

Math is hard. - mofeeta
http://fourthcheckraise.blogspot.com/2011/11/math-is-hard.html

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Daishiman
I disagree fundamentally with the article; it does not reflect the experience
of many people at all.

I excelled in all subjects in high school except for math, which I detested
and felt as difficult and, for the most part, uninteresting.

Fast forward to third year of Uni and I was looking at set theory, graph
theory, and logical proofs. They were all difficult, yet they sucked me in. It
was hard but I wasn't dissuaded from studying. And the reason why was because
thinking of interesting proofs and devising ways of solving puzzles is far,
far more interesting than doing arithmetic from rote memory.

It really doesn't surprise me at all that kids do badly in math when they're
introduced to such boring and dry topics. Kids are taught useless
trigonometric identities when they could be studying applied statistics, which
is not only substantially more useful, but it opens a lot more doors for
reasoning about the world. Learning statistics, graph theory and logic have
literally helped to mold my thinking. I can't really say the same about trig
of high-school level calculus (not that there's anything wrong with calculus,
but i think that in order to get something out of it you need to dedicate much
more time than what is available in high school).

~~~
blackhole
I want to say that while I did very well in math in high school, it didn't
hold my interest until I got into calculus in university, and am now deeply
interested in advanced vector analysis and other applied mathematics (I still
hate proofs). I very much agree that much of high school is spent drilling
useless topics into students heads that are completely unnecessary and never
even explained beyond a few ridiculous "real-life" applications. All the
interesting math is locked away, available only to those who suffer through
meaningless tests and bureaucratic madness. It would be much better to
introduce higher level topics first, showing students the incredible
usefulness of high level math, and then using their curiosity to dig into the
lower level concepts that make everything work, instead of forcing them to try
and be interested in boring low-level rigor that , without a high-level
structure, is of limited use.

It's like we're teaching kids mathematical assembly language instead of
Python.

~~~
abduhl
Math at the lower level never holds anybody's interest (even those who go on
to be very good at a STEM field). It is exactly (half of) what you said it is:
boring low-level rigor. It is absolutely not of "limited use".

Your comparison to assembly/Python doesn't fit at all. You cannot start in on
vector analysis without an understanding of geometry and algebra. You can
start Python without understanding assembly at all. You can go back and learn
assmebly after you've learned Python but this isn't true in most cases with
higher level math. How do I explain the chi-squared distribution without
wasting the entire semester on basic maths? Math isn't like an Apple product,
it doesn't "just work."

Some make the argument that how we teach STEM based courses can be adjusted so
that we start from high-level stuff and teach low-level mechanics along the
way. While this approach is intriguing, it will never work. It relies on an
assumption about students that isn't true: they are actually interested in the
subject. If I had to guess the percentage of students with a deep interest in
their subject I would put it at a little bit below the actual graduation
rates. Most students are in degree programs nowadays because it is the next
step, all of their friends are doing it, it is expected of them, and/or they
are trying to make their parents happy. Many of these students will find out
what it is they really want to do (whether it is in their first field or their
second field), many will recognize that they hate their field and still slog
through for social reasons, and many will fail. College is a life changing
experience for most people, no matter what category they fall in.

~~~
blackhole
Algebra is important. Knowing sum-to-product trig identities, limits to 0/0
and obscure trigonometric integral identities are not. I am not saying none of
it is required, I am saying some of it is not required, and that there is an
unnecessary emphasis on it.

My comparison to assembly/Python was a comparison, but of course I should have
expected people to take it to an extreme hyperbole. But then, your entire
argument is based on the assumption that most people are not interested in
mathematics, so I guess circular logic is totally fine in these arguments (and
hilariously ironic).

No really, let's look at this. I'm saying that teaching high level math
alongside low level math (or at least putting less emphasis on low level math)
will make more people interested in math. You're saying this won't work
because people aren't interested in math. That doesn't work.

------
Hyena
This is deeply incorrect.

If it were correct, mathematics education would have to begin with set theory
and physics probably could not begin with _F = ma_. Our _pedagogy_ is
cumulative but it is tellingly built on some hand-waving and "you'll have to
trust me on this part".

This means that we can take a different approach to it pretty easily. For
example, why does set theory often wait until college and probability until...
never? These concepts are much more analytically useful to the average person
than is the quadratic equation (which you can look up as needed) or (heaven
help me) angle-side-angle.

We teach math through loaded down problem sets instead of heading right after
the most conceptually useful (and therefore) meaty chunks first. We don't even
teach children mathematically-grounded science for the most part; that's a
missed opportunity to take those problem sets and make them analytically
powerful and memorable.

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inuhj
I agree completely with this article. Math and physics are hard. It requires a
certain disposition to be willing to sit with a problem for minutes or hours
and have faith that you will be able to find the solution. The fields are also
littered with geniuses and people with significantly more talent than
yourself. The gap between those who tried and those who were gifted was severe
at my alma mater(USC).

I remember being in an intermediate mechanics course with only physics majors
when our professor asked us how long it took us to complete the homework sets.
I was regularly spending 15-25 hours a week on them. Some of my classmates
were completing the sets in 2-3 hours. What shocked me wasn't that there were
students who could complete the assignments that quickly but that: 1) students
were either taking 2-5 hours or 10+ hours to complete the assignment. It was
very bimodal. 2) that the gap in efficiency between the best and worst
students was almost 10x.

In comparison my estimate of the gap in efficiency between the best and worst
medical students is 1.5-2x at the most. No medical student can claim that they
can accomplish in 2-5 hours what would take another medical student 15-25
hours to learn.

In the end I made the choice to go in to medicine where I was consistently in
the top 3% of my class. There were a handful of 'superheroes' in medicine but
not many. Most of us started in the same place and where we ended up ranking
in our class was a function of effort. It was a refreshingly level playing
field in comparison to physics.

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rjd
I struggled through high school never managing to get my head around
statistics. I changed majors from chemistry to microbiology my first year of
my science degree (because thats where all the girls where), and found
statistics really easy. So what was the difference? the teachers thats all,
some of the best tutors I every experienced where in the science area.

I had one tutor explain to me why he threw curve ball problems at the class.
He would use it to weed out which ones gave up quick, which ones powered on,
which ones just threw tantrums etc... he would then only really teach the
percentage of the class that wanted the degree. The rest he said he'd get to
passing, some just weren't worth teaching, but he'd make sure the real
scientists walked out of the class with the best training they could get
(albeit at the expense of others).

I'd hazard a guess that type of teaching behavior is endemic, so drop out
rates for people who can't get the initiative to put in the extra effort get
left behind pretty quickly and hence drop out.

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draggnar
A Mathematician's Lament

"TEXTBOOK PUBLISHERS : TEACHERS ::

A) pharmaceutical companies : doctors

B) record companies : disk jockeys

C) corporations : congressmen

D) all of the above

We have millions of adults wandering around with “negative b plus or minus the
square root of b squared minus 4ac all over 2a” in their heads, and absolutely
no idea whatsoever what it means."

[https://docs.google.com/viewer?a=v&q=cache:qcqr-s07yTgJ:...](https://docs.google.com/viewer?a=v&q=cache:qcqr-s07yTgJ:www.maa.org/devlin/LockhartsLament.pdf+article+math+creativity+art&hl=en&gl=us&pid=bl&srcid=ADGEEShtuWAC3pVdpPkCH-
J-
sRac3MAPc9S-NY4fSzssyuaD8rnZtvotVHKuQRvzhrvT_lfVMUW81NcYWaGkgZbk1bNUKNFmJ2UuhJPsN6vob3nSy23XoAaVUTnwq0b-GTssPJx7Mrwv&sig=AHIEtbQRktN05TaMgJJnirJUfMaXMeOHwQ&pli=1)

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ImprovedSilence
“In mathematics you don't understand things. You just get used to them.” -
Johann Von Neuman

I so related to that statement in college. I took all the necessary math and
engineering (fancy word for more math...) classes to get my EE degree. I was
able to apply the math well enough to be able to stick around in my
engineering program (although there were SEVERAL different points in time I
almost changed major, and I did dabble in getting a philosophy minor.) In
college, my mindset was: "study enough to get by. beer. boobs. football" (yeah
yeah, I went to a Big 10 football school) But I didn't really care about the
math too much, as long as I got my degree and a paycheck at the end.

Now, out in the wild, I find enjoyment in the application of math (I do signal
processing) and I only wish someone was there to help me see the "fun", or
applicable side of things back in school, so I could understand even more now.
I think the big problem with my college courses was that the course material
simply existed just to exist, whereas now in my job, it exists to perform a
function, and it's kinda cool to see how stuff works. But make no mistake, now
that I'm though with my studies, I'm more than thankful I had to take all
those ball beater math classes, so I actually (at one point at least) knew the
'math' behind the math i'm using, I knew more than the math, I knew how it was
derived, and THATS every course building on each other, and it's tough, and
there's distractions, but it's necessary.

~~~
abduhl
I hear a lot of the first half of your post but not a lot of your second half
of your post (I agree with both). Most people look back and remember how
hard/dumb/boring/useless that one class was and how they never use it in real
life. Barely anybody looks back and remembers how something that they learned
in their math class was integral to their ability succeed later on in their
career. For example, almost everybody complains about how hard/useless
calculus was. These same people are able to take a volume integral in
cylindrical coordinates no problem. There is a fundamental disconnect here.

And anything you don't remember? Well, being familiar with a concept makes it
a hundred times easier to learn the second time.

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georgefox
This post strikes me as absurd and offensive. First of all, the author comes
off as exceedingly arrogant. That aside, there is an implicit judgment made in
the post that STEM subjects are inherently more intellectual, more legitimate,
and more important than social fields and issues like feminism.

Unfortunately, having glanced at a few other posts on that blog, I feel like
the world would be a better place if the author had studied something like
sociology.

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Herring
There is something seriously wrong with the 'weeding out' mentality, in the
hard sciences. I can't tell if its hazing, or some superiority complex. You
end up with very hard boring work & teachers not being able to teach or
willing to help, and everyone thinking 'If you are good you will figure it out
yourself'. Hey, maybe math is hard, but you're not making it any easier & if I
see a better opportunity I'll take it in a heartbeat.

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aweSummer
I think Math is easier than Science. The formula is there, you just have to
solve it, done. It's always been my favorite subject.

~~~
derleth
That isn't how math is done at a high level. That is mechanical rote
computation, which in higher-level courses and in the real world is done by
computers.

Real math is all about, roughly, creating the formulas that the software will
use, which means you have to prove that the formula is both logically correct
and does what you want to do. It's a creative act.

If you remember nothing else, remember that high-level math is creative.

