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Re: Can Education Research Be "Scientific"? What's "Scientific"? (was "in Defense of. . . .")
Posted:
Nov 1, 2012 6:10 PM
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On Nov 1, 2012, at 3:44 PM, Richard Hake wrote:
> Some subscribers to MathEdCC might be interested in a recent post
> "Can Education Research Be 'Scientific'? What's 'Scientific'? (was
> 'in Defense of. . . .') " [Hake (2012)].
Because I think highly of Hake but do not understand at all his
position with respect to research in mathematics education, I read his
<http://bit.ly/Ujaogk> in toto. Not easy reading but here are my
reactions.
(1) First a disclosure: I am not a physicist but, in a first life, was
an All But Dissertation in (Fluid) Mechanics and, in a second life, an
All But Dissertation in Category-Topoi Theory. As such, I would say
that the difference between Physics and Mathematics, as subject
matters, is immense which in turn goes a long way towards explaining
why Research in Physics Education exists and produces results (E.g.
Hestenes) while Research in Mathematics Education does not and cannot:
(i) Physics HAS an experimental component which needs to be part of
the learning of Physics. That experimental component in turn has to be
taken care of by Physics Education. Moreover, the experimental
component MUST be reconciled with the theoretical component, both by
Physics Researchers and Physics Educators.
Mathematics on the other hand does NOT have an experimental
component. Mathematics is all on paper even if it is ABOUT the real
world---but not much in the way Physics is. Mathematics Education then
can only deal with what happens on paper.
(ii) Another major difference is that the learning of Mathematics
starts at the Piaget pre-operational stage, roughly somewhere around
5---even if it often has to restart at the age of 18 or later in
Developmental Mathematics courses---while Physics starts much later,
roughly at the Piaget Concrete Operational Stage. So while the
learning of Mathematics, a logic based discipline, starts way before
the students have reached the Formal Operational---aka hypothetico-
deductive---stage, the learning of Physics, at least its experimental
component, starts when the students are at a stage where
experimentation makes complete sense.
(2) What I find striking is that, in all this discussion, not a single
example has been examined, or even advanced or even mentioned. The
only one is BOX 5-5 Elementary School Students and Ratio and
Proportion which I quoted from the NRC on October 27, 2012 11:45:37
AM EDT.
So let me take an example. Let us say we are trying to decide which of
"lecture" or "reading pencil in hand with access to a mathematically
enabled person" works better in a given situation. Do we need a lot of
experimentation and then statistics or can we decide on just the basis
of an argument as in the case of the elephants and the eagles? I would
claim the latter, arguing that students in a lecture are essentially
passive which therefore leaves them with memorization as only means
while extracting information and understanding from a mathematical
text pencil in hand is extremely active and enables the students to
reconstruct things whenever memory does not serve.
And here is where the first of the above mentioned difference comes
in: Physics cannot be, and I think never has been, taught as lecture
only, the reason being that its "experimental component" cannot be
ignored. Mathematics on the other hand can very well be, and is still
overwhelmingly, taught ex-cathedra. Consider, for instance, how
research mathematicians learn (more) mathematics. Yes, they go to
meetings and attend lectures. But, as any working mathematician will
tell you, that is not where the action is and very few are still awake
after the first five or ten minutes of a talk.
In fact, to my mind, a great part of the "developmental math" disaster
originates in that, one way or the other, we mostly lecture---even if
with occasional pseudo discussions.
I would be curious to see specific examples being discussed in the
context of mathematics education research but I think that they will
be hard to find.
(3) I have only "speed-read" Hake's <http://www.physics.indiana.edu/~sdi/ajpv3i.pdf
> but it seems quite convincing to me if only because it does not
seem to cover up anything, e.g. does not use educando jargon.
(Disclosure: I am statistics-challenged.)
My conclusion then is that, while Hake seems well aware of the
educational problems in Physics and familiar with the research dealing
with these problems, this is not quite the case when it comes to
Mathematics where he seems to think that the issue remains, at least
roughly, the same. Which is probably why he disagreed with Greeno
so ... intensely.
Regards
--schremmer
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