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In his Math-Teach post of 14 Aug 2004 titled "Expert calls for
optional maths," mathematician Wayne Bishop (2004a) referred to BBC
News (2004) and commented:
"Not just age but make the decision by color as well? Or parental
affluence? I especially like his suggestion of age 11; put it
together with Benezet's inspired *avoidance* of math (for kids who
live on the wrong side of the tracks) until *past* age 11 and we
wind up not having to teach math to po' folk at all!!"
A few weeks ago Bishop (2004b) misleadingly implied that the "drill
and practice" brand of "direct instruction" advocated by himself and
Mathematically Correct <http://www.mathematicallycorrect.com/> was
validated by the research of cognitive scientist David Klahr [Klahr &
Nigam (2004)]. Nothing could be further from the truth, as indicated
in Hake (2004a).
Now Bishop misleadingly implies that Benezet (1935/36) "avoided"
math. Here again, nothing could be further from the truth, as
indicated by Mahajan & Hake (2000). In their abstract to the Physics
Education Research Conference of 2000
<http://www.sci.ccny.cuny.edu/~rstein/percabst.htm> Mahajan & Hake
wrote [bracketed by lines "M&H-M&H-M&H-M&H. . . . ."]:
M&H-M&H-M&H-M&H-M&H-M&H-M&H-M&H-M&H-M&H-M&H-M&H
Should teachers concentrate on critical thinking, estimation,
measurement, and graphing rather than college-clone algorithmic
physics in K-12? Thus far physics-education research offers little
substantive guidance. Mathematics education research addressed the
mathematics analogue of this question in the 1930's [Benezet
(1935/36), Berman (1935)]. Students in Manchester, New Hampshire were
not subjected to arithmetic algorithms until grade 6. In earlier
grades they read, invented, and discussed stories and problems;
estimated lengths, heights, and areas; and enjoyed finding and
interpreting numbers relevant to their lives. In grade 6, with 4
months of formal training, they caught up to the regular students in
algorithmic ability, and were far ahead in general numeracy and in
the verbal, semantic, and problem-solving skills they had practiced
for the five years before. Assessment was both QUALITATIVE - e.g.,
asking 8th grade students to relate in their own words why it is
"that if you have two fractions with the same numerator, the one with
the smaller denominator is the larger;" and QUANTITATIVE - e.g.,
administration of standardized arithmetic examinations to test and
control groups in the 6th grade.
M&H-M&H-M&H-M&H-M&H-M&H-M&H-M&H-M&H-M&H-M&H-M&H
One fervently hopes that the following quote from Bishop (2004c) is
the usual empty bombast:
"I'll also be at an intimate dinner tomorrow night. . . with a few
influential folks in California education, INCLUDING A COUPLE OF
STATE BOARD OF ED MEMBERS and some good press folk, so things are
going along fine here." [My CAPS.]
Bringing physics into the discussion, Timotha Trigg [who thinks
Benezet (1935/36 is a "bizarre study demonstrating students' ability
to hone their skills in responding to dumb questions"(Trigg 2004)]
wrote in her Math-Teach post of 20 Aug 04 11:02:54-0400 (EDT):
"I thought you [Kirby Urner] suggested (but now I don't see where)
that physics teachers teach the underlying mathematics along with the
physics. But since we do a notoriously poor job teaching physics even
*after* the math teachers have made a valiant effort to impart the
necessary foundational skills, piling that responsibility onto the
lap of physics teachers seems unlikely to improve things."
If math teachers have indeed made "a valiant effort to impart the
necessary foundational skills," as Trigg claims, they do not seem to
have been overly successful. According to physicist Jerry Epstein
(1997-98):
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
While it is now well known that large numbers of students arrive at
college with large educational and cognitive deficits many faculty
and administrative colleagues are not aware that many students lost
all sense of meaning or understanding in elementary school . . . In
large numbers our students . . . .[at Bloomfield College (New Jersey)
and Lehman (CUNY)] . . . . cannot order a set of fractions and
decimals and cannot place them on a number line. Many
do not comprehend division by a fraction and have no concrete
comprehension of the process of division itself. Reading rulers where
there are other than 10 subdivisions, basic operational meaning of
area and volume, are pervasive difficulties. Most cannot deal with
proportional reasoning nor any sort of problem that has to be
translated from English. Our diagnostic test, which has now been
given at more than a dozen institutions shows that there
are such students everywhere . . . . . .[even Wellesley (Epstein 1999)].
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
IMHO, what's needed by the return of Halley's comet in 2061 [AAAS
(1989)] is a Ken Ford (1989) "learning ramp," replacing the
transitional 9th-grade Leon Lederman (2001) Physics-First cliff. The
Ford Ramp would offer smooth and steady science/math advancement
from pre-school to grade 12, and hopefully lead to science/math
literacy for all. Along the ramp, math would be integrated into
physics, chemistry, biology, geography, and all other subjects by
*effective* teachers who are treated as the valued professionals they
are. For a cartoon depiction see page 4 of Hake (2002).
Treating teachers as valued professionals means drastically upgrading
teachers' salaries and working conditions. It also means GIVING THEM
CONTROL OF THEIR OWN TEACHING MATERIALS & PRACTICES, rather than
top-down dictation through adoption of only
direct-instruction-oriented texts and materials, as mandated by
direct-instruction-dominated Sacramento bureaucrats [Hake (2004b)}.
REFERENCES
AAAS. 1989. "Science for all Americans: A Project 2061 report on
literacy goals in science, mathematics, and technology," American
Association for the Advancement of Science; a description is at
<http://www.project2061.org/tools/sfaa/default.htm>: "Science for All
Americans" presents a unified vision of science literacy that serves
as a basis for discussions of the skills and knowledge that our
nation's students should have."
BBC News. 2004. "Expert calls for optional maths: A maths expert says
the subect should not be compulsory for children over the age of 14,"
13 August; online at
<http://news.bbc.co.uk/1/hi/education/3561678.stm>: "David Burghes,
from Exeter University, believes that most children learn all the
maths they need by the age of 14 or even 11.
Benezet, L.P. 1935-1936. The teaching of arithmetic I, II, III: The
story of an experiment, "Journal of the National Education
Association" 24(8), 241-244 (1935); 24(9), 301-303 (1935); 25(1), 7-8
(1936). The articles were (a) reprinted in the "Humanistic
Mathematics Newsletter" #6: 2-14 (May 1991); (b) placed on the web
along with other Benezetia at the Benezet Centre, online at
<http://www.inference.phy.cam.ac.uk/sanjoy/benezet/>. See also Mahajan & Hake
(2000).
Berman, E. 1935. "The result of deferring systematic teaching of
arithmetic to grade six as disclosed by the deferred formal
arithmetic plan at Manchester, New Hampshire," Masters Thesis, Boston
University, 1935.
Klahr, D. & M. Nigam. 2004. "The equivalence of learning paths in
early science instruction: effects of direct instruction and
discovery learning." In press at Psychological Science; online at
<http://www.psy.cmu.edu/faculty/klahr/papers.html>.