
Mathematical Education (1990) - slbenfica
https://arxiv.org/abs/math/0503081
======
edtechdev
There is actually a whole field of research on mathematics education. I'm sure
this 28 year old essay is nice, but probably the most up to date and
comprehensive guide to evidence-based teaching of college math is this free
Instructional Practices Guide from the MAA: [https://www.maa.org/programs-and-
communities/curriculum%20re...](https://www.maa.org/programs-and-
communities/curriculum%20resources/instructional-practices-guide)

For K-12 math education, I haven't been keeping as close an eye, but there are
several books and resources, such as work by Jo Boaler:
[https://www.youcubed.org/resource/books/](https://www.youcubed.org/resource/books/)

~~~
curuinor
Math education research is not math research: it's education research, which
is among the worst among social science, which is among the worst of all
sciences in evidentiary practices. There are almost no valid RCT's in
educational research by the standards of non-social science researchers. My
own impression is that folks who publish on this sort of thing and not
mathematics, like education and do not like mathematics per se.

I've read Boaler's stuff. I agree mostly in form with RJ Milgram's attack on
her claims, which basically accuse her of statistical incompetence.

It is possible to be a great research mathematician and to be an awful
mathematics teacher. It is not possible to teach great research mathematics
without being a great research mathematician. I also do not believe it
possible to inculcate in younger students an enduring love of mathematics
without having oneself an enduring love of mathematics.

~~~
drjesusphd
> It is not possible to teach great research mathematics without being a great
> research mathematician.

I'm not sure it makes any sense to talk about "teaching research mathematics".
If it's research mathematics (as in, discovering new math), it should not and
cannot be done in a classroom setting.

With that in mind, it is certainly possible to be a good math teacher while
being a poor or mediocre researcher. Their students are probably not be
prepared for an academic math career, but they can walk away with a solid
understanding of established mathematics nonetheless.

~~~
watwut
I mean, if we are talking about teaching elementary school, then you don't
need to be world class researcher to get them ready for next level. You need
to like math and, imo, you need to like problem solving, you need to
understand math instead of having it memorize etc.

However, you definitely don't need to be actual researcher. I would even argue
that it will be more beneficial to study psychology, child development, child
behavior etc then spending time doing serious math research.

~~~
drjesusphd
I'm not talking about elementary school, I'm talking about masters or
bachelor's level advanced mathematics that has nonetheless been established
for decades or centuries.

All I'm saying is that teaching and researching are different skill sets. One
does not prepare you for the other except indirectly, nor is one a
prerequisite for the other. One could just as easily say some pedagogy is
required to communicate original research. It's true to an extent, but you
don't need to be a excellent teacher to be an excellent researcher, or vice
versa.

~~~
watwut
Boaler work is all about children, so I interpreted it in that context. I
mostly agree with you.

------
sykh
This is a nice article. I teach mathematics at a community college and the
last section of article resonated with me. What can we do about education of
mathematics to improve it?

Years ago it dawned on me that most of the students taking a class of mine
needed the class so that they could take physics. It’s been a long time since
I took physics and I don’t really know what math problems students in physics
classes have. I went to the physics department and asked for a list of types
of mathematical mistakes that are common. Give me the list and I’ll make sure
I emphasize this in my classes. No response.

I’ve since learned that what my students really need to know to be successful
in physics really isn’t covered in course that is a prerequisite. I’m not
really sure why I teach the topics I’m required to cover. They mostly are to
give my students enough knowledge to take calculus and almost none of them end
up taking calculus. I think things are done the way they are because it’s
always been done this way.

Change is slow and hard.

~~~
analog31
>>> I went to the physics department and asked for a list of types of
mathematical mistakes that are common.

A couple of ideas. First, ask the students. Second, see if you can join in the
grading of physics exams, as an observer.

20 years ago, I spent a semester as an adjunct, teaching electrodynamics in
the electrical engineering department at a big university. The same semester,
I also taught two sections of the freshman college algebra course.

I'm going to make some educated guesses here. The math that's used in physics
isn't really high level, but because you're using math en route to something
else, you have to be fluent enough that it's not an obstacle to understanding
the physics concepts. So for me, just being able to crank through algebraic
manipulation using odd symbols _and getting it right_ were important.

My EE students used a handful of basic differential equations that were
actually given short shrift in the math curriculum, namely simple linear
equations that are conveniently solved using complex exponentials. An example
would be any kind of wave phenomena. Being able to bounce back and forth
between time space and frequency space got my EE students hung up.

I agree with you about the college math topics. As I understand it, certain
topics have to be covered in order to meet the accreditation requirements,
which makes it hard to develop new curriculum at the lowest levels where it's
the most needed.

I think that for students who aren't going to be STEM majors, I'd rather spend
the same course time getting them fluent with Excel. That's how they're going
to do math anyway.

------
CliffStoll
That's _the_ Bill Thurston! He's the guy that practically invented low-
dimensional topology. He sewed up the entire field of foliation theory, and
showed that most knots are hyperbolic. He won the Field's Medal ... he's
someone to listen to!

~~~
ocfnash
And I believe this is _the_
[https://en.wikipedia.org/wiki/Clifford_Stoll](https://en.wikipedia.org/wiki/Clifford_Stoll)
!

~~~
fapjacks
HFS! I just watched the Numberphile video literally today with those two
_incredible_ wire memory, oscilloscope display calculators from the 60s. What
a phenomenal piece of engineering! Cliff needs his own channel. I could listen
to him talk all day.

------
ocfnash
In this context I highly recommend Lockhart’s Lament:
[https://www.maa.org/external_archive/devlin/LockhartsLament....](https://www.maa.org/external_archive/devlin/LockhartsLament.pdf)

~~~
toomanybeersies
I was actually expecting this when I clicked on the post. I don't think that
Lockhart's criticisms are unique to mathematics, I think it's an endemic
problem with the educational system.

Music is more or less taught as Lockhart describes in in the musicians
nightmare. Art education isn't quite that dire, but it's close.

If you can't use a standardised test to evaluate somebody in a subject, it's
of no value to the educational system.

~~~
ocfnash
I completely agree (though it is some years since I was at school).

Still, as Lockhart points out: _at least art and music are recognised as
arts_. Surely even the ropiest music and art educations at least admit that
these arts are:

    
    
      1. ends in themselves, because
    
      2. they are beautiful.
    

I believe these opinions are entirely absent from most mathematics education.

~~~
toomanybeersies
Maybe I was asleep in the class, but I think they skipped this part for
English Literature.

------
rowaway93
> Mathematics education is in an unacceptable state

it's not halting?

------
codermonkey2245
The following quote from the paper in my opinion applies to coding interview
tests:

"The competitions reinforce the notion that either you ‘have good math genes’,
or you do not. They put an emphasis on being quick, at the expense of being
deep and thoughtful. They emphasize questions which are puzzles with some
hidden trick, rather than more realistic problems where a systematic and
persistent approach is important"

~~~
ItsMe000001
Decades ago when I was in school, East Germany's "polytechnical" 10 year
elementary school they sent me to "Mathe-Olympiaden" (at least county-level
math contests) and to after-school math courses because they thought I had
talent. Maybe I did, but when I saw the tasks they gave us, and when I saw how
the others solved it I simply stopped caring and just wasted time. We got a
nice food bag with sweets and the day off school, that was good enough for me.

For example, loooong before we ever heard anything about this mathematical
field, and this was way before the Internet so unless somebody tells you about
something you have no chance of having heard about it as a young kid, we got a
combinatorics question. Everybody in the room started writing down every
single combination - which is why I knew what they were doing, neat columns
and rows filling several pages that could only have been for this particular
problem, and I had _almost_ started doing the same. I thought it was WAY
beyond silly that I should spend my time on this problem. I knew how to solve
it in this simple fashion, there was no chance to come up with the _real_
solution on the spot, so I switched to "annoyed" mode and gave up.

The after-hours math club wasn't much better, nothing deep or substantial,
just some riddles.

TODAY I'd just go to Khan Academy, edX, Coursera and ignore my teachers. The
Internet is great. Oh and cat pictures.

