TEDxNYED
Dan Meyer: Math class needs a makeover
Den Mejer: Časovi matematike trebaju da se promene
Filmed:
Readability: 4.2
2,804,252 views
Današnji program matematike uči učenike da očekuju i budu uspešni na šablonskim zadacima, a uskraćuje veštinu koja je bitnija od rešavanja problema: njihovo formulisanje. Na TEDxNYED-u, Den Mejer pokazuje matematičke vežbe koje su testirane u učionici, a koje teraju učenike da zastanu i da razmisle.
Double-click the English transcript below to play the video.
00:15
Can I ask you to please recall a time
0
0
3000
Mogu li vas zamoliti da se setite vremena
00:18
when you really loved something --
1
3000
2000
kada ste stvarno voleli nešto,
00:20
a movie, an album, a song or a book --
2
5000
2000
film, album, pesmu ili knjigu,
00:22
and you recommended it wholeheartedly
3
7000
3000
i preporučili ste to širokog srca
00:25
to someone you also really liked,
4
10000
2000
nekome ko vam se stvarno sviđao,
00:27
and you anticipated that reaction, you waited for it,
5
12000
2000
i očekivali ste reakciju, čekali ste je,
00:29
and it came back, and the person hated it?
6
14000
3000
i došla je, i ta osoba je to mrzela.
00:32
So, by way of introduction,
7
17000
2000
Pa, čisto zbog uvoda,
00:34
that is the exact same state
8
19000
2000
to je tačno stanje
00:36
in which I spent every working day of the last six years. (Laughter)
9
21000
3000
u kojem provodim svaki radni dan poslednjih 6 godina.
00:39
I teach high school math.
10
24000
2000
Predajem matematiku u srednjoj školi.
00:41
I sell a product to a market
11
26000
3000
Prodajem proizvod tržištu
00:44
that doesn't want it, but is forced by law to buy it.
12
29000
3000
koje ga neće, ali je obavezno po zakonu kupiti ga.
00:47
I mean, it's just a losing proposition.
13
32000
3000
Mislim, to je unapred izgubljen slučaj.
00:50
So there's a useful stereotype about students that I see,
14
35000
3000
Postoji korisan stereotip o učenicima koje viđam,
00:53
a useful stereotype about you all.
15
38000
2000
korisan stereotip o svima vama.
00:55
I could give you guys
16
40000
2000
Mogu da vam dam
00:57
an algebra-two final exam,
17
42000
2000
finalni test iz algebre 2,
00:59
and I would expect no higher
18
44000
2000
i očekivao bih prolaznost
01:01
than a 25 percent pass rate.
19
46000
2000
ne veću od 25 posto.
01:03
And both of these facts say less about you or my students
20
48000
3000
I oba podatka govore manje o vama ili mojim studentima
01:06
than they do about what we call math education
21
51000
2000
nego što govore o matematičkom obrazovanju
01:08
in the U.S. today.
22
53000
2000
danas u SAD-u.
01:10
To start with, I'd like to break math down into two categories.
23
55000
3000
Na početku, hteo bih da podelim matematiku na 2 kategorije.
01:13
One is computation; this is the stuff you've forgotten.
24
58000
3000
Jedna je računanje. Ovo je stvar koju ste zaboravili.
01:16
For example, factoring quadratics with
25
61000
2000
Na primer, faktorizacija kvadratnih jednačina
01:18
leading coefficients greater than one.
26
63000
2000
glavnim koeficijentom većim od 1.
01:20
This stuff is also really easy to relearn,
27
65000
2000
Lako je opet naučiti ovu stvar,
01:22
provided you have a really strong grounding
28
67000
2000
ako imate jako dobru osnovu
01:24
in reasoning. Math reasoning --
29
69000
2000
u razumevanju, matematičkom razumevanju.
01:26
we'll call it the application
30
71000
2000
Zvaćemo ga aplikacija
01:28
of math processes to the world around us --
31
73000
2000
matematičkih procesa svetu oko nas.
01:30
this is hard to teach.
32
75000
2000
Ovo je teško predavati.
01:32
This is what we would love students to retain,
33
77000
2000
Ovo bi hteli da učenici zadrže,
01:34
even if they don't go into mathematical fields.
34
79000
2000
čak iako ne nastave sa matematikom.
01:36
This is also something that, the way we teach it in the U.S.
35
81000
2000
Ovo je takođe nešto, s obzirom na način na koji predajemo u SAD-u,
01:38
all but ensures they won't retain it.
36
83000
2000
što sigurno neće zapamtiti.
01:41
So, I'd like to talk about why that is,
37
86000
1000
Dakle, reći ću vam zašto je to tako,
01:42
why that's such a calamity for society, what we can do about it
38
87000
3000
zašto je to tolika nesreća za društvo, šta možemo da uradimo,
01:45
and, to close with, why this is an amazing time
39
90000
2000
i, da završim, zašto je ovo neverovatno vreme
01:47
to be a math teacher.
40
92000
2000
da se bude profesor matematike.
01:49
So first, five symptoms
41
94000
2000
Prvo, 5 simptoma
01:51
that you're doing math reasoning wrong
42
96000
2000
da loše predajete matematiku
01:53
in your classroom.
43
98000
2000
u vašoj učionici.
01:55
One is a lack of initiative; your students don't self-start.
44
100000
3000
Jedan je manjak inicijative; vaši učenici nemaju volje.
01:58
You finish your lecture block
45
103000
2000
Završite predavanje
02:00
and immediately you have five hands going up
46
105000
2000
i odmah imate 5 ruku koje se dižu
02:02
asking you to re-explain the entire thing at their desks.
47
107000
2000
i pitaju da opet objasnite celo predavanje.
02:04
Students lack perseverance.
48
109000
2000
Učenicima nedostaje istrajnost.
02:06
They lack retention; you find yourself
49
111000
2000
Imaju teškoće sa pamćenjem; i nađete sebe
02:08
re-explaining concepts three months later, wholesale.
50
113000
2000
kako opet objašnjavate isti koncept 3 meseca kasnije.
02:10
There's an aversion to word problems,
51
115000
2000
Postoji odbojnost prema tekstualnim problemima,
02:12
which describes 99 percent of my students.
52
117000
2000
a to navodi 99 posto mojih učenika.
02:14
And then the other one percent
53
119000
2000
I onda onih jedan odsto
02:16
is eagerly looking for the formula
54
121000
2000
jedva čekaju formulu
02:18
to apply in that situation.
55
123000
2000
da primene u toj situaciji.
02:20
This is really destructive.
56
125000
2000
To je destruktivno.
02:22
David Milch, creator of "Deadwood" and other amazing TV shows,
57
127000
3000
Dejvid Milč, koji je stvaralac "Deadwood"-a i još nekih neverovatnih TV serija,
02:25
has a really good description for this.
58
130000
3000
je ovo dobro opisao.
02:28
He swore off creating
59
133000
2000
Odrekao se stvaranja
02:30
contemporary drama,
60
135000
2000
modernih drama,
02:32
shows set in the present day,
61
137000
2000
serija u sadašnjem vremenu,
02:34
because he saw that when people fill their mind
62
139000
2000
jer je video da kada ljudi pune svoje glave
02:36
with four hours a day of, for example, "Two and a Half Men," no disrespect,
63
141000
3000
sa 4 sata dnevno, recimo, "Dva i po muškarca", bez uvrede,
02:39
it shapes the neural pathways, he said,
64
144000
2000
to oblikuje neuronske putanje, kako on kaže,
02:41
in such a way that they expect simple problems.
65
146000
3000
na takav način da oni očekuju slične probleme.
02:44
He called it, "an impatience with irresolution."
66
149000
3000
On to zove "nestrpljivost bez rešenja".
02:47
You're impatient with things that don't resolve quickly.
67
152000
3000
Nestrpljivi ste sa stvarima koje se ne rešavaju brzo.
02:50
You expect sitcom-sized problems that wrap up in 22 minutes,
68
155000
3000
Očekujete probleme kao iz sitkoma koji se reše za 22 minuta,
02:53
three commercial breaks and a laugh track.
69
158000
3000
3 bloka reklama i smehom.
02:56
And I'll put it to all of you,
70
161000
2000
I svima ću reći,
02:59
what you already know, that no problem worth solving is that simple.
71
164000
3000
iako znate, nijedan problem vredan rešavanja nije jednostavan.
03:02
I am very concerned about this
72
167000
2000
I ovo me veoma brine,
03:04
because I'm going to retire in a world that my students will run.
73
169000
3000
jer ću se penzionisati u svetu u kojem će moji učenici vladati.
03:07
I'm doing bad things
74
172000
2000
Radim loše stvari
03:09
to my own future and well-being
75
174000
2000
mojoj budućnosti i dobrobiti
03:11
when I teach this way.
76
176000
2000
kada predajem ovako.
03:13
I'm here to tell you that the way our textbooks -- particularly
77
178000
3000
Ovde sam da vam kažem da način na koji naše knjige,
03:16
mass-adopted textbooks -- teach math reasoning
78
181000
3000
naročito opšteprihvaćene, uče matematičko razmišljanje
03:19
and patient problem solving,
79
184000
2000
i strpljivo rešavanje problema,
03:21
it's functionally equivalent to turning on "Two and a Half Men" and calling it a day.
80
186000
3000
funkcionalno jednako gledanju "Dva i po muškarca", i mislite da je to to.
03:24
(Laughter)
81
189000
2000
(Smeh)
03:26
In all seriousness. Here's an example from a physics textbook.
82
191000
3000
Ozbiljno, evo ga primer iz knjige iz fizike.
03:29
It applies equally to math.
83
194000
2000
Isto važi i za matematiku.
03:31
Notice, first of all here,
84
196000
2000
Pre svega, primetićete
03:33
that you have exactly three pieces of information there,
85
198000
2000
da su ovde date tačno 3 informacije,
03:35
each of which will figure into a formula
86
200000
2000
svaka od njih će se uvrstiti u formulu
03:37
somewhere, eventually,
87
202000
2000
negde, eventualno,
03:39
which the student will then compute.
88
204000
2000
koju će učenik onda da računa.
03:41
I believe in real life.
89
206000
2000
Ja verujem u stvaran život.
03:43
And ask yourself, what problem have you solved, ever,
90
208000
2000
I pitajte se, koji ste to problem rešili, ikada,
03:45
that was worth solving
91
210000
2000
koji je bio vredan rešavanja,
03:47
where you knew all of the given information in advance;
92
212000
2000
gde ste sve informacije znali unapred,
03:49
where you didn't have a surplus of information and you had to filter it out,
93
214000
3000
ili gde niste imali višak informacija koje ste morali da filtrirate,
03:52
or you didn't have sufficient information
94
217000
2000
ili gde niste imali dovoljno informacija
03:54
and had to go find some.
95
219000
2000
i morali ste da pronađete još.
03:56
I'm sure we all agree that no problem worth solving is like that.
96
221000
3000
Siguran sam da nijedan problem vredan rešavanja nije takav.
03:59
And the textbook, I think, knows how it's hamstringing students
97
224000
3000
I knjiga, mislim, zna kako je teško učenicima.
04:02
because, watch this, this is the practice problem set.
98
227000
3000
Jer, gledajte ovo, ovo je set zadataka.
04:05
When it comes time to do the actual problem set,
99
230000
2000
Kada dođe vreme da se stvarno reši problem,
04:07
we have problems like this right here
100
232000
2000
imamo probleme kao ovaj ovde
04:09
where we're just swapping out numbers and tweaking the context a little bit.
101
234000
3000
gde samo zamenjujemo brojeve i malo podešavamo kontekst.
04:12
And if the student still doesn't recognize the stamp this was molded from,
102
237000
3000
I ako učenik i dalje ne prepoznaje šablon,
04:15
it helpfully explains to you
103
240000
2000
uspešno vam objašnjava
04:17
what sample problem you can return to to find the formula.
104
242000
3000
kom primeru problema možete da se vratite da nađete formulu.
04:20
You could literally, I mean this,
105
245000
2000
I bukvalno možete, da uradite to,
04:22
pass this particular unit without knowing any physics,
106
247000
3000
da prođete ovaj deo bez znanja fizike,
04:25
just knowing how to decode a textbook. That's a shame.
107
250000
3000
samo da znate kako da dekodirate knjigu. To je šteta.
04:28
So I can diagnose the problem a little more specifically in math.
108
253000
3000
Tako mogu malo tačnije da dijagnoziram problem u matematici.
04:31
Here's a really cool problem. I like this.
109
256000
2000
Evo jednog sjajno primera. Sviđa mi se ovo.
04:33
It's about defining steepness and slope
110
258000
2000
Radi se definisanju strmine i spusta
04:35
using a ski lift.
111
260000
2000
koristeći ski prevoz.
04:37
But what you have here is actually four separate layers,
112
262000
2000
Ali ovde imate 4 odvojena sloja.
04:39
and I'm curious which of you can see the four separate layers
113
264000
3000
I radoznao sam ko od vas može da ih vidi,
04:42
and, particularly, how when they're compressed together
114
267000
3000
i, naročito, kako su spojeni zajedno i
04:45
and presented to the student all at once,
115
270000
2000
predstavljeni studentima odjednom,
04:47
how that creates this impatient problem solving.
116
272000
3000
kako to stvara nestrpljivo rešavanje problema.
04:50
I'll define them here: You have the visual.
117
275000
2000
Definisaću ih ovde. Imate vizuelni prikaz.
04:52
You also have the mathematical structure,
118
277000
2000
Imate takođe matematičku strukturu,
04:54
talking about grids, measurements, labels,
119
279000
2000
govorimo o mreži , merenjima, oznakama,
04:56
points, axes, that sort of thing.
120
281000
2000
tačkama, osama, i takvim stvarima.
04:58
You have substeps, which all lead to what we really want to talk about:
121
283000
3000
Imate potkorake, koji svi vode onome o čemu hoćemo da govorimo,
05:01
which section is the steepest.
122
286000
2000
koji deo je najstrmlji.
05:03
So I hope you can see.
123
288000
2000
Nadam se da možete da vidite.
05:05
I really hope you can see how what we're doing here
124
290000
2000
Stavrno se nadam da vidite da ono što ovde radimo
05:07
is taking a compelling question, a compelling answer,
125
292000
2000
je da uzimamo nesavladivo pitanje, nesavladiv odgovor,
05:09
but we're paving a smooth, straight path
126
294000
2000
i od toga pravimo gladak, prav put
05:11
from one to the other
127
296000
2000
od jednog do drugog,
05:13
and congratulating our students for how well
128
298000
2000
i čestitamo našim učenicima što mogu
05:15
they can step over the small cracks in the way.
129
300000
2000
dobro da savladaju male pukotine na putu.
05:17
That's all we're doing here.
130
302000
2000
To je sve što radimo ovde.
05:19
So I want to put to you that if we can separate these in a different way
131
304000
2000
Hoću da vam pokažem da ako možemo da razdvojimo ove na različite načine
05:21
and build them up with students,
132
306000
2000
i da ih izgradimo sa učenicima,
05:23
we can have everything we're looking for in terms of patient problem solving.
133
308000
3000
možemo da imamo sve što tražimo što se tiče strpljivog rešavanja problema.
05:26
So right here I start with the visual,
134
311000
2000
Tako da ovde, počeću slikovito,
05:28
and I immediately ask the question:
135
313000
2000
i odmah pitati:
05:30
Which section is the steepest?
136
315000
2000
Koji deo je najstrmiji?
05:32
And this starts conversation
137
317000
2000
I ovo otvara razgovor
05:34
because the visual is created in such a way where you can defend two answers.
138
319000
3000
jer je vizuelizacija napravljena tako da možete da definišete 2 odgovora.
05:37
So you get people arguing against each other,
139
322000
2000
Tako da imate ljude koji se međusobno raspravljaju,
05:39
friend versus friend,
140
324000
2000
prijatelj protiv prijatelja,
05:41
in pairs, journaling, whatever.
141
326000
2000
u parovima, kao novinari, kako god.
05:43
And then eventually we realize
142
328000
2000
I onda na kraju shvatimo
05:45
it's getting annoying to talk about
143
330000
2000
da nervira pričanje o
05:47
the skier in the lower left-hand side of the screen
144
332000
2000
skijaču dole levo na ekranu
05:49
or the skier just above the mid line.
145
334000
2000
ili skijaču iznad srednje linije.
05:51
And we realize how great would it be
146
336000
2000
I shvatimo kako bi bilo super
05:53
if we just had some A, B, C and D labels
147
338000
2000
da samo imamo oznake A, B, C i D
05:55
to talk about them more easily.
148
340000
2000
da bi o njima lakše pričali.
05:57
And then as we start to define what does steepness mean,
149
342000
3000
I dok počinjemo da definišemo pojam strmine,
06:00
we realize it would be nice to have some measurements
150
345000
2000
shvatimo da bi bilo dobro da imamo neke mere
06:02
to really narrow it down, specifically what that means.
151
347000
3000
da suzimo, specifišemo značenje.
06:05
And then and only then,
152
350000
2000
I tada i samo tada,
06:07
we throw down that mathematical structure.
153
352000
2000
ubacimo matematčku strukturu.
06:09
The math serves the conversation,
154
354000
2000
Matematika služi konverzaciji.
06:11
the conversation doesn't serve the math.
155
356000
2000
Konverzacija ne služi matematici.
06:13
And at that point, I'll put it to you that nine out of 10 classes
156
358000
3000
I u tom trenutku, pokazaću vam da je 9 od 10 odeljenja
06:16
are good to go on the whole slope, steepness thing.
157
361000
2000
dobro na celom spustu, strmoj stvari.
06:18
But if you need to,
158
363000
2000
Ali ako trebate,
06:20
your students can then develop those substeps together.
159
365000
2000
vaši studenti mogu da razviju te potkorake zajedno.
06:22
Do you guys see how this, right here, compared to that --
160
367000
3000
Da li, ljudi, vidite, kako ovo, ovde, u poređenju s tim--
06:25
which one creates that patient problem solving, that math reasoning?
161
370000
3000
koje od njih stvara strpljivo rešavanje problema, matematčko razumevanje?
06:28
It's been obvious in my practice, to me.
162
373000
3000
Bilo mi je očigledno u mojoj praksi.
06:31
And I'll yield the floor here for a second to Einstein,
163
376000
2000
I zovem na pozornici ovde drugog Ajnštajna,
06:33
who, I believe, has paid his dues.
164
378000
2000
koji, je verujem, platio svoj ceh.
06:35
He talked about the formulation of a problem being so incredibly important,
165
380000
3000
On je pričao kako je formulacija problema neverovatno bitna,
06:38
and yet in my practice, in the U.S. here,
166
383000
2000
i ipak u mojoj praksi, ovde u SAD-u,
06:40
we just give problems to students;
167
385000
2000
samo dajemo probleme učenicima,
06:42
we don't involve them in the formulation of the problem.
168
387000
3000
ne uključujemo ih u formulaciji problema.
06:46
So 90 percent of what I do
169
391000
2000
Tako da 90% onoga što radim
06:48
with my five hours of prep time per week
170
393000
2000
sa mojih 5 sati pripremanja nedeljno
06:50
is to take fairly compelling elements
171
395000
3000
je da uzmem nesalomive elemente
06:53
of problems like this from my textbook
172
398000
2000
problema kao ovaj iz knjige
06:55
and rebuild them in a way that supports math reasoning and patient problem solving.
173
400000
3000
i da ih opet izgradim da podržavaju matematičko razmevanje i strpljivo rešavanje problema.
06:58
And here's how it works.
174
403000
2000
I evo kako to radi.
07:00
I like this question. It's about a water tank.
175
405000
2000
Volim ovo pitanje. U pitanju je vodeni tenk.
07:02
The question is: How long will it take you to fill it up?
176
407000
2000
Pitanje je : Koliko vremena je potrebno da se napuni?Ok?
07:04
First things first, we eliminate all the substeps.
177
409000
2000
Prvo, eliminišemo sve potkorake.
07:06
Students have to develop those,
178
411000
2000
Učenici moraju da ih razviju
07:08
they have to formulate those.
179
413000
2000
Moraju da ih formulišu.
07:10
And then notice that all the information written on there is stuff you'll need.
180
415000
3000
I onda da primete da su im potrebne sve informacije tu napisane.
07:13
None of it's a distractor, so we lose that.
181
418000
2000
Ništa ne odvlači pažnju, tako da gubimo to.
07:15
Students need to decide, "All right, well,
182
420000
2000
Učenici trebaju da odluče, u redu, dobro,
07:17
does the height matter? Does the side of it matter?
183
422000
2000
da li je visina bitna? Da li je veličina bitna?
07:19
Does the color of the valve matter? What matters here?"
184
424000
3000
Da li je boja ventila bitna? Šta je bitno ovde?
07:22
Such an underrepresented question in math curriculum.
185
427000
3000
Toliko nedovoljno predstavljeno pitanje u programu matematike.
07:25
So now we have a water tank.
186
430000
2000
Tako da sada imamo vodeni tenk.
07:27
How long will it take you to fill it up? And that's it.
187
432000
2000
Koliko vam treba vremena da ga napunite, i to je to.
07:29
And because this is the 21st century
188
434000
2000
I pošto je ovo 21. vek,
07:31
and we would love to talk about the real world on its own terms,
189
436000
3000
voleli bismo sa pričamo o realnom svetu u njegovim uslovima,
07:34
not in terms of line art or clip art
190
439000
3000
ne u uslovima linija i slika
07:37
that you so often see in textbooks,
191
442000
2000
koje često vidite u knjigama,
07:39
we go out and we take a picture of it.
192
444000
2000
mi izađemo i slikamo.
07:41
So now we have the real deal.
193
446000
2000
I sada imamo pravu stvar.
07:43
How long will it take it to fill it up?
194
448000
2000
Koliko treba da se napuni?
07:45
And then even better is we take a video,
195
450000
2000
I još bolje, ako uzmemo video,
07:47
a video of someone filling it up.
196
452000
3000
video nekog ko ga puni.
07:50
And it's filling up slowly, agonizingly slowly.
197
455000
2000
I polako se puni, sporo do agonije.
07:52
It's tedious.
198
457000
2000
Dosadno je.
07:54
Students are looking at their watches, rolling their eyes,
199
459000
2000
Učenici gledaju u njihove satove, prevrću očima,
07:56
and they're all wondering at some point or another,
200
461000
3000
i pitaju se u nekom trenutku
07:59
"Man, how long is it going to take to fill up?"
201
464000
3000
"Čoveče, koliko mu vreme treba da se napuni?"
08:02
(Laughter)
202
467000
5000
(Smeh)
08:07
That's how you know you've baited the hook, right?
203
472000
3000
Tako znate da su su se upecali, da.
08:11
And that question, off this right here, is really fun for me
204
476000
3000
I to pitanje, ovo ovde, mi je zabavno,
08:14
because, like the intro,
205
479000
2000
jer, kao uvod,
08:16
I teach kids -- because of my inexperience --
206
481000
3000
učim decu, jer zbog mog iskustva,
08:19
I teach the kids that are the most remedial, all right?
207
484000
2000
učim decu da se ovo najviše popravlja, da.
08:21
And I've got kids who will not join a conversation about math
208
486000
3000
I imam decu koja neće da se pridruže razgovoru o matematici
08:24
because someone else has the formula;
209
489000
2000
jer neko drugi ima formulu,
08:26
someone else knows how to work the formula better than me,
210
491000
3000
neko drugi zna da koristi formulu bolje od mene.
08:29
so I won't talk about it.
211
494000
2000
Tako da neću da pričam o tome.
08:31
But here, every student is on a level playing field of intuition.
212
496000
3000
Ali ovde, svi su na istom nivou gde se igra intuicijom.
08:34
Everyone's filled something up with water before,
213
499000
3000
Svako je nekad nešto napunio sa vodom,
08:37
so I get kids answering the question, "How long will it take?"
214
502000
3000
tako da nateram decu da odgovore, koliko treba da se napuni.
08:40
I've got kids who are mathematically and conversationally intimidated
215
505000
3000
Imam decu koja su matematički i konverzaciono zastrašena
08:43
joining the conversation.
216
508000
2000
da se pridruže razgovoru.
08:45
We put names on the board, attach them to guesses,
217
510000
3000
Stavljamo imena na tablu, ostavljamo ih da pogađaju,
08:48
and kids have bought in here.
218
513000
2000
i deca su to prihvatila.
08:50
And then we follow the process I've described.
219
515000
2000
I onda pratimo proces koji sam opisao.
08:52
And the best part here, or one of the better parts
220
517000
2000
I najbolji deo ovde, ili jedan od najboljih delova
08:54
is that we don't get our answer from the answer key
221
519000
2000
je taj da ne dobijamo naš odgovor iz rešenja
08:56
in the back of the teacher's edition.
222
521000
2000
na kraju profesorovog predavaja.
08:58
We, instead, just watch the end of the movie.
223
523000
3000
Mi, ustvari, samo gledamo kraj filma.
09:01
(Laughter)
224
526000
2000
(Smeh)
09:03
And that's terrifying,
225
528000
2000
I to je zastrašujuće, da.
09:05
because the theoretical models that always work out
226
530000
2000
Jer teoretski modeli koji uvek rade
09:07
in the answer key in the back of a teacher's edition,
227
532000
2000
u rešenjima na kraju knjige,
09:09
that's great, but
228
534000
2000
to je super, ali
09:11
it's scary to talk about sources of error
229
536000
2000
strašno je pričati o izvorima grešaka
09:13
when the theoretical does not match up with the practical.
230
538000
2000
kada se teorija ne poklapa sa praktičnim.
09:15
But those conversations have been so valuable,
231
540000
2000
Jer su ti razgovori bili toliko vredni,
09:17
among the most valuable.
232
542000
2000
među najvrednijima.
09:19
So I'm here to report some really fun games
233
544000
2000
Tako da sam ovde da izvestim o zabavnim dobicima
09:21
with students who come pre-installed
234
546000
2000
sa učenicima koju su došli prethodno instalirani
09:23
with these viruses day one of the class.
235
548000
2000
prvog dana predavanja sa ovim virusima.
09:25
These are the kids who now, one semester in,
236
550000
3000
Ovo su deca koja sada, posle jednog polugodišta,
09:28
I can put something on the board,
237
553000
2000
ako stavim nešto na tablu,
09:30
totally new, totally foreign,
238
555000
2000
totalno novo, strano,
09:32
and they'll have a conversation about it for three or four minutes more
239
557000
2000
oni će da pričaju o tome 3-4 minuta više
09:34
than they would have at the start of the year,
240
559000
2000
nego na početku godine,
09:36
which is just so fun.
241
561000
2000
što je baš zabavno.
09:38
We're no longer averse to word problems,
242
563000
3000
Više nemamo averziju prema tekstualnim problemima,
09:41
because we've redefined what a word problem is.
243
566000
3000
jer smo redefinisali šta je tekstualni problem.
09:44
We're no longer intimidated by math,
244
569000
2000
Nismo više zastrašeni matematikom,
09:46
because we're slowly redefining what math is.
245
571000
2000
jer polako redefinišemo šta je matematika.
09:48
This has been a lot of fun.
246
573000
2000
Ovo je bilo baš zabavno.
09:50
I encourage math teachers I talk to to use multimedia,
247
575000
3000
Ohrabrujem nastavnike matematike sa kojima pričam da koriste multimediju,
09:53
because it brings the real world into your classroom
248
578000
2000
jer to uvodi realni život u vašu učionicu
09:55
in high resolution and full color;
249
580000
2000
sa visokom rezolucijom i bojom,
09:57
to encourage student intuition for that level playing field;
250
582000
3000
da podstičemo intuiciju učenika da dođe na taj nivo igre,
10:00
to ask the shortest question you possibly can
251
585000
2000
da pitate najkraća pitanja koja možete
10:02
and let those more specific questions come out in conversation;
252
587000
3000
i da dopustite da se ta specifičnija pitanja jave u razgovoru,
10:05
to let students build the problem,
253
590000
2000
da dozvolite učenicima da sagrade problem,
10:07
because Einstein said so;
254
592000
2000
jer je Ajnštajn rekao tako,
10:09
and to finally, in total, just be less helpful,
255
594000
3000
i na kraju, sve u svemu, da manje pomažete,
10:12
because the textbook is helping you in all the wrong ways:
256
597000
2000
jer knjiga vam pomaže na pogrešne načine.
10:14
It's buying you out of your obligation,
257
599000
3000
To vas vadi iz obaveze da strpljivo
10:17
for patient problem solving and math reasoning, to be less helpful.
258
602000
3000
rešavate problem i matematički razmišljate, da manje pomažete.
10:20
And why this is an amazing time to be a math teacher right now
259
605000
3000
I zato je ovo neverovatno vreme da budete nastavnik matematike
10:23
is because we have the tools to create
260
608000
2000
jer imamo alate da stvorimo
10:25
this high-quality curriculum in our front pocket.
261
610000
2000
program visokog kvaliteta u našem prednjem džepu.
10:27
It's ubiquitous and fairly cheap,
262
612000
2000
To je sveprisutno i dosta jeftino.
10:29
and the tools to distribute it
263
614000
2000
I alat za njihovu slobodnu distribuciju
10:31
freely under open licenses
264
616000
2000
sa otvorenim licencama
10:33
has also never been cheaper or more ubiquitous.
265
618000
3000
takođe nikada nije bilo jeftinije i sveprisutnije.
10:36
I put a video series on my blog not so long ago
266
621000
2000
Postavio sam seriju klipova na mom blogu ne tako davno,
10:38
and it got 6,000 views in two weeks.
267
623000
3000
i imali su 6 000 pregleda za 2 nedelje.
10:41
I get emails still from teachers in countries I've never visited
268
626000
3000
I dalje dobijam mailove od profesora iz zemalja koje nikada nisam posetio
10:44
saying, "Wow, yeah. We had a good conversation about that.
269
629000
3000
gde kažu:"Vauv da. Imali smo dobar razgovor o tome.
10:47
Oh, and by the way, here's how I made your stuff better,"
270
632000
3000
Oh, i usput, evo kako sam popravio tvoju stvar.",
10:50
which, wow.
271
635000
2000
što je sjajno.
10:52
I put this problem on my blog recently:
272
637000
2000
Postavio sam ovaj problem skoro na mom blogu.
10:54
In a grocery store, which line do you get into,
273
639000
2000
U prodavnici, u koji red da stanete,
10:56
the one that has one cart and 19 items
274
641000
2000
onaj koji ima jedna kolica i 19 stvari,
10:58
or the line with four carts and three, five, two and one items.
275
643000
3000
ili onaj sa 4 kolica i 3, 5, 2 i jednom stvari.
11:01
And the linear modeling involved in that was some good stuff for my classroom,
276
646000
3000
I linearno modeliranje ovde uključeno, bila je dobra stvar za moju učionicu,
11:04
but it eventually got me on "Good Morning America" a few weeks later,
277
649000
3000
ali me je na kraju stiglo u "Dobro jutro Ameriko" nekoliko nedelja kasnije,
11:07
which is just bizarre, right?
278
652000
2000
što je bizarno, da.
11:09
And from all of this, I can only conclude
279
654000
2000
I iz svega ovoga mogu samo da zaključim
11:11
that people, not just students,
280
656000
2000
da ljudi, ne samo učenici,
11:13
are really hungry for this.
281
658000
2000
željni ovoga.
11:15
Math makes sense of the world.
282
660000
2000
Matematika daje smisao svetu.
11:17
Math is the vocabulary
283
662000
2000
Matematika je rečnik
11:19
for your own intuition.
284
664000
2000
vaše intuicije.
11:21
So I just really encourage you, whatever your stake is in education --
285
666000
3000
Tako da vas podržavam, kako god da učestvujete u obrazovanju,
11:24
whether you're a student, parent, teacher, policy maker, whatever --
286
669000
3000
bilo da ste učenik, roditelj, nastavnik, stvarate pravila, svejedno,
11:27
insist on better math curriculum.
287
672000
3000
insistirajte na boljem matematičkom programu.
11:30
We need more patient problem solvers. Thank you. (Applause)
288
675000
3000
Treba nam više strpljivih rešavača 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