjeti, kako
05:07
is taking a compelling question, a compelling answer,
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uzmijaći izazovno pitanje, izazovni odgovor
05:09
but we're paving a smooth, straight path
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mi utiremo glatki, ravni put
05:11
from one to the other
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od jednog prema drugom,
05:13
and congratulating our students for how well
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i čestitamo našim učenicima koliko dobro
05:15
they can step over the small cracks in the way.
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mogu savladati male pukotine po tom putu.
05:17
That's all we're doing here.
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To je ono što radimo.
05:19
So I want to put to you that if we can separate these in a different way
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Tako vas ja želim potaknuti da razmišljamo na drugačiji način
05:21
and build them up with students,
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i sagradimo taj put zajedno sa učenicima,
05:23
we can have everything we're looking for in terms of patient problem solving.
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možemo imati sve ono što želimo s aspekta strpljivog rješavanja zadatka.
05:26
So right here I start with the visual,
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Ovdje ću započeti sa skicom
05:28
and I immediately ask the question:
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i odmah vas upitati:
05:30
Which section is the steepest?
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Koji dio staze je najstrmiji?
05:32
And this starts conversation
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I time ćemo započeti razogovor
05:34
because the visual is created in such a way where you can defend two answers.
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jer je skica napravljena na takav način da mogu biti dva odgovora.
05:37
So you get people arguing against each other,
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Pa će se ljudi prepirati
05:39
friend versus friend,
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prijatelji protiv prijatelja,
05:41
in pairs, journaling, whatever.
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u parovima, bilokako.
05:43
And then eventually we realize
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I onda ćemo na kraju spoznati
05:45
it's getting annoying to talk about
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postaje zamorno nekome govoriti o
05:47
the skier in the lower left-hand side of the screen
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skijašu u donjoj lijevoj strani ekrana
05:49
or the skier just above the mid line.
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ili o skijašu iznad srednje linije.
05:51
And we realize how great would it be
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I shvatimo koliko bi sjajno bilo
05:53
if we just had some A, B, C and D labels
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kada bismo imali samo A, B, C i D oznake
05:55
to talk about them more easily.
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o kojima možemo jednostavno razgovarati.
05:57
And then as we start to define what does steepness mean,
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A kad počnemo definirati što strmina znači,
06:00
we realize it would be nice to have some measurements
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shvatimo, kako bi bilo dobro imati neku mjeru
06:02
to really narrow it down, specifically what that means.
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kako bismo suzili značenje, na specifično značenje.
06:05
And then and only then,
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I tek tada,
06:07
we throw down that mathematical structure.
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ubacimo matematičku strukturu.
06:09
The math serves the conversation,
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Matematika služi razgovoru.
06:11
the conversation doesn't serve the math.
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Razgovor ne služi matematici.
06:13
And at that point, I'll put it to you that nine out of 10 classes
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U tom trenutku, uvjeravam vas, 9 od 10 razreda
06:16
are good to go on the whole slope, steepness thing.
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je sposobno razmatrati problem kosine, strmine.
06:18
But if you need to,
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Ali ako je potrebno
06:20
your students can then develop those substeps together.
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vaši učenici mogu onda razviti te podkorake zajedno.
06:22
Do you guys see how this, right here, compared to that --
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Vidite li vi kako ovo ovdje, uspoređeno s ovime --
06:25
which one creates that patient problem solving, that math reasoning?
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koji od njih uči, dovodi do strpljivog rješavanja problema, matematičkog promišljanja?
06:28
It's been obvious in my practice, to me.
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Prema praksi koju imam meni je odgovor očit.
06:31
And I'll yield the floor here for a second to Einstein,
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I podijeliti ću podij na sekundu s Einsteinom,
06:33
who, I believe, has paid his dues.
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koji je, vjerujem, to shvatio iskustvom.
06:35
He talked about the formulation of a problem being so incredibly important,
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On je govorio o tome koliko je iznimno važno formuliranje problema,
06:38
and yet in my practice, in the U.S. here,
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ipak u mojoj praksi, ovdje u SAD-u,
06:40
we just give problems to students;
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mi jednostavno dzadajemo učenicima zadatke;
06:42
we don't involve them in the formulation of the problem.
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ne uključujemo ih u formuliranje problema.
06:46
So 90 percent of what I do
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Tako je 90% onoga što radim
06:48
with my five hours of prep time per week
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u svojih pet sati priprema tjedno
06:50
is to take fairly compelling elements
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jest da uzmem poticajne elemente
06:53
of problems like this from my textbook
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zadataka poput ovih iz mog udžbenika i preoblikujem ih tako
06:55
and rebuild them in a way that supports math reasoning and patient problem solving.
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da podržavaju matematičko promišljanje i strpljivo rješavanje problema.
06:58
And here's how it works.
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I ovdje je prikazano kako to radi.
07:00
I like this question. It's about a water tank.
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Volim ovakva pitanja. Radi se o spremniku za vodu.
07:02
The question is: How long will it take you to fill it up?
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Pitanje je: Koliko je vremena potrebno da se napuni? Dobro?
07:04
First things first, we eliminate all the substeps.
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Kao prvo, eliminiramo sve pod korake.
07:06
Students have to develop those,
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Učenici ih sami moraju razviti.
07:08
they have to formulate those.
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Oni ih moraju formulirati.
07:10
And then notice that all the information written on there is stuff you'll need.
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I sada možete primjetiti kako su sve informacije napisane ovdje one stvari koje trebate.
07:13
None of it's a distractor, so we lose that.
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Niti jedna od njih ne zbunjuje, tako ćemo ih propustiti.
07:15
Students need to decide, "All right, well,
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Učenici moraju odlučiti,
07:17
does the height matter? Does the side of it matter?
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je li visina važna? Je li veličina važna?
07:19
Does the color of the valve matter? What matters here?"
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Je li važna boja ventila? Što je važno ovdje?
07:22
Such an underrepresented question in math curriculum.
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Ovo je podcjenjeno pitanje u nastavi matematike.
07:25
So now we have a water tank.
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Tako imamo spremnik za vodu.
07:27
How long will it take you to fill it up? And that's it.
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Koliko dugo će trebati da se napuni, i to je to.
07:29
And because this is the 21st century
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I zato jer je ovo 21. stoljeće,
07:31
and we would love to talk about the real world on its own terms,
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i zato jer bismo htjeli raspravljati o stvarnom svijetu kakav jest,
07:34
not in terms of line art or clip art
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a ne kao skica, crtež,
07:37
that you so often see in textbooks,
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što tako često vidimo u udžbenicima,
07:39
we go out and we take a picture of it.
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izađemo i fotografiramo ga.
07:41
So now we have the real deal.
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Sada imamo zadatak iz stvarnog života.
07:43
How long will it take it to fill it up?
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Koliko je potrebno da se napuni?
07:45
And then even better is we take a video,
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Ili, čak bolje, napravimo video,
07:47
a video of someone filling it up.
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snimku nekoga tko ga puni.
07:50
And it's filling up slowly, agonizingly slowly.
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A puni se polako, agonizirajuće polako.
07:52
It's tedious.
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To je mučno.
07:54
Students are looking at their watches, rolling their eyes,
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Učenici gledaju na svoje satove, okreću očima,
07:56
and they're all wondering at some point or another,
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i svatko od njih u jednom trenutku pomisli,
07:59
"Man, how long is it going to take to fill up?"
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"Čovječe, koliko dugo će trebati da se napuni?"
08:02
(Laughter)
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(Smijeh)
08:07
That's how you know you've baited the hook, right?
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Tako znate da su zagrizli mamac, zar ne?
08:11
And that question, off this right here, is really fun for me
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I to je pitanje meni stvarno zabavno,
08:14
because, like the intro,
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jer, kao što sam rekao u uvodu,
08:16
I teach kids -- because of my inexperience --
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ja poučavam klince, zbog vlastitog neiskustva,
08:19
I teach the kids that are the most remedial, all right?
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ja učim klince koji najviše zaostaju.
08:21
And I've got kids who will not join a conversation about math
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I imam klince koji se neće uključiti u razgovor o matematici
08:24
because someone else has the formula;
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jer netko drugi ima formulu,
08:26
someone else knows how to work the formula better than me,
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netko drugi zna bolje kako doći do formule od mene.
08:29
so I won't talk about it.
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Tako da neću o tome govoriti.
08:31
But here, every student is on a level playing field of intuition.
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svi su ravnopravni kad je riječ o intuiciji.
08:34
Everyone's filled something up with water before,
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Svatko je jednom punio nešto vodom,
08:37
so I get kids answering the question, "How long will it take?"
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tako dobijem klince da traže odgovor na pitanje, koliko dugo će trajati.
08:40
I've got kids who are mathematically and conversationally intimidated
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Imam klince koji se boje i matematike i razgovora
08:43
joining the conversation.
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koji se uključuju u ovaj razgovor.
08:45
We put names on the board, attach them to guesses,
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Stavljamo imena na ploču, vežemo ih uz nagađanja,
08:48
and kids have bought in here.
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i klinci su ovdje uključeni.
08:50
And then we follow the process I've described.
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I onda pratimo proces koji sam opisao.
08:52
And the best part here, or one of the better parts
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I najbolja stvar u tome, ili jedna od boljih
08:54
is that we don't get our answer from the answer key
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je da ne dođemo do rezultata metodom
08:56
in the back of the teacher's edition.
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koja je opisana u priručniku za nastavnike.
08:58
We, instead, just watch the end of the movie.
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Mi, umjesto toga, samo pogledamo kraj filma.
09:01
(Laughter)
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(Smijeh)
09:03
And that's terrifying,
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I to je zastrašujuće, zar ne?
09:05
because the theoretical models that always work out
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Jer teoretski modeli koji uvijek rade
09:07
in the answer key in the back of a teacher's edition,
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u priručniku za nastavnika
09:09
that's great, but
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to je sjajno, ali
09:11
it's scary to talk about sources of error
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je zastrašujuće govoriti o uzrocima grešaka
09:13
when the theoretical does not match up with the practical.
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kada se teoretski ne podudara s praktičnim.
09:15
But those conversations have been so valuable,
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Ali ti su razgovori toliko dragocjeni,
09:17
among the most valuable.
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među najvrednijim stvarima.
09:19
So I'm here to report some really fun games
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Ovdje sam došao kako bih vas izvjestio o nekim zabavnim poboljšanjima
09:21
with students who come pre-installed
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kod učenika koji su došli predinstalirani
09:23
with these viruses day one of the class.
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s tim virusima prvog dana u razredu.
09:25
These are the kids who now, one semester in,
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To su djeca kojoj sada, nakon jednog semestra,
09:28
I can put something on the board,
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mogu staviti nešto na ploču,
09:30
totally new, totally foreign,
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skroz novo i potpuno nepoznato,
09:32
and they'll have a conversation about it for three or four minutes more
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i oni razgovarati o tome 3-4 minute dulje
09:34
than they would have at the start of the year,
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nego što bi o tome raspravljali na početku godine,
09:36
which is just so fun.
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što je tako zabavno.
09:38
We're no longer averse to word problems,
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Više nismo neskloni problemskim zadacima
09:41
because we've redefined what a word problem is.
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jer smo redefinirali što znače ti problemski zadaci.
09:44
We're no longer intimidated by math,
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Više nismo zaplašeni matematikom,
09:46
because we're slowly redefining what math is.
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jer polagano redefiniramo što predstavlja matematika.
09:48
This has been a lot of fun.
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To je bilo tako zabavno.
09:50
I encourage math teachers I talk to to use multimedia,
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Želim ohrabriti nastavnike matematike kojima se obraćam, da koriste multimediju,
09:53
because it brings the real world into your classroom
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jer ona donosi stvarni svijet u učionice
09:55
in high resolution and full color;
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u visokoj rezoluciji i punoj boji,
09:57
to encourage student intuition for that level playing field;
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ona ohrabruje učenikovu intuiciju
10:00
to ask the shortest question you possibly can
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da postavlja najkraća moguća pitanja
10:02
and let those more specific questions come out in conversation;
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i pusti da se ona specifična pitanja iznjedre u razgovoru,
10:05
to let students build the problem,
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da učenici sami izgrade problem
10:07
because Einstein said so;
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jer je Einstein tako rekao,
10:09
and to finally, in total, just be less helpful,
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i da, na kraju, budemo manje pri ruci
10:12
because the textbook is helping you in all the wrong ways:
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jer vam udžbenik pomaže na krivi način.
10:14
It's buying you out of your obligation,
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Oduzima vam obvezu
10:17
for patient problem solving and math reasoning, to be less helpful.
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strpljivog rješavanja problema i matematičkog promišljanja.
10:20
And why this is an amazing time to be a math teacher right now
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Zašto je ovo zadivljujuće vrijeme za nastavnike matematike
10:23
is because we have the tools to create
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jer u džepu imamo alat za kreiranje
10:25
this high-quality curriculum in our front pocket.
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tog jako kvalitetnog nastavnog programa.
10:27
It's ubiquitous and fairly cheap,
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Sveprisutan je i prilično jeftin.
10:29
and the tools to distribute it
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A alati za njegovu distribuciju
10:31
freely under open licenses
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bez plaćanja, pod otvorenom licencom
10:33
has also never been cheaper or more ubiquitous.
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također nikada nisu bili jeftiniji i lakše dostupni.
10:36
I put a video series on my blog not so long ago
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Stavio sam seriju videa na moj blog nedavno
10:38
and it got 6,000 views in two weeks.
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i 6000 ljudi je to došlo pogledati u samo dva tjedna.
10:41
I get emails still from teachers in countries I've never visited
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Još uvijek dobijam e-mailove od nastavnika iz zemalja u kojima nikad nisam bio
10:44
saying, "Wow, yeah. We had a good conversation about that.
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koji govore. "Vau, da. Imali smo dobar razgovor o tome.
10:47
Oh, and by the way, here's how I made your stuff better,"
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I evo kako ja unapređujem ono što vi radite."
10:50
which, wow.
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Što je sjajno.
10:52
I put this problem on my blog recently:
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Ovaj sam zadatak nedavno stavio na svoj blog.
10:54
In a grocery store, which line do you get into,
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U dućanu, u koji red ćete stati?
10:56
the one that has one cart and 19 items
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Onaj s jednim kolicima u kojima se nalazi 19 predmeta,
10:58
or the line with four carts and three, five, two and one items.
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ili u onaj s četvero kolica s po tri, pet, dva i jednim proizvodom?
11:01
And the linear modeling involved in that was some good stuff for my classroom,
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Linearno modeliranje koje je potrebno za ovaj zadatak je sjajna stvar za moja predavanja
11:04
but it eventually got me on "Good Morning America" a few weeks later,
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ali sam se ovoga sjetio nekoliko tjedana kasnije dok sam gledao "Dobro jutro Ameriko",
11:07
which is just bizarre, right?
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što je bizarno, zar ne?
11:09
And from all of this, I can only conclude
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Iz svega ovoga mogu zaključiti
11:11
that people, not just students,
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da su ljudi, ne samo učenici,
11:13
are really hungry for this.
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stvarno gladni ovoga.
11:15
Math makes sense of the world.
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Matematika nas uči kako shvatiti svijet.
11:17
Math is the vocabulary
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Matematika je riječnik
11:19
for your own intuition.
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za vašu vlastitu intuiciju.
11:21
So I just really encourage you, whatever your stake is in education --
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Dakle ja vas samo ohrabrujem, kakvu god ulogu u obrazovanju imali
11:24
whether you're a student, parent, teacher, policy maker, whatever --
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jeste li učenici, roditelji, nastavnici, političari, štogod,
11:27
insist on better math curriculum.
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inzistirajte na boljem programu matematike.
11:30
We need more patient problem solvers. Thank you. (Applause)
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Treba nam više strpljivih rješavača problema. Hvala vam.
ABOUT THE SPEAKER
Dan Meyer - EducatorDan Meyer is exploring the way we teach teachers to teach kids.
Why you should listen
Dan Meyer asks, "How can we design the ideal learning experience for students?" As a part-time Googler, a provocative blogger and a full-time high-school math teacher, his perspective on curriculum design, teacher education and teacher retention is informed by tech trends and online discourse as much as front-line experience with students.
Meyer has spun off his enlightening message -- that teachers "be less helpful" and push their students to formulate the steps to solve math problems -- into a nationwide tour-of-duty on the speaking circuit.
Dan Meyer | Speaker | TED.com