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ABSTRACT: GS Chandy implied, in his Math-Teach post, that Alexander
Calandra's 1968 version of the "The Old Barometer Story" carried a
good moral for math teachers: recognize sound and creative "outside
the box" thinking rather than only pedantic thinking. But the rather
obscure last paragraph of Calandra's piece appears to carry the
opposite message. It seems likely that a Saturday Review editor may
have been responsible for both the last paragraph and the title
"Angels on the Head of a Pin: A Modern Parable."
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GS Chandy, in his Math-Teach post of 27 Feb 2008 titled "Free Versus
Pedantic Thinking," implied that Alexander Calandra's (1968) Saturday
Review version of the "The Old Barometer Story" carried a good moral
for math teachers. Chandy wrote [bracketed by lines "ChChChCh. . . .
."]:
ChChChChChChChChChChChChChChChCh
I've pasted what I believe is an excellent piece from "Cut-The-Knot".
. . .[<http://www.cut-the-knot.org/manifesto/thinking.shtml>]. . . .
that illustrates that it is entirely possible to think outside the
box in physics. Perhaps the story is *somewhat apocryphal*, perhaps
'made up' to an extent - but the moral of the story should be
understood by all teachers.
I believe there could be a parallel in math, and that math teachers
would do well to develop themselves to recognize sound (and creative)
thinking from their students as opposed to pedantic thinking with a
view to get high marks in exams.
ChChChChChChChChChChChChChChChCh
But the rather obscure last paragraph of Calandra (1986) seems to
convey an anti-"thinking outside the box" message. Calandra [or was
it the Saturday Review editor? - see Hake (2007b)] wrote:
CaCaCaCaCaCaCaCaCaCaCaCaCaCaCaCa
At this point, I asked the student if he really did not know the
conventional answer to this question. He admitted that he did, but
said that he was fed up with high school and college instructors
trying to teach him how to think, to use the "scientific method," and
to explore the deep inner logic of the subject in a pedantic way, as
is often done in the new mathematics, rather than teaching him the
structure of the subject. With this in mind, he decided to revive
scholasticism as an academic lark to challenge the Sputnik-panicked
classrooms of America.
CaCaCaCaCaCaCaCaCaCaCaCaCaCaCaCa
For my own take on Calandra's piece see "The Old Barometer Story (was
Tower height joke)" [Hake (2007a)]. The abstract reads:
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ABSTRACT: The Phys-L discussion list has recently resurrected the
"Old Barometer Story" (OBS) with a 7-post thread titled "Tower height
joke." As is typical of discussion lists, the subject is treated de
novo, even though it's previously been discussed ad nauseam on the
same list - in this case in the 100 or so OBS posts on Phys-L dating
from 1996. One of the recent Phys-L posts quotes Alexander
Calandra's 1968 "Saturday Review" version of the OBL, and with its
diatribe on the evils of the 1960's "new math," and suggests that
physics education researchers should take note. But there's nothing
worth noting in Callendra's vacuous screed - or was it the Saturday
Review editor's screed? How long will it be before an OBS story with
an "anti-new-new-math" (i.e., "anti-fuzzy-math") message appears at
the Mathematically Correct website
<http://www.mathematicallycorrect.com/>?
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SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
As a bit of humor it is nicely constructed. As a parable with a
moral, it falls flat. What is the author's point, one wonders? Is it
an argument against a particular kind of pedantry in teaching? Is it
a demonstration that exam questions can be subject to multiple
interpretations? Is it an example of how a clever student can find
ingenious ways to answer a question?
Just what is the difference between exploring "the deep inner logic
of the subject" and teaching "the structure of the subject."
Calandra doesn't make that difference clear, yet his student seems
not to like the first, but would rather have the second.
The title. . . . .["Angels on the Head of a Pin: A Modern Parable" -
omitted from the "Cut-The-Knot" version]. . . . . (which most people
forget) is a clue. Medieval scholastics were fond of debating such
meaningless questions as "How many angels can dance on the point of a
pin," "Did Adam have a navel," and "Do angels defecate." The emerging
sciences replaced such "scholarly" debates with experimentation and
appeals to observable fact. Calandra seems to be suggesting that
"exploring the deep inner logic of a subject in a pedantic way" is
akin to the empty arguments of scholasticism. He compares this to the
"new math," so much in the news in the 60s, which attempted to
replace rote memorization of math with a deeper understanding of the
logic and principles of mathematics, and he seems to be deriding that
effort also. So it still seems to me that we get no clear and useful
message from this essay.
On almost every level, this essay falls apart on critical analysis. I
wonder why it has become such a legend in the physics community?
SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
BTW: A search for "barometer" at the Math-Teach search engine
<http://mathforum.org/kb/search!default.jspa?advanced=true&forumID=206>
yielded 13 posts (not counting responses to those posts), dating from
1996, that mention the "Old Barometer Story" in one or more of its
various guises.
"Parents' organizations such as, 'Mathematically Correct,' 'New York
City Honest and Open Logical Debate,' and 'Where's the Math?' among
dozens of others, continue to resist the imposition of 'fuzzy math'
in their schools."
David Klein (2007) in (would you believe?) the American
Journal of Physics
"EDITOR: A person employed on a newspaper. . . [or journal]. . . ,
whose business it is to
separate the wheat from the chaff, and to see to it that the
chaff is printed."
Elbert Hubbard (1856-1915)
<http://en.wikipedia.org/wiki/Elbert_Hubbard>
REFERENCES
Calandra, GS. 1968 "Angels on the Head of a Pin: A Modern Parable,"
Saturday Review, 21 December; online, courtesy Donald Simanek, at
<http://www.xs4all.nl/~jcdverha/scijokes/2_12.html#subindex>; along
with [as of 10 Sept 2007] 132 mostly hair-brained ways to measure the
height of a building with a barometer, submitted by divergent
thinkers to Joachim Verhagen's science jokes page
<http://www.xs4all.nl/~jcdverha/scijokes/>.
Hake, R.R. 2007a. "The Old Barometer Story (was Tower height joke)," online at
<http://listserv.nd.edu/cgi-bin/wa?A2=ind0709&L=pod&P=R8382&I=-3>.
Post of 10 Sep 2007 15:04:13-0700 to Math-Teach, Math-Learn,
PhysLrnR, POD, and RUME. See also Hake (2007b).
Klein, D. 2007. "School math books, nonsense, and the National
Science Foundation," Am. J. Phys. 75(2): 101-102; online at
<http://www.csun.edu/~vcmth00m/nsf.html>.