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Can Mathematicians Learn Anything from Physics/Astronomy Education Research? - PART 1



PART 1
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In his Phys-L post of 1 Sep 2003 23:41:39-0500 titled "Communications
Breakthrough - Dick Hake please note," Jack Uretsky wrote (slightly
edited, my CAPS"):

"See the paper by Andrew Izsak . . . (2003). . . At last, a math
teacher who seems to recognize that algebra was invented to
facilitate problem solving, and who seems to recognize that learning
comes from experience, the more kinesthetic, the better. He even
includes . . . [well known physics education researcher Lillian] . .
. McDermott among his citations. MAY THE COMMUNICATIONS GAP WITH
MATH TEACHERS EVER NARROW!"

In my opinion, Izsak's (2003) paper can only be explained in terms of
quantum-mechanical tunneling through an otherwise impenetrable
communications gap between math and physics education. Jack's post
has stimulated me to illustrate the gap by extending my recent
discussion list posting theme "Can X Learn Anything from
Physics/Astronomy Education Research?" from X = Biologists (Hake
2003a) and X = Chemists (Hake 2003b) to X = Mathematicians.

As indicated in Hake (2003a,b), biologists and chemists [with a few
notable exceptions - see Wood (2003) and Klymkowsky et al. (2003)]
seem unaware of the lessons of the physics education reform effort
(Hake 2002a), in particular:

"Lesson #3. High-quality standardized tests of the cognitive and
affective impact of courses are essential for gauging the
effectiveness of non-traditional educational methods relative to
traditional methods."

Elaborating on Lesson #3. I wrote in Hake (2002a) [bracketed by lines
"HHHHHH. . . ."; see that article for references other than Hake
(2003a,b,c)]:

HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
As indicated in the introduction, so great is the inertia of the
educational establishment (Lesson #13) that three decades of
physics-education research demonstrating the futility of the
passive-student lecture in introductory courses were ignored until
high-quality standardized tests that could easily be administered to
thousands of students became available. These tests are yielding
increasingly convincing evidence that interactive engagement (IE)
methods enhance conceptual understanding and problem solving
abilities far more than do traditional methods. . . . As far as I
know, disciplines other than physics, astronomy (Adams et al. 2000;
Zeilik et al. 1997, 1998, 1999), and possibly economics (Saunders
1991, Kennedy & Siegfried 1997, Chizmar & Ostrosky 1998, Allgood and
Walstad 1999) have yet to develop any such tests and therefore cannot
effectively gauge either the need for or the efficacy of their reform
efforts. . . .[But more recently pre/post testing is beginning to
gain a foothold in other disciplines (Hake 2003a,b,c]. . . In my
opinion, ALL DISCIPLINES SHOULD CONSIDER THE CONSTRUCTION OF
HIGH-QUALITY STANDARDIZED TESTS OF ESSENTIAL INTRODUCTORY COURSE
CONCEPTS.
HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

Mathematicians as well as biologists; chemists; the Boyer Commission
(1998); the National Center for Postsecondary Improvement [NCPI
(2002)]; the National Research Council's expert committees [NRC
(1997, 1999, 2003a,b); McCray et al. (2003); Pellegrino et al.
(2000), and Shavelson & Towne (2002)]; the physicists who took part
in the McCray et al. (2003) workshop; and all academic disciplines
generally, have ignored the lessons of the physics education reform
effort, and are generally oblivious of the landmark
quantitative/qualitative physics-education-research leading to the
"Mechanics Diagnostic" test (precursor to the FCI) by Halloun &
Hestenes (1985a,b).

For mathematics, a good case in point is the recent undergraduate
calculus reform movement. According to the listing by Przemyslaw
Bogacki at <http://archives.math.utk.edu/calculus/crol.html>, 42
(primarily U.S.) universities took part. One can estimate that
millions of dollars and hundreds of wo(man) years have been expended
on calculus reform.

Was calculus reform really needed? Has it really succeeded? Has it
really failed? Diametrically opposite answers will be given by the
two opposing armies of the Math Wars [see, e.g., "Mathematically
Correct" <http://www.mathematicallycorrect.com/>; Mathematically Sane
<http://MathematicallySane.com/home.asp>; "Could the Math Wars End In
a Treaty of Benezet?" (Hake 2001a,b); "What are the 'Math Wars' in
California All About? Reasons and Perspectives" (Sowder 1998)].

As far as I know:

(a) Mathematicians have not bothered to develop a valid, consistently
reliable, and widely accepted calculus version of the physics "Force
Concept Inventory" (FCI) [Hestenes et al. (1992)] to gauge the need
for, or the effects of, their calculus reform efforts.

(b) Lacking a generally accepted assessment instrument, there is no
definitive evidence for the success, failure, or even need for the
calculus reform effort. Instead little more than math wars rhetoric
generally prevails [to see this search for the exact phrase "calculus
reform" (without the quotes) at the antediluvian MathTeach search
engine <http://mathforum.org/discussions/epi-search/nctm.l.html>].

In my opinion, the fact that a Force Concept Inventory (FCI) exits,
while a Calculus Concept Inventory (CCI) does not, is due in part to
the distinct differences in the orientation and practice of physics
education research (PER) and mathematics education research (MER).
For a Galilean dialogue on the differences between PER and MER see
(Hake 2003d). In so far as the FCI/CCI contrast is concerned, perhaps
the most important difference is that mathematicians generally ignore:

"Lesson #4. Education Research and Development (R&D) by disciplinary experts
(DE's), and of the same quality and nature as traditional
science/engineering R&D, is needed to develop potentially effective
educational methods within each discipline. But the DE's should take
advantage of the insights of
(a) DE's doing education R&D in other disciplines, (b) cognitive scientists,
(c) faculty and graduates of education schools, and (d) classroom teachers."

Elaborating on the above, in Hake (2002a) I wrote:

HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
Redish (1999) has marshaled the arguments for the involvement of
physicists in physics departments - not just faculty of education
schools - in physics-education research. Similar arguments may apply
to other disciplines. . . . The education of disciplinary experts in
education research requires Ph.D. programs at least as rigorous as
those for experts in traditional research. The programs should
include, in addition to the standard disciplinary graduate courses,
some exposure to: the history and philosophy of education, computer
science, statistics, political science, social science, economics,
engineering - see L11, and, most importantly, cognitive science
(i.e., philosophy, psychology, artificial intelligence, linguistics,
anthropology, and neuroscience). . . .In the U.S. there are now about
a dozen Ph.D. programs in physics education within physics
departments and about half that number of interdisciplinary programs
between physics and education or cognitive psychology (UMd-PERG
2003.). In my opinion, ALL SCIENTIFIC DISCIPLINES SHOULD CONSIDER
OFFERING PH.D. PROGRAMS IN EDUCATION RESEARCH.
HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

Why aren't mathematics departments engaged in mathematics education
research? In my opinion, mathematician Herb Clemens (1998) explained
it perfectly (my CAPS):

"Why don't mathematicians from universities and industry belong in
math education? THE FIRST REASON IS THAT IT IS SELF-DESTRUCTIVE. The
quickest way to be relegated to the intellectual dustbin in the
mathematics departments of most research universities today is to
demonstrate a continuing interest in secondary. . .(or tertiary). . .
mathematics education. Colleagues smile tolerantly to one another in
the same way family members do when grandpa dribbles his soup down
his shirt. Math education is certainly an acceptable form of retiring
as a mathematician, like university administration (unacceptable
forms being the stock market, EST. . .[Erhard Seminar Training?
<http://www.working-minds.com/werner.htm>]. . ., or a mid-life love
affair). BUT YOU DON'T DO GOOD RESEARCH AND THINK SERIOUSLY ABOUT
EDUCATION." [Clemens' comments regarding the self-destructive effects
of SERIOUS concern for education in research universities apply as
well to biologists, chemists, physicists, other non-Ed-school
academics, and most non-Ed-school members of the NRC's expert
committees on education.]


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>

"Human beings, who are almost unique in
having the ability to learn from the
experience of others, are also remarkable
for their apparent disinclination to do so."
Douglas Adams in "Last Chance to See."

REFERENCES ARE IN PART 2