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Re: NCLB: Benezet/Whitney Thinking



If you respond to this long post (18kB) please don't hit the reply
button (bane of discussion lists) unless you pare the original
message normally contained in your reply down to a few lines,
otherwise you will inflict the entire message yet again on all list
subscribers [see Hake (2004)].

Stimumalated by responses to Jerry Becker's (2004) seminal post
"NCLB: Benezet/Whitney Thinking," Timotha Trig (2004), in her
Math-Teach post of 12 Sep 04 titled "Re: NCLB: Benezet/Whitney
Thinking," gave a "bare URL" :-( reference to Hake (2002) and then
asked:

"Does 'R2' (below) indicate that that passage was written by Richard Hake?

R2-R2-R2-R2-R2-R2-R2-R2-R2-R2-R2-R2-R2-R2-R2-R2-R2-R2-R2-R2
R2. I disagree that "Related Article #7" has NOTHING to do with
Benezet's articles." Furthermore, that "some one called Arthur
Whimbey" is relatively well known in the U.S. math education
community and Whimbey's connection to Benezet (1935/36) is explained
below
. . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . "

The answer to Timothy's question is "YES, the passage was written by
Richard Hake."

Timothy apparently failed to carefully read the last sentence of the
third paragraph in the passage below [bracketed by lines
"HHHHHHHHHHH. . . . .; see that post for references other than
Dehaene (1997), Clement (of Massachusetts) et al. (1981), diSessa
(2000), and Lochhead (2000)]:

HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
I have set off most quotes by bracketing them with the authors NAME, as:

NAME-NAME-NAME-NAME-NAME-NAME-NAME-NAME-NAME-NAME-NAME-NAME
Name wrote "Blah, blah, blah."
NAME-NAME-NAME-NAME-NAME-NAME-NAME-NAME-NAME-NAME-NAME-NAME

In the recent Math-Learn thread "Arithmetic and Algebra," initiated
by Michael Paul Goldenberg's 29 Jan 2002 00:10:11-0500 post regarding
Andre Dehaene's (1997) conclusion that algebraic calculation and
arithmetic are processed in different brain regions, there have
recently been several interesting comments regarding the ground
breaking work of Louis Paul Benezet (1935/36). Some of the relevant
posts may be accessed by typing "Benezet" (without the quotes) in
the "Search Archive" slot at the primitive Math-Learn archives
<http://groups.yahoo.com/group/math-learn/>, for 10 hits as of 5
February 2002 8:00:00-0800 [cf. on 14 Sept 2004 13:00-0700: 55 hits
on Math-Learn for "Benezet" (without the quotes), and 272 on "Benezet
arithmetic" (without the quotes) on Google <http://www.google.com/>.
The following are *MY RESPONSES (R)* to four *MATH-LEARN COMMENTS
(C)* on Benezet:
. . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . .


C2-C2-C2-C2-C2-C2-C2-C2-C2-C2-C2-C2
REX BOGGS wrote on 1 Feb 2002 17:02:43+1000:


BOOGS-BOOGS-BOOGS-BOOGS-BOOGS-BOOGS
"The articles that I found fascinating . . . (at the Benezet Centre
<http://www.inference.phy.cam.ac.uk/sanjoy/benezet/>. . . . and I
suggested folks read if they were still following this thread, were
the three written by Benezet (1935/36) himself. Number 7 has NOTHING
to do with Benezet's articles. It . . . ("Related Article #7") . . .
relates to books by someone called Arthur Whimbey, probably written
after Benezet was dead. To what is his connection to the three
Benezet articles. . .(Benezet 1935/36)?
BOOGS-BOOGS-BOOGS-BOOGS-BOOGS-BOOGS

R2-R2-R2-R2-R2-R2-R2-R2-R2-R2-R2-R2
R2. I disagree that "Related Article #7" has NOTHING to do with
Benezet's articles." Furthermore, that "someone called Arthur
Whimbey" is relatively well known in the U.S. math education
community and Whimbey's connection to Benezet (1935/36) is explained
below.

Article #7 reads (CAPS indicate hot-linking):

"Material at <HTTP://WWW.WHIMBEY.COM>, especially the ALGEBRA-FREE
CHALLENGE. Just as calculators can turn mathematics into button
pushing, algebra can turn it into symbol pushing . . . [see, e.g.,
the classic Clement et al. (1981)]. . . . Solving problems without
algebra encourages graphical, visual methods of solution -- methods
that require thought."

Clicking on the above hot-linked <HTTP://WWW.WHIMBEY.COM>, yields the
web page of "Whimbey.com" where it is stated that: "We plan to post
here, from time to time, various items of interest to the users of
the many different books. . .
<http://www.whimbey.com/Books/books.htm>. . . by Arthur Whimbey and
his vast cast of co-authors . . . [see e.g., Whimbey & Lochhead
(1999), Whimbey et al. (1999), Lochhead (2000)]."

Whimbey and Lochhead are relatively well known in the U.S. for, among
other things, their contributions - very much in the spirit of
Benezet - to the heralded program SOAR (Stress On Analytical
Reasoning) <http://www.xupremed.com/a.SSA/soar.html> at Xavier, a
small historically black University in New Orleans [see, e.g.,
Lochhead (2000), pp. 3-5].

Clicking on the above hot-linked "ALGEBRA-FREE CHALLENGE" yields
<http://www.whimbey.com/Problems/problems.htm> where it is stated:

"If you send us a postal address we will mail you worked solutions to
these problems. These solutions are completely free of ALGEBRA
CONTAMINATION!" (My EMPHASIS.)]

What is the meaning of "ALGEBRA CONTAMINATION"? According to Jack
Lochhead (2001):

LOCHHEAD-LOCHHEAD-LOCHHEAD-LOCHHEAD-LOCHHEAD-LOCHHEAD
"The term 'algebra contamination' is not intended to be technical
jargon. It simply refers to the fact that the solutions (which can be
requested -though no one ever has) do not use algebra. They use
other, I think more transparent, means of mathematical thinking. . .
. diSessa (2000) . . . points out that Galileo did not know algebra
(it hadn't yet been invented) and really had to struggle to make his
arguments. The things Galileo had to work through are probably
exactly what we should be putting our introductory physics students
through. Only with algebra (like with calculators) the students can
get answers without really thinking. ACTUALLY THIS ALL TIES IN VERY
NICELY TO BENEZET (BUT THEN EVERYTHING IMPORTANT DOES).
LOCHHEAD-LOCHHEAD-LOCHHEAD-LOCHHEAD-LOCHHEAD-LOCHHEAD
. . . . . . . . . . . . . . . . . . . . . .
HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH


Timothy's post is a reminder that the same topics, in this case
Benezet, tend to be discussed over and over again on Discussion List
(DL's), each time starting from scratch with near total ignorance of
what's gone before on the part of many list subscribers.

As pointed out most recently in my post "Lively Listservs" [Hake (2003)]

HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
. . . . most DL's fail [paraphrasing Roschelle and Pea (1999)]:

"to move beyond forums for exchanging tidbits and opinions, to
structures which rapidly capture knowledge-value and foster rapid
accumulation and growth of the community's capability . . . providing
tools to allow contributors to share partially completed resources,
and enable others to improve upon them."

For example: some DL list owners impose draconian line limitations
that force subscribers into vacuous "sound bites"; some DL's do not
have archives or else have archives that are not easily searchable. .
. [such at Math-Learn, Math-Teach, and AP-Physics]; few DL
subscribers:

(a) even notice literature references in posts (except to inveigh
against them as "useless busy work"), let alone place them in their
posts;

(b) take advantage of hot linking - a prime capability of the internet;

(c) abide by common-sense posting suggestions [Hake (2004)] that
might facilitate efficient communication.
HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

Furthermore, some DL subscribers are vehemently opposed to
cross-posting, even though such is a good way to tunnel through the
disciplinary barriers, caused in part by the traditional departmental
structure of universities. The potential of the web as a mechanism
for promoting interdisciplinary synergy in education reform is
emphasized and schematically pictured on page 3 of the 204KB pdf at
<http://www.physics.indiana.edu/~hake/WhatLearn-013100g.pdf>.


Richard Hake, Emeritus Professor of Physics, Indiana University
24245 Hatteras Street, Woodland Hills, CA 91367
<rrhake@earthlink.net>
<http://www.physics.indiana.edu/~hake>
<http://www.physics.indiana.edu/~sdi>

"If once a man indulges himself in murder, very soon he comes to
think little of robbery; and from robbery he next comes to
Sabboth-breaking, and from that to incivility, procrastination. . .
and finally to cross-posting."
Thomas DeQuincy


REFERENCES
Becker, J. 2004. "NCLB: Benezet/Whitney Thinking," Math-Learn post of
5 Sept 2004 10:56 am; online at
<http://groups.yahoo.com/group/math-learn/message/6436>. Becker's
seminal post has thus far (14 Sept 2004 14:30-0700:) netted 55
responses on Math-Learn <http://groups.yahoo.com/group/math-learn/>
and 32 responses on Math-Teach
<http://mathforum.org/epigone/math-teach>. See also Hake (2004b).

Butterworth, B. 1999. "What Counts: How every brain is hardwired for
math." Free Press; especially Chapter 4 "Numbers in the Brain."

Clement, J., J. Lochhead, & G. Monk. 1981. "Translation difficulties
in learning mathematics," Am. Math. Monthly 88(4), 286-290 (1981);
online as "Related article #5" at the Benezet Centre
<http://www.inference.phy.cam.ac.uk/sanjoy/benezet/>: "To investigate
the source of the errors we had observed . . .(in translating
practical situations into mathematical notation). . . . we collected
data on the following simpler problem. . . "Write an equation for
the following statement: 'There are six times as many students as
professors at this university.' Use S for the number of students and
P for the number of professors. On a written test with 150
calculus-level students, 37 percent missed this problem, and
two-thirds of the errors took the form of a reversal of variables
such as 6S = P. In a sample of 47 non-science majors taking college
algebra, the error rate was 57 percent."

diSessa, A.A. 2000. "Changing Minds: Computers, Learning, and
Literacy" MIT Press.

Dehaene, S. 1997. "The Number Sense: How the Mind Creates
Mathematics" (Oxford University Press). See also Butterworth (1999).

Hake, R.R. 2002. "Arithmetic, Algebra, and Benezet (was Re:
Arithmetic and Algebra)," online at
<http://lists.nau.edu/cgi-bin/wa?A2=ind0202&L=phys-l&P=R13268> and
also
<http://mathforum.org/epigone/math-learn/thukhiskel/p05010400b886293d3dda@%5B209.179.245.25%5D>.
Post of 5 Feb 2002 20:46:00-0800 to Math-Learn, PhysLrnR, Physhare,
and POD.

Hake. R.R. 2003. "Re: Lively Academic Listservs," online at
<http://listserv.nd.edu/cgi-bin/wa?A2=ind0312&L=pod&P=R3771>. Post of
5 Dec 2003 16:02:18-0800 to POD, PhysLrnR, Phys-L, Physhare.

Hake, R.R. 2004a. "Thirteen Posting Suggestions," AERA-K post of 26
Jan 2004 16:44:44-0800; online at
<http://lists.asu.edu/cgi-bin/wa?A2=ind0401&L=aera-k&T=0&O=D&P=3392>.
Most importantly Suggestion #5: Quote or repeat only the relevant
sections of the post to which you are responding and not the complete
post (as may occur when you hit the "reply" button - THE FINGER-JERK
HIT-REPLY-BUTTON SYNDROME IS
THE BANE OF DISCUSSION LISTS. It litters the list with superfluous
already posted once ">", twice ">>", thrice ">>>", etc., etc.
material. Why can't list members take the few extra seconds to copy
and paste addresses into the 'To' and 'cc' slots?"

Hake, R.R. 2004b. "Re: NCLB: Benezet/Whitney Thinking," online at
<http://lists.nau.edu/cgi-bin/wa?A2=ind0409&L=phys-l&O=D&P=9704>.
Post of 11 Sep 2004 17:35:02-0700 to Math-Learn (bounced), with cc's
to AERA-C, AERA-K, AP-Physics, ASSESS, EvalTalk, Math-Teach,
PhysLrnR, Physhare, POD, and RUME.

Lochhead, J. 2000. "Thinkback: A User's Guide to Minding the Mind."
Erlbaum. See also at <http://www.whimbey.com/Books/Thinkback/thinkback.htm>.

Pea, R. 1999. "New Media Communications Forums for Improving
Education Research and Practice," in E. C. Lagemann and L.S. Shulman,
eds., "Issues In Education Research" (Jossey-Bass, 1999); online at
<http://scil.stanford.edu/about/staff/bios/pea.html>. Under "Articles
and Chapters."

Roschelle, J & R. Pea. 1999. "Trajectories from Today's WWW to a
Powerful Educational Infrastructure," Educational Researcher,
June-July: 22-25, 43; online as a pdf at
<http://ctl.sri.com/publications/displayPublication.jsp?ID=120>; see
also Pea (1999).

Trigg, T. 2004. "Re: NCLB: Benezet/Whitney Thinking," Math-Teach post
of 12 Sep 04 03:56:32-; online at
<http://mathforum.org/epigone/math-teach/frexgauwhon/ok3160t3l571@legacy>.