Some subscribers to Phys-L might be interested in a recent post "Do
We Learn All the Math We Need For Ordinary Life Before 5th Grade?"
[Hake (2013)]. The abstract reads:
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ABSTRACT: In response to my post "Einstein on Testing" [Hake (2013)]
at <http://bit.ly/UHjqET> the following lively exchange was recorded
on the archives <http://yhoo.it/iNTxrH> of EDDRA2 [non-subscribers
may have to set up a "Yahoo account" as instructed at
<http://yhoo.it/iNTxrH>]:
a. Literature major and Standardista-basher Susan Ohanian
<http://www.susanohanian.org/> stated that she (paraphrasing) "never
seemed to gain any insight from solving the calculus problems in
Courant's text, which struck her then as plodding and now as without
meaning."
b. Susan Harman then opined (my CAPS) "WE LEARN ALL THE MATH WE NEED
FOR ORDINARY LIFE BEFORE 5TH GRADE."
c. Guy Brandenberg countered by calling attention to David
Berlinski's "Tour of the Calculus" <http://amzn.to/11sZIUv> whose
publisher states: "Were it not for the calculus, mathematicians would
have no way to describe the acceleration of a motorcycle or the
effect of gravity on thrown balls and distant planets, or to prove
that a man could cross a room and eventually touch the opposite wall."
d. Then Susan Ramlo pointed out that students in her algebra-based
physics class "almost always make a comment about how suddenly . .
.[[after exposure to the *real-world* of physics]]. . . much more of
calculus makes sense."
With regard to Harman's opinion that "We Learn All the Math We Need
For Ordinary Life Before 5th Grade," basic to "ordinary life" is
motion and change, requiring the rudiments of calculus for proper
understanding (see the Bartlett signature quote).
And I agree with Ramlo's point about students' better understanding
calculus after exposure to the *real world* of physics. In
"Interactive-engagement methods in introductory mechanics courses" at
<http://bit.ly/aH2JQN> I wrote: "the term 'substantive
non-calculus-based mechanics course' is an oxymoron."
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"The greatest shortcoming of the human race is our inability to
understand exponential change."
- Albert Bartlett <http://bit.ly/VpN2pm> [I have taken the
liberty of substituting
"exponential change" for Bartlett's more esoteric "the
exponential function."]
REFERENCES [URL shortened by <http://bit.ly/> and accessed on 13 Jan 2013.]
Hake, R.R. 2013."Do We Learn All the Math We Need For Ordinary Life
Before 5th Grade?" online on the OPEN! AERA-L archives at
<http://bit.ly/10sYmKl>. Post of 13 Jan 2013 16:52:01-0800 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/RQkucu> with a provision for
comments.