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Re: Math Education Research Doesn't Exist? Response to Schremmer
Posted:
Nov 7, 2012 11:45 AM
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I am not going to bottom post because I do not want to start
(continue) a discussion that I think would be time consuming but
leading nowhere. Still, I would like to expound on a few things.
(1) When I was first confronted with Physics---as opposed to
Mechanics, I indeed had to copy the book that the instructor was
writing on the board and which he was reading aloud while writing. At
the time---the early fifties (in France), none of us even knew what
lecturing was (there is in fact no equivalent term in French) but, in
retrospect, I don't see that this qualified as lecturing. However, we
did have labs even if it was left to us to make the connections
between "the book" and what we were doing in the labs. I will be the
first to concede that this was not exactly efficient but the labs did
exist which was more than could be said about our mathematics classes
in which, there too, all we would do was to copy "the book" from the
board.
(2) But I should also say that, each week, both in Physics and in
Mathematics, we were given a long multi-stage problem which we often
did "collectively", that is a few friends would get together and start
on the problem: after a while, someone might say "OK, I can prove aaa
but I cannot get anywhere further". A bit later, someone else might
then say "If someone can prove mmm, then from that I can prove ttt".
This would continue, sometimes for several evenings and, with a bit of
luck we might get to a point where we felt that all the pieces
together settled the problem. Then, each one of us, separately, would
write up the "solution" and hand it in.
(3) As it turns out, I found out about Hestenes a few years ago
because one of our sons, a PhysicIAN, came across his Geometric
Algebra and brought it to our attention---my wife is a real (=
research) mathematician (As for me, I have long given up). Even though
I didn't have the time to really read it, that is pencil in hand, I
was absolutely fascinated---and, occasionally read a bit more of the
book. And then I came across the Oersted Lecture in which I found
common grounds: I too think that "[That c]ourse content is taken [by
many] as given [...] ignores the possibility of improving pedagogy by
reconstructing course content." In fact, my very first publication,
1965, already was about course contents as a means to better
understanding. And, our experiences with the NSF were strikingly
similar.
(4) I "speed read" Hestenes' MODELING GAMES IN THE NEWTONIAN WORLD(*)
and it is a masterful analysis to which I wish I could put my name.
But I would not call it "research in physics education". Another one
of my heroes is Z.P. Dienes who developed "games" for, say, third
graders that provide a deep understanding in logic and in the ways to
code whole numbers. But Dienes never bothered, rightfully so, to check
statistically that eagles fly better than elephants. As such, I would
not call it "research in mathematics education". And, if I may allude
to my own work, I would never call it "research in mathematics
education" either and for the same reason. Finally, one reason that
Piaget's work is not really recognized in this country is that he too
did not bother with statistical validation. But then he also kept
repeating that: a) Whatever it was he was doing---he called it genetic
epistemology---was NOT psychology and b) that it had NO application to
education.
(*) All figures were missing.
(5) Trying to find ONE piece of actual "research in mathematics
education", I opened:
<http://www.maa.org/features/rumec.html> Usual MAA stuff. Not actual
research.
<http://gse.berkeley.edu/faculty/ahschoenfeld/ahschoenfeld.html> The
complete works of Schoefeld but impossible to access anything. Seems
to me, though, to be all ABOUT "research in mathematics education".
I will also mention
<http://83.212.201.83:8080/ltme/uploads/users/4/publications/Chronaki_2011_Atweh_etal_Book_Chapter.pdf
>
published by no less than Springer:
<http://www.springerlink.com/content/978-90-481-9803-0?MUD=MP>
but ... really ... . Disclosure:
<http://www.freemathtexts.org/ChapterThirteen.php>
I have long been impressed by Atherton's
<http://www.doceo.co.uk/original/learnloss_1.htm>
who dealt with what I consider a major problem in so-called
developmental education but "researchers in mathematics education"
seem completely unconcerned with the issue and of course dismiss
Atherton's article as amateurish. A very great shame.
Last, but certainly not least: The calculus concept inventory.
<http://math.unipa.it/~grim/21_project/
21_charlotte_EpsteinPaperEdit.pdf>
"The idea of such a test follows the Force Concept Inventory (FCI) in
physics (Halloun and Hestenes, 1985a, b, Hake et al 1998a, b)" It
seems most interesting. This is probably the closest I have seen to
what I would call "Research in mathematics education" and I emailed
Epstein on Nov 1 to get a copy but, so far, got no response.
(6) So, what does all this amount to? Yes, there is research in
mathematics education---David Tall's comes to mind but it is
invariably dealing with isolated pieces of mathematics---and so should
probably be called "research in piecewise mathematics education". The
reason, as Greeno mentioned recently, is that pieces of mathematics is
really all that most of these researchers know so that they cannot
focus on what makes mathematics---as opposed to math, namely the
connective tissues---along which learning mathematics proceeds. But
then, maybe Greeno (and myself) is asking for the impossible.
Regards
---schremmer
P.S. With all due respect, I think that the discussion on "the six
principles" should be closed and so I will abstain.
On Nov 6, 2012, at 5:30 PM, Richard Hake wrote:
> Some subscribers to MathEdCC might be interested in a recent post
> "Math Education Research Doesn't Exist? Response to Schremmer" [Hake
> (2012)]. The abstract reads:
>
> ****************************************
> ABSTRACT: MathEdCC's Alain Schremmer at <http://bit.ly/VNUvPV>
> opined that: (a) research in mathematics education does not exist;
> (b) physics cannot be taught as lecture only; (c) Hake (2002b) at <http://bit.ly/VtXvAV
> > disagreed with Greeno (2002a) at <http://bit.ly/T64H49> because
> Hake is unfamiliar with math education and thinks its problems are
> similar to those in physics education.
>
> I argue in opposition to the above that:
> (a) Research in mathematics education *does* exist, see e.g., the 18
> entries preceded by double asterisks ** in the REFERENCE list of my
> *complete* post at <http://bit.ly/U7dJi3>.
>
> (b) Physics *has been* taught essentially as lecture only (where
> *taught* does not mean *learned*), witness the fourteen
> "traditional" (T) courses (N = 2084) in Hake (1998a) at <http://bit.ly/9484DG
> >.
> (c) I disagreed with Greeno, *not* because of my unfamiliarity math
> education, but because Greeno denounced as "glibly superficial and
> badly unknowing about the nature of science" the six guiding
> principles suggested in "Scientific Research in Education" at <http://bit.ly/VjrQaV
> >, as underlying all education research; whereas I think those
> principles *are* consistent with the nature of science as I have
> experienced it and as has been explained by Ziman (2002) at <http://bit.ly/VtdoHR
> >.
> ****************************************
> To access the complete 21 kB post please click on <http://bit.ly/U7dJi3
> >.
>
>
> Richard Hake, Emeritus Professor of Physics, Indiana University
> Links to Articles: <http://bit.ly/a6M5y0>
> Links to Socratic Dialogue Inducing (SDI) Labs: <http://bit.ly/9nGd3M>
> Academia: <http://bit.ly/a8ixxm>
> Blog: <http://bit.ly/9yGsXh>
> GooglePlus: <http://bit.ly/KwZ6mE>
> Twitter: <http://bit.ly/juvd52>
>
> "He . . . .[or she]. . . . that wrestles with us strengthens our
> nerves, and sharpens our skill. Our antagonist is our helper."
> Edmund Burke (1790)
>
>
> REFERENCES [URL shortened by <http://bit.ly/> and accessed on 06 Nov
> 2012.]
> Burke, E. 1790. "Reflections on the Revolution in France."
> Available as a 2006 edition by Dover; Amazon.com information at <http://amzn.to/c4wbfS
> >. Online at <http://bit.ly/WwBMOQ> thanks to McMaster University,
> See also the Wikipedia entry at <http://bit.ly/hMaGfn>.
>
> Hake, R.R. 2012. "Math Education Research Doesn't Exist? Response to
> Schremmer," online on the OPEN! AERA-L archives at <http://bit.ly/U7dJi3
> >. Post of 6 Nov 2012 11:12:48-0800 to AERA-L and Net-Gold. The
> abstract and link to the complete post are being transmitted to
> several discussion lists and are also on my blog "Hake'sEdStuff" at <http://bit.ly/YTQzk0
> > with a provision for comments.
>
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