No more M in STEM | David Brown | TEDxUSU

Translator: Jim Taylor
Reviewer: Denise RQ Does anyone even know
how to operate one of these things? (Laughter) I’m expecting buttons. When I tell people
I’m a card-carrying mathematician, sometimes, they believe I can operate
this thing like nobody’s business. I can, in fact, make it play like Jimmy
Hendrick’s used to play the guitar. Check it out. (mock rock music guitar playing) But this is actually more my style. (mock hard rock music playing) I have no use for this thing.
In fact, I’d like to give it away. Does anyone need one of these things? (Laughter) I’m serious. Come on up. It’s right here. It’s yours. Take it, if you want it. Other times when I tell people
what I do for a living, I get this response
[Oh, I hated math.] which is surprising to me
where the typical decorum is politeness. Anyway, it’s not that offensive to me, and I do understand that by ‘hated’ they don’t mean they used to hate math,
and now they’re OK with it. (Laughter) I know that they mean that they hated it,
and they’re done with it, and they’ll never have anything
to do with it again. That’s not exactly
a personal affront to me. The offense I take in it is
that it’s a reflection of my profession. After all, I went through the experience
that this person I’m talking to went with. I went and saw the movie
that is the math curriculum. Which, by the way, it would be called “The Big Foist”
if it was actually a movie. The taglines would be
unambitious and offensive. Offensive because it’s offensive to any student who actually wants
to learn something and doesn’t want to be treated
like they’re stupid. It’s unambitious
because if you’re a teacher, you actually have nothing but a goal
of having your students take a test; whether they pass or not,
I claim that’s not an issue. Think about it. I showed up to this movie,
and this is what happened. Wax on, wax off, wax on, wax off. Wax on! Paint the fence.
Paint the house. Sand the floor. Wax on! Wax off! And then I’m done. (Laughter) (Applause) I could’ve gone out
into the world and got a job. After all, I did pretty well
on those exams that I took, and speaking of exams,
they’re very tricky things. Consider this prompt for example. I was involved in a workshop
to help construct the core curriculum, and a good teacher, like a good lawyer,
knows the answer to any question that you’re going to ask. But a really good teacher knows every possible response
to a question they ask, and the depth and breadth
that that response implies about their knowledge
that they’re testing for. So, here was a prompt
that we had to consider. The response that we had
to think about was this one. I can’t remember if we were told
by the person running the workshop or if we figured it out, but what I came away with was the student apparently
used the number line as the vinculum for the fraction which is doing exactly
what the prompt says. (Laughter) Looking back, I honestly wonder
about how much is actually evinced in these tests that we give. Numbers aren’t a line; why should anyone know
what a number line even is? Is this actually testing whether I know that 3/4 lies
between 1/2 and 1? Why don’t you just ask me that instead of telling me
to do something like this. Another prompt that everyone
who I’ve ever asked has been on the receiving end of
or at least of a prompt like this … And we all know that the answer
that’s desired is E. But think about it; the real answer is G. But that’s never there. That’s an answer for every possible
prompt like this, every single one. Because we have no idea
what’s causing that sequence of numbers. It could be the number of goos
that their baby has uttered since they woke up. During the first minute,
well, they were sleeping. The second minute: five goos. The next minute, ten –
because they’re getting awake I guess. I don’t know how many goos
are going to happen next. It certainly has an upper bound.
It’s not increasing to infinity. Goo, goo, goo, goo, goo, goo!
I actually don’t know. But having done well on these tests
and not ready for the real world, certainly not really wanting
to get a job, I went back to college. Because I was told
when I was in high school that when a teacher
actually gave an honest response, “What is this crap good for?” – We didn’t usually say crap – “What is this stuff good for?”, the only response I came to respect
was the one that said, “Well, you’re probably going
to use it in college,” or the better one was, “Well,
you’re going to use it on the test later.” So I went back to college thinking, “I’ve been prepped
for 14 years to come to this. I want to learn more math.
I don’t know why. I want to do
some more substantive learning.” So I went back to college, and wax on, wax off,
wax on, wax off, wax on minus three, arbitrary constant. I nailed the arbitrary constant,
got my degree, and went on. I got a real job and suffered. Suffered under the stymying, terrible, day-to-day, creativity-killing job that was just making me money. I got caught up in climbing
the corporate ladder, I’ll admit. But I didn’t know that I didn’t know anything
about mathematics until I went back to graduate school
and was knee-deep in it facing real challenges, facing problems that forced me
to be creative, to be clever, and by the way, mathematics is a place
where creativity is definitely needed. And that creativity is put to the test in a way that’s different
from any other art form. Yeah, it’s an art form. Why it’s in the college of science?
I have no idea. But I also realize
that these misconceptions that that curriculum generated
are present in colleagues that I have on my university. For example, administrators. For example, people that might control what the math department does,
what it needs to teach. Let me give you an example.
Here’s a story. There are these departments
in the college of science: Mathematics, Chemistry,
Geology, Physics, and Biology. These are the logos
that are currently in use. We were asked to revamp our logo, not sure why, maybe because it wasn’t
e-sexy, or iHot, or whatever, or hashtag cool, or something. But we were asked to reevaluate our logo
which is the one in the center there which is of course, an M on its side,
which stands for math because that’s what mathematicians do:
is they obfuscate things. That’s all we’re here to do. In fact, here’s a quote
from a physics colleague, someone in the Physics Department
who was explaining a problem and said – this is a quote – “And then some mathematicians
got a hold of the problem, and it was completely incomprehensible.” (Laughter) My internal response was, “No, you just don’t know
enough math to understand it. There’s a likelihood that your problem was actually solved
by those mathematicians, but I can’t blame you
for not knowing enough math. There’s no sin in that. Our curriculum, our universities optimize
the amount of math you don’t take. And they stop you at an arbitrary point
which is typically ridiculous.” People’s last experience
with mathematics is something terrible, filled with inane stuff
they will never use unless they go on to calculus,
but not everyone goes on to calculus. So, we were actually recommended … Someone was hired
to come up with a new logo, I guess because mathematicians certainly
couldn’t make them sexy enough. So, this was the logo
that was recommended to us. (Laughter) The damn calculator. So, this started a flurry of emails
that I still have – this was years ago – and I love to reread these things. The initiating one came
from our Department Head, and he was clearly irate. He said, “I don’t know exactly what we’re supposed to do
with a nine-digit calculator, but we need to do something. “We’ve got to come up with something.” So, the responses
from this were fantastic. My favorite one was, “Well, how about a five-digit calculator
with the middle one extended?” (Laughter) I really wish that was our logo. But the things that actually happened were one colleague requested
this one, or suggested this one: some logical notation. If it were translated into English,
it’s “If P, then Q.” What properties guarantee
what other properties? If you have property or structure P, then you’re guaranteed to have
property or structure Q. It’s a set containment relationship,
so we could’ve used this notation as well: everything that contains property P is contained in the things
that contain property Q. You are guaranteed to have property Q
if you have property P. P is a sufficient condition for Q,
and so on, and so forth. I said that’s fantastic, we all agreed that was a great piece
of notation for our logo, but I went up to them and said,
“What about this one? P if and only if Q.
If P, then Q, if Q, then P.” That means they’re precisely the same. That’s one of the most
important characteristics, that’s the bread and butter
of doing mathematics – invariance. If you ask a human a question –
as opposed to an alien or a dog, I guess – if you ask a person a question,
and they don’t know the answer to it, perhaps it’s a complicated one. For example, maybe you’re
a senator on a jury, and you’re asked, “How much should a financial predator
who preys on the elderly pay for some of the crimes they commit?” That’s a complicated question that you probably
cannot just blurt out an answer for which I’m not an English major. (Laughter) You’d probably replace
that question with something like, “How would I feel if that person
preyed on my grandmother?” The point is we often do this. But if we train ourselves,
we train our mathematical abilities and enhance them through taking
substantive, real mathematics courses, you begin to notice when things are actually invariant,
when you can change that perspective. If I don’t like perspective P,
if that’s not solving my problem, I can use perspective Q. And sometimes, solving a problem
is all about changing your perspective. But when can you do that? Another person said,
“Why don’t we use this symbol?” – the infinity cartouche. The reasoning was it reminds
our colleagues in the college of science that they’re relegated
to deal with finite stuff. They go out into their finite fields,
and weigh finite fish, and pet finite numbers of ducks,
and measure finite numbers of rocks, in finite terms of years. We deal with infinite quantities, we can solve
an infinite number of problems by our powers of abstraction, which we practice
all the time in mathematics. And this reminds me of how I think we actually should think
about mathematics. If I were to ask you to define
what a sixth sense is, I don’t know what you would say, but I would say
it is some way, some mechanism by which we can experience things we cannot possibly experience
with the other five. Some way to predict the future, perhaps. But this is exactly what mathematics does: we create models that uncannily, eerily
are able to predict the future. We can count quantities that we could never physically –
one, two, three – enumerate. We can deduce what’s going to happen
in 4, 5, 50 dimensions, with mathematics. We’d never experience those dimensions. But then, if you’d wanted to put
a little biological constraint on it and say, “Our five senses
have real estate in our brains,” math does, too. There’s some fantastic research showing
we have real estate in our brain that’s devoted to
some of the substantive stuff that we can grow into mathematics. The mathematics understands
relations, even calculus, all kinds of things;
anything in mathematics. I think we should think of it
as our sixth sense, because if we did, then there wouldn’t be
much of an excuse to not know it. It wouldn’t be OK, socially OK,
to not know any mathematics, because then, it would be clear that you’re walking around
basically blinded in such a way that you can’t see things
that you would see with an enhanced mathematical skill, you’re not hearing things
you could potentially be hearing. Back to the logo. The logo that we have actually reflects
exactly the state of affairs, it’s quite poetic, because when I took calculus 20 years ago, it’s the same calculus that I teach now. When I was in the math curriculum
20 years ago, it’s the same curriculum
that I’m in right now. Twenty years ago, the only way I could talk
to a person at a great distance was by using this thing
that was in the shape of a banana. It had a twirly cord that was attached
to the wall and always getting tangled. The world has changed
a great deal in 20 years, but the mathematics curriculum
hasn’t changed at all, so our symbol is still this one. And we keep feeding this monster
that is devouring any chance of students having
a real experience with mathematics and actually coming away from it
with the correct sensation that it is a creative art,
a creative endeavor that is challenging,
and it develops yourself. Every time I solved something significant
as a graduate student, I felt like I became a better person,
I felt like I became smarter, I felt like I made
new connections in my brain. I don’t feel that when I do
calculus or do arithmetic. It’s clear that we don’t.
It’s largely a function of memory. The solution to this, if it were up to me, would be to detonate everything
and start all over again, but we could change things in a way
that is not exactly easy to implement because these types of things
are not scantronable. Take that ridiculous prompt about telling me what the next term
in the sequence is and replace it with this prompt. You actually have to write something, and as a teacher,
you have to read something to assess whether the person knows
what they’re talking about, how much depth of understanding
of mathematics do they have, how much flexibility do they have
with the mathematics. Our symbol should be this one because this is what we keep doing:
we keep throwing money into mathematics to try and get people
through these classes that shouldn’t even be taught. A modest proposal from me is:
don’t teach those classes anymore. And this is the point
where I really have to hijack my talk because I really didn’t want
to give you an idea, I don’t really have one to share other than to blow up
the mathematics curriculum and start over. But what was that I wanted
to offer you is an apology, a deep, heartfelt apology. I am truly sorry that the experience
that you’ve had with mathematics is what it is. Because it’s a shame. It’s a negative reflection
on my profession. I try and do something about it
every time I teach class, but I know that many of you
will never go back to mathematics, and for that, I am truly sorry. (Applause)

37 thoughts on “No more M in STEM | David Brown | TEDxUSU

  1. Every talk should be this riveting.  A brilliant analysis of perceptions of Mathematics, and of its true – unheralded – powers.
    Observing mathematical ability to be nothing less than the human 6th sense is genius.  This recognizes both the true nature of the human brain and of math itself:  we possess an innate capacity for the kind of abstract reasoning and critical thinking that underlies mathematics.
    Dave gave us fascinating insights into the beautiful and magnificent nature of Math.
    Thank you!

  2. Dr. Brown is an amazing teacher, and the class I was lucky enough to have with him was the best math class I've ever taken. He shows his students why the things he talks about here are true–that math is deeply misunderstood, taught incorrectly, and can be a creative and interesting art form if approached and taught in the right way.

  3. Math is cool, but you have to make it practical, and then it becomes very exciting. The majority of people, never see anything best grade school math used in their life, which is why people say they "hate" math. I use math in some of the computer programming I do, and believe me, know math helps make jobs easier.

  4. Math songs. I failed algebra in high school and I don't think passing notes to the guy in front of me from Brazil really made it that much easier to fail. I did the whole book in 6 weeks that summer and loved it. I haven't come to a place like that since with math. I am exploring math now. I did well in physics and astronomy.

  5. I never felt like I was any good at mathematics. Or at least the evaluation of equations anyway. I was more interested in the predictions and especially the visualizations that mathematics makes possible. I remember in physics after looking at the relativistic equations, I would daydream what it would be like to be aboard a relativistic spaceship. Toying with those parameters as the spaceship accelerated. What would the scenery look like? More importantly, what does the perception of time look like? Maybe as my spaceship went faster I would be able to watch those planets whiz around the star in orbit. Fascinating stuff. But man, evaluating equations, that stuff is hard. It amazes me that anyone survives.

  6. He is angry and emotional that people don't respect the mathematics as a field out of their ignorance may be or their disinterest and that's a wide known fact now. But i really don't see anthing significant comming out of his talk.

  7. I think he is right on several things certainly the sequence question(something that incredibly annoys me I would ban the question in the way it is posed at the moment as it is mathematically incorrect).However, I think he doesn't realise that you need to learn the tools before you can get creative and solve more advanced problems(how could you do solve a complicated problem in Calculus without learning what Calculus is?) and he also doesn't realise the importance of the tool like nature of Mathematics to fields outside Mathematics(most students of Mathematics will end up in these fields), like a lot of Physics problems requires one to think a lot about the Physics and then solve the problem using computational Mathematics(these computational techniques must be learned and an awful lot of them).I do think there should be more challenging problems in Mathematics introduced into GCSE and A Level that are completely unfamiliar(the student shouldn't know how to solve the problem beforehand) but computational Mathematics is also important.I also dislike how the title seems to indicate Mathematics shouldn't be included in STEM when it is the language of Science.

  8. Education is the most important thing out there. Which is why we must BURN THE SCHOOLS DOWN! D:<

  9. this may be super prejudice and stereotypical but he's one swole mathmatician

  10. The problem with math as it is currently taught is that it is too abstract, too isolated, and there is too much awkward and unfamiliar vocabulary and too many unfamiliar symbols. People can and do easily learn an equivalently difficult level of thinking in computer programming. Make math more like computer science.

    Seven modest proposals:
    🖝 Throw out the stupid Greek letters. Use English words instead. If you're counting apples and balls, use apples and balls as your variable names, not alpha and beta or a and b.
    🖝 Find simple English terms for things instead of relying on ancient Greek and Latin vocabulary. Abscissa? Sounds painful! Better take an antibiotic for that. Do not reduce mathematics to Greek and Latin vocabulary lessons. If you can't explain it in plain English, you don't know your subject well enough yet.
    🖝 Relate Algebra better to Geometry, even computer graphics. Algebra is meaningless symbolic manipulation unless it is related to other, more concrete, things.
    🖝 Don't bother to prove trivial things. That's a waste of everybody's time. If it's intuitively obvious it's an insult to require a proof.
    🖝 Don't rely only on proof to teach a concept in depth. No learning actually takes place until the student sees multiple demonstrations by example. Before the Greeks, math had no concept of proof at all, and they managed to build the pyramids and ziggurats! Proof in most cases is not necessary and not desirable as it is an impediment to learning.
    🖝 Probability and statistics are much more important than calculus. In the real world nobody ever actually solves a problem using calculus (in the few cases where that's necessary we use a computer program), but you can't read a newspaper and look at a graph or chart and truly understand what it implies without knowing probability and statistics.
    🖝 Set theory is wrong. Cantor's diagonal proof is a fallacy. Infinity is not a number, much less is it a hierarchy of numbers. It's a signed limit, and that's all.

  11. What happens if you do JUST the math XOR the muscles stuff instead of both together in your life, or do one much more than the other? Is it WRONG to do just one xor the other? Is it REQUIRED to do both together?

    Also, regarding questions of the form @4:20 — this is bad, I note that these are some of the same questions that are used in the "IQ" tests used by racists to show that some races are inferior and so deserve discrimination, hatred, and rejection from society. And then we have the gall to conclude with extraordinary ambition (as a lot of "researchers" like Jared Taylor, Rushton Jensen, Lynn, etc.) that it is "50 – 80% genetic inferiority" that makes Blacks get 85 and Whites get 100 on the standard IQ test. What wonderful ambition! So full of respect and humility! Lofty and beautiful! (/sarc)

  12. So, according to this guy students should not learn math because he doesn't like the way it is taught? That doesn't make any sense.

  13. Through most of this, he mispronounces mathematics as "mathmatics". There are actually four syllables: ma' the ma' tics. (Stress before the comma.) You pronounce the 'e'. I suspect some people fear that pronouncing the 'e' would be making the same mistake some people make when pronouncing athletics as "ath' uh le' tics". In any case, it's MATH uh MAT ics.

  14. A series assumes that the pattern will continue. I went back to math, and it is because I had an open mind and wondered what eluded me; I concluded that you will not make an effort to do something if you convince yourself that you cannot do it, and if you believe that all learning should be utilitarian. And if it is not, it should not be pursued. I like the pursuit of knowledge; hence, I never questioned the usefulness of anything I had to learn.

  15. So…. ted talk in 6 words: Math can/should be better for everyone. And my responses are as follows:

    1. what if GI Joe took the Khan academy approach and used his passion, knowledge, and experience as an educator who wants to make math more accessible and made educational videos for the world (and generations to come) to see and experience…
    (Sorry for the run on… I'm not an English major)

    2. Or what if he implemented a flipped classroom, where students would learn math at home (eg. through Khan academy) and do homework, solve problems, and actually engage the material in class with a super facilitator helping connect students to real world applications ?

    3. Or what if he taught math to his gym buddies? Buff mathematicians trying to save the world and start a revolution? Eureka!

  16. Thanks for this talk David! I agree with everything you say, but you should be directing this energy at the whole education system, which has always been more about sorting and ranking than inspiring.

  17. I guess I should maybe go back to math….. definitely was a captivated audience…

  18. This guy has been a PhD too long. Yiu have to learn how to use math before you get fancy and creative with it. What needs to be taught is how to apply math, how a manager or a retail worker makes use of it.

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