On Mar 19, 3:37=A0pm, Dom <DR...@[EMAIL PROTECTED]
> wrote:
> http://www.maa.org/devlin/devlin_03_08.html
As I see it, Paul Lockhart's essay, which is at:
http://www.maa.org/devlin/LockhartsLament.pdf
would be much more powerful if it were not written in such a complete
historical vacuum. Although Lockhart decries the sterile formalism in
which mathematics courses have been and continue to be taught, he
makes absolutely no reference to the fact that the traditional
mathematics curriculum was demolished by the excessive formalism and
abstractions of the SMSG new math, as incor****ated in the Houghton
Mifflin series of books co-authored by Mary P. Dolciani. This apparent
ignorance on Lockhart's part is likely due to the fact that he was
educated with Dolciani-type books, and he may not be aware of the
preceding textbooks.
The manner in which Lockhart ridicules Thales' Theorem (which he does
not name), on page 19 of the PDF file, is utterly unacceptable--and it
raises serious questions about the rest of his lament about Euclidean
Geometry. When I studied 10th-grade Euclidean Geometry in 1963-64, at
Everett High School, in the factory city of Everett, MA, we used the
textbook by William G. Shute, William W. ****rk, George F. ****ter,
"Plane and Solid Geometry," American Book Company (1960). On page
25-27, the textbook contains a historical Note about Thales (640-546
B.C.), Thales' demonstration that all vertical angles are equal
(considered to be the first theorem ever proved), deductive reasoning,
and the components of a proof of a theorem. According to the Note,
when Thales visited Egypt, he observed that whenever the Egyptians
drew two intersecting lines, they would measure the vertical angles to
make sure that they were equal. Thales concluded that one could prove
that all vertical angles are equal if one accepted some general
notions such as:
1. all straight angles are equal
2. equals added to equals are equal, etc.
At the top of page 10 on the PDF file, Lockhart writes: "So put away
your lesson plans and overhead projectors, your full-color textbook
abominations, your CD-ROMs and the whole rest of the traveling circus
freak show of contem****ary education, and simply do mathematics with
the students!" Although this advice is quite sound, it is unfortunate
that Lockhart conveniently makes absolutely no reference to the fact
that all this rubbish has been produced and promoted by the self-
styled math reformers of the past two decades.
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