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*From*: Richard Hake <rrhake@EARTHLINK.NET>*Date*: Fri, 20 Aug 2004 15:49:42 -0700

Although cross-posting offers a way to tunnel through disciplinary

barriers, some list subscribers vehemently object to it. If you are

one such, please hit the DELETE button now! If you respond to this

long post (16kB) please don't hit the reply button (bane of

discussion lists) and thereby inflict it yet again on all list

subscribers.

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)}.

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>

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.

Bishop, W. 2004a."Expert calls for optional maths," Math-Teach post

of 14 Aug 2004 07:17:36-0700; online at

<http://mathforum.org/epigone/math-teach/sneithastem/5.1.0.14.2.20040814070008.04371790@exchange.calstatela.edu>

Bishop, W. 2004b. "Direct Instruction in Science" Math-Teach post of

26 Jul 2004 07:43:03-0700; online at

<http://mathforum.org/epigone/math-teach/quunphelthee/5.1.0.14.2.20040726073633.04440bd8@exchange.calstatela.edu>.

Bishop, W. 2004c. "Re: About your health," Math-Teach post of 21 Apr

2004 23:54:45-0700; online at

<http://mathforum.org/epigone/math-teach/dwoxjimverl/5.1.0.14.2.20040421233558.03ddb6b0@exchange.calstatela.edu>.

Epstein, J. 1997-98. Cognitive development in an integrated

mathematics and science program. J. of College Science Teaching 12/97

& 1/98:194-201.

Epstein, J. 1999. What is the real level of our students? unpublished.

Ford, K.W. 1989. "Guest Comment: Is physics difficult?" Am J. Phys.

57(10), 871-872 (1989).

Hake, R.R. 2002. "Physics First: Opening Battle in the War on

Science/Math Illiteracy?" Submitted to the American Journal of

Physics on 27 June 2002; online as ref. 29 at

<http://www.physics.indiana.edu/~hake/>.

or download directly by clicking on

<http://www.physics.indiana.edu/~hake/PhysFirst-AJP-6.pdf> (220kB).

Hake, R.R. 2004a. "Re: Direct Instruction in Science," online at

<http://listserv.nd.edu/cgi-bin/wa?A2=ind0407&L=pod&O=A&P=14775>.

Post of 29 Jul 2004 to Math-Teach, AERA-C, AERA-K, AP-Physics,

Math-Learn, Phys-L, PhysLrnR, Physhare, & POD.

Hake, R.R. 2004b. "Direct Science Instruction Suffers a Setback in

California - Or Does It?" AAPT Announcer 34(2): 177; online as

reference 33 at <http://www.physics.indiana.edu/~hake>, or download

directly as a 420

kB pdf by clicking on

<http://www.physics.indiana.edu/~hake/DirInstSetback-041104f.pdf>

[about 160 references and 180 hot-linked URL's].

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>.

Lederman, L. 2001. "Revolution in Science Education: Put Physics

First." Physics Today 54(9): 11-12; online at

<http://physicstoday.org/pt/vol-54/iss-9/p11.html>.

Mahajan, S. & R.R. Hake. 2000. "Is it time for a physics counterpart

of the Benezet/Berman math experiment of the 1930's? Physics

Education Research Conference 2000: Teacher Education; online as ref.

6 at <http://www.inference.phy.cam.ac.uk/sanjoy/benezet/>, and as an

abstract at <http://www.sci.ccny.cuny.edu/~rstein/perc2000.htm>.

Trigg, T. 2004. "Re: Research Based Instruction," Math-Teach post of

24 Jul 04 04:20:25 -0400 (EDT); online at

<http://mathforum.org/epigone/math-teach/snimtamsmor/afii8hmo8xsa@legacy>.

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