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The Benezet-Berman Experiment (LONG!)



Please excuse this LONG(1a) cross-posting to PHYSHARE(1b),
PHYSLRNR(1c), Phys-L(1d), and Math-Teach(1e).

In his 10/2/00 PHYSHARE post "Re: arguments about pedagogy," Nicholas
Park posed three important questions Q:

Q1. "Ok, so how do successful experiments like this . . . . The
Benezet/Berman Experiment (see refs. 2,3) . . . . . inform the way
everybody else is to be taught?

Q2. Is whole-scale reform necessary?

Q3. And if so, don't the standards prevent any movement toward such reform?"

Sanjoy Mahajan gave his responses in a 10/6/00 message forwarded to
PHYSHARE by Jane Jackson under the title "Re: arguments about
pedagogy (Benezet expt.)"

Here are my responses R:

111111111111111111111111111111111111111111111111111111
R1. How can the Benezet/Berman Experiment inform the way other
students are taught? In my opinion the Benezet-Berman Experiment
indicates a possible way to drastically improve K-12 education. As
indicated in ref. 4:

"Students in Manchester, New Hampshire WERE NOT SUBJECTED TO
ARITHMETIC ALGORITHMS(5) 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."

Having attempted to bring "interactive-engagement" methods(6-8) to
about 1300 introductory-physics-course pre-med students over the past
two decades, I am seriously concerned about their rapidly
deteriorating preparation for any substantive introductory physics
course. On average, present-day in-coming university students are
sadly deficient in mathematics, science, English, drawing, problem
solving, and the ability to think critically. IT SEEMS TO ME THAT
ALL K-12 STUDENTS MIGHT BENEFIT FROM THE BENEZET METHODS. As
indicated in ref. 4, prominent mathematicians such as Hassler Whitney
and Andrew Gleason have expressed a similar view; and the National
Research Council's Mathematical Education Sciences Board(9) has
stated:

"Mastery of subject matter has for years been the predominant focus
of mathematics education research . . . . . . Contrary to much
present practice, it is generally most effective to engage students
in meaningful, complex activities focusing on conceptual issues
rather than to establish all building blocks at one level before
going on to the next level (Hatano, 1982; Romberg and Carpenter,
1986; Collins et al., 1989). . . . .There is some evidence to suggest
that paper and pencil calculation involving fractions, decimal long
division, and possibly multiplication are introduced far too soon in
the present curriculum. Under currently prevalent teaching practice,
a very high percentage of high school students worldwide never
masters these topics - just what one would expect in a case where
routinized skills are blocking semantic learning (e.g., BENEZET,
1935). The challenge for curriculum development (and research) is to
determine when routinized rules should come first and when they
should not, as well as to investigate newer whole-language strategies
for teaching that may be more effective than traditional methods.
THIS IS AN AREA WHERE MORE RESEARCH NEEDS TO BE DONE." [Our CAPS.]


222222222222222222222222222222222222222222222222222222222
R2. Is whole-scale reform necessary? Aside from the lack of
understanding and critical thinking uncovered (and at least partially
corrected) in elementary-school students by Benezet, consider:

1. Donald Simanek's 9/28/00 PHYSHARE post "Re: Do real physicists use
analogies?":

"Experts in math education tell me that the point where many students
'miss the boat' is the 4th grade, where fractions, ratios and
proportion are introduced. Curiously these are just the concepts so
important in physics. My other point was that such problems must be
addressed *promptly* or they accumulate. Too many schools deny the
problem, or sweep it under the rug, hoping that it will be addressed
in later courses. A student who cannot handle proportions by the time
he/she reaches high school is not likely to do well in physics. This
cannot easily be remedied at this late a time in the class time
available."

2. The research of Jerry Epstein(10)(consistent with Simanek's comments):

"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 (NJ) 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 been given now at more than a dozen
institutions shows that there are such
students everywhere . . . . . (even Wellesley! - see J. Epstein,
"What is the Real Level of Our Students," 1999, unpublished).

3. The Nation's Report Card(12), The National Assessment of
Educational Progress (NAEP):

"Three percent of the nation's students reached the Advanced level at
all three grade levels. Twenty-six percent of fourth- and
eighth-grade students and 18 percent of the twelfth-grade students
performed within the Proficient level, while 38 percent, 32 percent,
and 36 percent performed within the Basic level for grades 4, 8, and
12, respectively." Paul Gross(13) states that "in the Massachusetts
assessment system, the category matching NAEP's 'Basic' is called
'Needs Improvement.' That is much more honest."

4. The TIMSS results(16):

"U.S. students worst showing was in population 3. . . . (final year
of secondary School. . . . .corresponding to U.S. high school
seniors). . . . . .In the assessment of general mathematics and
science knowledge, U.S. high school seniors scored near the bottom of
the participating nations. In the assessments of advanced mathematics
and physics given to a subset of students who had studied those
topics, no nations had significantly lower mean scores than the
United States. The TIMSS results indicate that a considerably smaller
percentage of U.S. students meet high performance standards than do
students in other countries."

I would conclude from the Benezet/Berman experiment(2,3) and from
"1", "2", "3", and "4" above that WHOLE-SCALE REFORM OF THE K-12
SYSTEM IS NEEDED.


3333333333333333333333333333333333333333333333333333333333
R3. Don't the standards prevent any movement toward such reform? In
my opinion it depends on the standards. Certainly standards that
demand mastery of e.g., the long-division algorithm by grade 4 would
stifle the Benezet method. But to paraphrase Donald Simanek's
10/3/00 PHYSHARE post "Re: standards movement":

"Can we have standards and an emphasis on understanding and critical
thinking? Sure. Devise a standards assessment instrument which
rewards the results of understanding and critical thinking, and
de-emphasizes rote memorization and plug-and-chug. Devise an
instrument such that the only way to 'teach for the test' is to
encourage understanding and critical thinking."


44444444444444444444444444444444444444444444444444444444
R4. An important question reqarding the Benezet method, not raised by
Nicholas Park, was phrased by Arnold Arons(17) as follows:

Q4. "Whence do we get the teachers with the background,
understanding, and security to implement such. . .(Benezet-type) . .
. instruction? They will certainly not emerge from the present
production mills."

I agree with Arons that Benezet-type teachers "will certainly not
emerge from the present production mills." Some of my own thoughts on
this issue are given in ref. 18.

Perhaps some PHYSHARE'ers, PHYSLRNR's, Phys-L'ers, or Math-Teach'ers
have some answers to Arons's crucial question.


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


REFERENCES & FOOTNOTES
1a. If you wish to respond to this very L--O--N--G post (I
apologize), PLEASE, out of courtesy to other list subscribers, avoid
the finger-jerk reaction of hitting the reply button!! Why distribute
yet again the replied-to post and clutter everyone's hard drive? Some
sage Netiquette advice is given by the Phys-L list at
<http://purcell.phy.nau.edu/phys-l/#etiquette>:

"Quote Sparingly: avoid excessively large replies created by quoting
complete original messages (a real problem for DIGEST-mode readers).
Instead, select and keep only appropriate quoted text, indicating
what is quoted and what is not from the original message (many email
programs will do this automatically) and manually pruning out
irrelevant sections. Indicate deletions. Leave enough original so
you are not enigmatic."

1b. PHYSHARE is a discussion forum for sharing resources among
about 550 high-school physics teachers. The archives are at
<http://lists.psu.edu/archives/physhare.html>.

1c. PHYSLRNR is a discussion forum with about 475 subscribers
interested in physics education research. The archives are at
<http://listserv.boisestate.edu/archives/physlrnr.html>.

1d. Phys-L is a discussion forum with about 650 subscribers
interested in physics education. The archives are at
<http://mailgate.nau.edu/archives/phys-l.html>.

1e. Math-Teach is a forum for mathematics educators with archives at
<http://forum.swarthmore.edu/epigone/math-teach>.

2. L. P. Benezet, "The Teaching of Arithmetic I, II, III: The Story of
an Experiment, "Humanistic Mathematics Newsletter #6, May 1991,
pp. 2-14 (reprinted from The Journal of the National Education
Association, Nov. 1935, Dec. 1935, Jan. 1936); on the web
<http://wol.ra.phy.cam.ac.uk/sanjoy/benezet>.

3. Etta Berman, "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.

4. S. Mahajan & R.R. Hake, "Is It Finally Time for a Physics
Counterpart of the Benezet/Berman Math Experiment of the 1930's?"
Physics Education Research Conference 2000: Teacher Education, Univ.
of Guelph, August 2-3, 2000; the abstract is at
<http://www.sci.ccny.cuny.edu/~rstein/perc2000.htm>.

5. CAUTION!! As stated in ref. 4:

"Benezet did NOT advocate abandoning arithmetic instruction, only the
mindless drill that goes with most formal instruction. This
distinction has often been neglected. Here is the editors'
introduction to Benezet's paper as abridged and adapted in C.W.
Hunnicutt and William J. Iverson, eds., "Research in the Three R's"
(Harper, 1958), pp. 397-400:

'A great controversy in arithmetic has centered on the question "When
should systematic instruction in arithmetic begin?" Superintendent
Benezet heaped fuel on the flames with his famous series of articles
describing a city-wide tryout of an idea. He forcefully advocated
"postponement of arithmetic" to Grade 7 or at least until Grade 6,
though the reader will discover that he advocated postponement only
of formal arithmetic. Actually he filled the early years with
'meaningful' and 'significant' arithmetic experiences. This study,
often misquoted, has been used to support postponement of all
organized arithmetic teaching.' "

6. R.R. Hake, "Socratic Pedagogy in the Introductory Physics Lab,"
Phys. Teach. 30, 546 (1992); a version updated on 4/27/98 is
available at
<http://www.physics.indiana.edu/~sdi/>.

7. R.R. Hake, "Interactive-engagement vs traditional methods: A
six-thousand-student survey of mechanics test data for introductory
physics courses," Am. J. Phys. 66, 64-74 (1998); on the Web at
<http://www.physics.indiana.edu/~sdi/>.

8. R.R. Hake, "Interactive-engagement methods in introductory
mechanics courses," on the Web at
<http://www.physics.indiana.edu/~sdi/> and
submitted on 6/19/98 to the "Physics Education Research Supplement to
AJP"(PERS).

9. National Research Council, "Reshaping School Mathematics: A
Philosophy and Framework for Curriculum" (Mathematical Sciences
Education Board, 1990); pp. 30-31. See at
<http://books.nap.edu/catalog/1498.html>.

10. J. Epstein, "Cognitive Development in an Integrated Mathematics
and Science Program," J. of College Science Teaching, 12/97 & 1/98,
pp. 194-201. See also ref. 11.

11. J. Epstein, "The "0.7 Barrier" on the FCI -- a suggestion of the
underlying problem and a proposal for further research," Physics
Education Research Conference 2000: Teacher Education, Univ. of
Guelph, August 2-3, 2000; the abstract is at
<http://www.sci.ccny.cuny.edu/~rstein/perc2000.htm>.

12. The Nation's Report Card, The National Assessment of Educational
Progress (NAEP); on the web at
<http://nces.ed.gov/nationsreportcard/site/home.asp>.
C. Y. O'Sullivan, C. M. Reese, and J. Mazzeo, "NAEP 1996 Science:
Report Card for the Nation and the States," on the web at
<http://nces.ed.gov/nationsreportcard/96report/97497.shtml>.

13. P.R. Gross, "Politicizing Science Education" on the web at
<http://www.edexcellence.net/library/gross.html>. In my opinion,
Gross's discussions of the anti-evolution movement and the need for
improvement of science education are on target, but his near blanket
condemnation of "constructivism" is inconsistent with the results of
physics-education research of the past four decades. The latter (see
e.g., refs. 7,14,15) demonstrates the relative effectiveness of
constructivist-oriented educational strategies such as "interactive
engagement" and "collaborative learning."

14. E.F. Redish, "Millikan Lecture 1998: Building a Science of
Teaching Physics," Am. J. Phys. 67(7), 562-573 (1999); on the web at
<http://www.physics.umd.edu/rgroups/ripe/perg/cpt.html>.

15. L.C. McDermott and E.F. Redish, "Resource Letter on Physics
Education Research" Am. J. Phys., 67(9), 755-767 (1999); on the web
at <http://www.physics.umd.edu/rgroups/ripe/perg/cpt.html>.
Reviews over four decades of primarily qualitative and some
quantitative research (largely ignored by the physics and education
communities) on both cognitive and affective aspects of physics
instruction.

16. National Research Council (NRC), "Global Perspectives for Local
Action: Using TIMSS to Improve U.S. Mathematics and Science
Education" (National Academy Press, 1999); on the web at
<http://books.nap.edu/catalog/9723.html>.

17. A.B. Arons, private communication of 6/30/00 to R.R.Hake.

18. R.R. Hake, "The General Population's Ignorance of Science
Related Societal Issues: A Challenge for the University," AAPT
Announcer 30(2), 105 (2000); on the web at
<http://www.physics.indiana.edu/~hake/> as [GuelphSocietyG.pdf,
8/22/00, 2100K] (62 References). It is argued (with tongue only
partially in cheek) that the failure of universities THROUGHOUT THE
UNIVERSE to properly educate pre-college teachers is responsible for
our failure to observe any signs of extraterrestrial intelligence.