John Clement (2007), in his PhysLrnR post of 7 Feb 2007 titled
"Letter in latest AJP " wrote [bracketed by lines "CCCCCC. . . . .";
my insert at ". . . .[insert]. . . ."; my CAPS; slightly edited]:
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I noticed the letter . . . .[Klein (2007)]...... in the latest
American Journal of Physics (AJP) written by a mathematician. .
.[David Klein <http://www.csun.edu/~vcmth00m/>]. . . . While I
cannot comment on the particular curricula that he castigates, THE
PROBLEM IS THAT HIS COMMENTS REPRESENT ONE SIDE OF THE MATH WARS. I
HOPE THAT AJP WILL BE PUBLISHING A LETTER FROM THE OTHER SIDE.
The disturbing thing about the letter is his use of automaticity.
This is the rallying cry of the conservative math educators. These
same math educators also advocate the types of things that Physics
Education Research has found to be ineffective. Automaticity leads
to mindless application of procedures, often when they are
inappropriate. Reflection and cognition are often sacrificed in the
goal of achieving automaticity.
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Instead of contributing still further to "The Needless War Between
Traditionalists and Progressives" [Bickman (2004)], I would hope
that AJP might consider publishing an editorial proposing a "Math
Wars Peace Treaty," as proposed by Berkeley's Phil Daro (2003).
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Even though the. . . [math]. . . wars rage, partly because there are
some true believers on both sides and partly because some stand to
profit from the conflict, I remain convinced that there is a large
middle ground. I believe that the vocal extremes, partly by screaming
for attention and partly by claiming the middle ground ("it's the
other camp that is extreme"), have exerted far more influence than
their numbers should dictate.
One way to reclaim the middle ground, suggested by Phil Daro (2003),
is to define it clearly-to specify a set of propositions that will
call for some degree of compromise from reformers and traditionalists
alike. That middle ground would be broadly encompassing, containing
propositions that most people would find reasonable (or at least
livable). Daro offered a draft "Math Wars Peace Treaty" (or perhaps
"Math Wars Disarmament Treaty") that includes the following
stipulations:
WE HAVE AMONG OURSELVES VARIOUS AGREEMENTS AND DISAGREEMENTS. BUT
ABOUT THESE THINGS WE AGREE:
a. The status quo is unacceptable. Its defenders are wrong,
mathematics instruction must improve.
b. Teachers, especially K-8 teachers, should learn more mathematics
throughout their careers.
c. No students should be denied a fair chance to learn mathematics
because they have been assigned unqualified mathematics teachers.
d. All students should have a copy of the basic instructional
materials (textbooks, handouts, etc.) to take home.
e. Research and evidence should be used whenever it is available to
inform decisions.
WE ALSO AGREE THAT STUDENTS SHOULD LEARN TO:
f. add, subtract, multiply, and divide single-digit numbers
automatically and accurately;
g. add, subtract, multiply, and divide integers, decimals, and
fractions accurately, efficiently, and flexibly without calculators;
h. understand the mathematics they study and use;
I. use the mathematics they know to solve problems with calculators
and computers;
j. be fluent with the symbolic language of algebra and understand
how to use the basic laws of algebra when solving mathematics
problems;
k. explain and justify their reasoning and understand the reasoning of others;
l. reason with increasing rigor and mathematical maturity as they
advance through the curriculum.
The hope is that if such a list is put together well, most people
will feel comfortable with most of it and be willing to part with a
few things they would rather keep in the interests of making peace
and working together in the interests of our children. If so, those
who refuse to sign on will reveal themselves for the extremists they
are.
It is not clear how optimistic one should be. There already exist
documents that appear to have some consensus behind them: e.g., . . .
. .[CBMS (2001), NCTM (2000), Kilpatrick et al. (2001)]. . . The
tactic of the extremists has been to ignore such volumes and to
attack what they can attack. To date, they have been fairly
successful.
Not only have some of THE MAJOR STATE BOARDS (TEXAS AND CALIFORNIA,
FOR EXAMPLE) MADE THE TRADITIONAL CHOICE but current federal
legislation (e.g., the No Child Left Behind Act of 2001 . . .[USDE
(2007)]. . .) puts substantial force behind rather narrow and
traditional assessments as well. Moreover, much of the public, ill
served by media that seek to profit from conflict, sees curriculum
choice as dichotomous-it is either traditional or reform. At the same
time, there are grounds for some optimism. At the college level,
"calculus reform" stimulated a great deal of controversy but then
settled in as part of the mainstream. The same may well happen with
regard to standards-based mathematics. One cannot simply turn the
clock back; too much is known about mathematical thinking and
learning.
Despite extremist proposals (and mandates), there is a rational
middle ground, and many teachers seek it. . . . . . The short-term
goal, however, must be to capture the middle ground for the majority.
Efforts must be made publicly to identify the extremists for what
they are and to marginalize them. THE MATH WARS HAVE CASUALTIES-OUR
CHILDREN, WHO DO NOT RECEIVE THE KIND OF ROBUST MATHEMATICS EDUCATION
THEY SHOULD.
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REFERENCES [Tiny URL's courtesy <http://tinyurl.com/create.php>.]
Bickman, M. 2003. "Minding American Education: Reclaiming the
Tradition of Active Learning," Teachers College Press; for a
description see <http://www.mindingamericaneducation.com/>. Winner
of the "Outstanding Book Award," 2003 from the Curriculum and
Curricular Studies Division of the American Education Research
Association.
Bickman. M. 2004. "Won't You Come Home John Dewey?" Los Angeles Times
OpEd piece, online on the Dewey-L archives at
<http://tinyurl.com/3bzl7c>. Originally more meaningfully titled
"The Needless War Between Traditionalists and Progressives and How to
End It," but retitled by the LA Times OpEd editor [God save us from
such!]. Bickman wrote: "American education has seemed more like a
battleground between warring factions than an evolving and cumulative
field of increasingly refined concepts and methods." See also Bickman
(2003).
CBMS. 2001. Conference Board of the Mathematical Sciences. "The
Mathematical Education of Teachers: CBMS Issues in Mathematics
Education." American Mathematical Society. Amazon.com information at
<http://tinyurl.com/2fgl2g>. Note the "Search inside this book"
feature.
Clement, J. 2007. "Letter in latest AJP " PhysLrnR post of 7 Feb 2007
23:07:02 -0600; online at <http://tinyurl.com/2z7tks>.
Daro, P. 2003. "Math Wars Peace Treaty," Manuscript in preparation.
See also Daro (2007).
Kilpatrick, J., J. Swafford, & B. Findell, eds. 2001. "Adding It Up:
Helping Children Learn Mathematics," Mathematics Learning Study
Committee, National Research Council, National Academy Press, online
at <http://books.nap.edu/catalog/9822.html>.
Klein, D. 2007. "School math books, nonsense, and the National
Science Foundation," Am. J. Physics 75(2): 101-102; a preprint of
the published version is online at
<http://www.csun.edu/~vcmth00m/nsf.html>; the published version is
online to AJP subscribers (or for $19 to non-subcribers) at
<http://tinyurl.com/2qvjxq> (but the references only are free to all
at that URL).
NCTM. 2000. National Council of Teachers of Mathematics. "Principles
and standards for school mathematics," information at
<http://standards.nctm.org/>, including 120 day free access to
document.
Schoenfeld, A. H. 2004. "The Math Wars," Educational Policy 18(1):
253-286; online at
<http://gse.berkeley.edu/faculty/AHSchoenfeld/Schoenfeld_MathWars.pdf>
(160 kB). For Schoenfeld's dim view of the machinations of math
warrior David Klein, use the binocular icon to search for "Klein"
(without the quotes).