Some subscribers to Phys-L might be interested in
a discussion-list post "Re: A Question: Where
Does Current Reform Come From? " [Hake (2011)].
The abstract reads:
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ABSTRACT: Joshua Fisher (2011) in his Math-Teach
post "A Question: Where Does Current Reform Come
From?" wrote (paraphrasing): "How does one enable
middle school kids to know the formula for the
area of a sphere as required by the standards? .
. . .So just give it to 'em, right? Yet, my
supervisor tried to avoid this consequence. My
question is . . . . "What is the incentive to
promote Not Telling over Telling?"
For physics education, Fisher's last question
might be better posed as "What is the incentive
to promote "Interactive Engagement" (IE) over
"Direct Instruction" (DI). The answer is that
over 40-years worth of physics education research
has demonstrated that IE is far more effective in
promoting students' conceptual understanding of
physics than DI.
I suspect that a similar statement might be made
for math education, but except for the work of
Jerry Epstein (2007) at <http://bit.ly/bqKSWJ>,
there's been little, if any, pre- to post-course
testing of math concepts. Thus math educators
have little information on the relative
effectiveness of IE and DI courses in promoting
conceptual understanding.
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"I point to the following unwelcome truth: much
as we might dislike the implications, research is
showing that didactic exposition of abstract
ideas and lines of reasoning (however engaging
and lucid we might try to make them) to passive
listeners yields pathetically thin results in
learning and understanding - except in the very
small percentage of students who are specially
gifted in the field."
Arnold Arons in "Teaching Introductory Physics" (p. vii, 1997)
REFERENCES [URL's shortened by <http://bit.ly/> and accessed on 26 June 2011.]
Arons, A.B. 1997. "Teaching Introductory
Physics." Wiley. Amazon.com information at
<http://amzn.to/bBPfop>. Note the searchable
"Look Inside" feature.
Hake, R.R. 2011. ""Re: A Question: Where Does
Current Reform Come From? " AERA-L archives at
<http://bit.ly/iHzGwm>. Post of 26 Jun 2011
15:07:50-0700 to Math-Teach, AERA-L, and NetGold.
The abstract and link to the complete 19 kB post
are being transmitted to various discussion lists
and are also on my blog "Hake'sEdStuff" at
<http://bit.ly/izN28y> with a provision for
comments.