TED2009
Arthur Benjamin: Teach statistics before calculus!
Arthur Benjamins formel for en ændring af matematikundervisningen
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Der er altid nogen der spørger matematiklæreren, "kommer jeg til at bruge infinitesimalregning i virkeligheden?" og for de fleste af os, siger Arthur Benjamin, er svaret nej. Han fremlægger et modigt forslag til hvordan matematikundervisningen kan gøres relevant i vores digitale tidsalder.
Arthur Benjamin - Mathemagician
Using daring displays of algorithmic trickery, lightning calculator and number wizard Arthur Benjamin mesmerizes audiences with mathematical mystery and beauty. Full bio
Using daring displays of algorithmic trickery, lightning calculator and number wizard Arthur Benjamin mesmerizes audiences with mathematical mystery and beauty. Full bio
Double-click the English transcript below to play the video.
00:12
Now, if President Obama
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Hvis Præsident Obama
00:15
invited me to be the next Czar of Mathematics,
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inviterede mig til at blive den næste matematik-Zar,
00:19
then I would have a suggestion for him
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så ville jeg have et forslag til ham
00:22
that I think would vastly improve
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som jeg tror ville forbedre
00:24
the mathematics education in this country.
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matematikundervisningen i dette land gevaldigt.
00:27
And it would be easy to implement
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Og det ville være nemt at indføre
00:29
and inexpensive.
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og billigt.
00:31
The mathematics curriculum that we have
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Matematik pensummet som vi har idag
00:33
is based on a foundation of arithmetic and algebra.
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er baseret på et grundlag af aritmetik og algebra.
00:37
And everything we learn after that
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Og alt det som vi lærer efterfølgende
00:39
is building up towards one subject.
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bygger op imod én disciplin.
00:42
And at top of that pyramid, it's calculus.
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Og i toppen af den pyramide, finder man infinitesimalregning.
00:46
And I'm here to say
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Og jeg er her for at sige
00:48
that I think that that is the wrong summit of the pyramid ...
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at jeg synes at dét er den forkerte top i pyramiden ...
00:52
that the correct summit -- that all of our students,
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at den korrekte top -- som alle vores studerende,
00:54
every high school graduate should know --
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som enhver student skulle kende --
00:56
should be statistics:
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skulle være statistik:
00:59
probability and statistics.
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sandsynlighed og statistik.
01:01
(Applause)
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(Klapsalver)
01:03
I mean, don't get me wrong. Calculus is an important subject.
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Jeg mener, og misforstå mig nu ikke. Infinitesimalregning er en vigtig disciplin.
01:07
It's one of the great products of the human mind.
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Det er et af det menneskelig hjernes store skabelser.
01:09
The laws of nature are written in the language of calculus.
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Naturens love er skrevet i infinitesimalregningens sprog.
01:13
And every student who studies math, science, engineering, economics,
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Og enhver student der studerer matematik, naturvidenskab, ingeniørvidenskab, økonomi,
01:17
they should definitely learn calculus
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skal helt afgjort lære om infinitesimalregning
01:19
by the end of their freshman year of college.
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før slutningen af deres første år på universitetet.
01:21
But I'm here to say, as a professor of mathematics,
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Men jeg er her for at sige, som professor i matematik,
01:24
that very few people actually use calculus
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at meget få mennesker rent faktisk bruger infinitesimalregning
01:28
in a conscious, meaningful way, in their day-to-day lives.
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på en bevidst og meningsfuld måde, i deres hverdag.
01:31
On the other hand,
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På den anden side,
01:33
statistics -- that's a subject that you could,
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statistik -- dét er et fag som man kan,
01:36
and should, use on daily basis. Right?
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og bør bruge på en daglig basis. Ikke sandt?
01:39
It's risk. It's reward. It's randomness.
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Det handler om risiko, belønning, tilfældighed.
01:42
It's understanding data.
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Det handler om dataforståelse.
01:44
I think if our students, if our high school students --
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Jeg tror at, hvis vores studerende, hvis vores gymnasieelever --
01:46
if all of the American citizens --
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hvis alle de amerikanske borgere --
01:48
knew about probability and statistics,
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kendte til sandsynlighed og statistik,
01:51
we wouldn't be in the economic mess that we're in today. (Laughter) (Applause)
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så ville vi ikke være i det økonomiske rod som vi er i i dag
01:54
Not only -- thank you -- not only that ...
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Ikke bare -- tak -- ikke bare det ...
01:57
but if it's taught properly, it can be a lot of fun.
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[men] hvis det er undervist ordenligt, kan det være meget sjovt.
02:00
I mean, probability and statistics,
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Altså, sandsynlighed og statistik,
02:02
it's the mathematics of games and gambling.
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det er matematikken bag spil og hasard.
02:06
It's analyzing trends. It's predicting the future.
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Det er at analysere tendenser. Det er at forudsige fremtiden.
02:10
Look, the world has changed
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Verden har forandret sig
02:12
from analog to digital.
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fra analog til digital.
02:15
And it's time for our mathematics curriculum to change
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Og det er tid til en forandring af vores matematik pensum
02:18
from analog to digital,
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fra analog til digital.
02:20
from the more classical, continuous mathematics,
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Fra det mere klassiske, kontinuerte matematik,
02:24
to the more modern, discrete mathematics --
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til det mere moderne, diskrete matematik.
02:27
the mathematics of uncertainty,
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Matematiken af usikkerheden,
02:29
of randomness, of data --
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af tilfældigheden, af data --
02:31
that being probability and statistics.
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og det er jo netop sandsynlighed og statistik.
02:34
In summary, instead of our students
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Kort sagt, i stedet for at vores studerende
02:36
learning about the techniques of calculus,
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lærer om teknikkerne bag infinitesimalregning,
02:39
I think it would be far more significant
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så tror jeg det vil være meget mere betydningsfyldt
02:42
if all of them knew what two standard deviations
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hvis de alle sammen vidste hvad to standardafvigelser
02:45
from the mean means. And I mean it.
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fra middeltallet betyder. Og jeg mener det.
02:48
Thank you very much.
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Mange tak.
02:50
(Applause)
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(Klapsalver)
ABOUT THE SPEAKER
Arthur Benjamin - MathemagicianUsing daring displays of algorithmic trickery, lightning calculator and number wizard Arthur Benjamin mesmerizes audiences with mathematical mystery and beauty.
Why you should listen
Arthur Benjamin makes numbers dance. In his day job, he's a professor of math at Harvey Mudd College; in his other day job, he's a "Mathemagician," taking the stage in his tuxedo to perform high-speed mental calculations, memorizations and other astounding math stunts. It's part of his drive to teach math and mental agility in interesting ways, following in the footsteps of such heroes as Martin Gardner.
Benjamin is the co-author, with Michael Shermer, of Secrets of Mental Math (which shares his secrets for rapid mental calculation), as well as the co-author of the MAA award-winning Proofs That Really Count: The Art of Combinatorial Proof. For a glimpse of his broad approach to math, see the list of research talks on his website, which seesaws between high-level math (such as his "Vandermonde's Determinant and Fibonacci SAWs," presented at MIT in 2004) and engaging math talks for the rest of us ("An Amazing Mathematical Card Trick").
Arthur Benjamin | Speaker | TED.com