In his PhsLrnR post of 22 Aug 2002 20:16:53-0500, enigmatically
titled "Interesting question?" John Clement commented on the
difficulties his students and an English teacher acquaintance had
with this question:
"You are in the center of Boston, traveling South at 60 mph. What is
your position?"
In a later PhysLrnR post of 24 Aug 2002 15:44:06-0500, John wrote:
"Unfortunately all of the good information that my original question
elicited never answered my original inquiry. IS THE QUESTION A GOOD
ONE? . . . I really think that the question has some striking
resemblance to the questions that Benezet. . .(see, e.g. Mahahan &
Hake 2000). . . used to evaluate the success of his program." (My
CAPS.)
In my opinion Clement's question is:
a. also a question that Arnold Arons might have asked.
b. AN EXCELLENT QUESTION that gets to the heart of one of the prime
barriers to physics learning - the specialized language of physics.
I agree with Arons that OPERATIONAL DEFINITIONS are the KEY to
student understanding of specialized physics terms such as
"position," "velocity," and "acceleration." However, I was
disappointed to find that in the 38 PhysLrnR responses (as of 6 Sep
2002 12:00-0700) to John's post THERE IS NO MENTION OF OPERATIONAL
DEFINITIONS. Have physics education researchers (PER's) missed a
central feature of the Arons-advocated method of physics instruction?
Here is Arons (1990), pages 1 & 2 in his oft-referenced but seldom
read "Guide to Introductory Physics Teaching," on the importance of
the operational definition of the word "area" (my CAPS):
ARONS-ARONS-ARONS-ARONS-ARONS-ARONS-ARONS-ARONS-ARONS-ARONS
The concept of area is the foundation of many of the other basic
physical concepts such as pressure, stress, energy flux, and
coefficients of diffusion and heat conduction. It underpins all the
ratio reasoning associated with geometrical scaling. . . . If you ask
students how one arrives at numerical values for "area" or "extent of
surface," many - if they have any response at all - will say "length
times width." If you then sketch some very irregular figure without
definable length or width and ask about assigning a numerical value
to the area of the figure, very little response of any kind is
forthcoming. STUDENTS WHO RESPOND IN THIS WAY HAVE NOT FORMED A CLEAR
OPERATIONAL DEFINITION OF "AREA." . . . They have never been asked to
define "area.". . . virtually none of the students have had any
significant exposure to the notion of operational definition. They
have had little or no practice in defining a term by reference to
shared experience or by describing, in simple words of prior
definition, the actions through which one goes to develop the
numerical value being referred to in the name of a technical concept."
ARONS-ARONS-ARONS-ARONS-ARONS-ARONS-ARONS-ARONS-ARONS-ARONS
Likewise, I suspect that those who give non-physics answers to
Clement's question have never been asked to define "position" and
"speed" in terms of the actions which one goes through to develop the
numerical value being referred to in the name of "position" and
"speed," i.e., to formulate OPERATIONAL DEFINITIONS of those terms.
Unfortunately "operational definitions" are rarely discussed in
physics texts and are not stressed in most of the various PER-based
pedagogical methods described in the literature. Exceptions are the
Arons-inspired (Hake 1991) Socratic Dialogue Inducing (SDI) Labs
(Hake 1987, 1992, 2001a; Tobias & Hake 1988). But SDI labs are
virtually unknown to most physics teachers and PER's, and generally
ignored in standard PER reference volumes (e.g., Redish & Rigden
1997).
I should like to suggest once again (see Hake 2001b) that it might be
worthwhile to take a look at:
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
A. SDI Lab #0.1 "Frames of Reference, Position, and Vectors"
<http://physics.indiana.edu/~sdi/>, especially "Operational
Definition of 'Position'" on page 10:
"To properly understand mechanics, it is necessary to appreciate the
meaning and significance of operational definitions (Holton & Brush
1985), defined as:
OPERATIONAL DEFINITION: a description which specifies the
experimental significance of a word or concept in terms of
well-defined measurement methods."
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
B. SDI Lab #1, "Newton's First and Third Laws," especially Sec. II
"Operational Definitions" on pages 7-11. These exercises represent a
further attempt to get the idea of operational definitions (OD's)
across to university pre-meds, by means of Socratic discussions of
OD's for "vertical," "horizontal," "force," "up," "down," and
"equilibrium." Here we are simply following Arons (1990).
UNFORTUNATELY, THE OD ASPECT OF SCIENCE EDUCATION IS GENERALLY
IGNORED IN CURRENT K-16 EDUCATION, INCLUDING AP PHYSICS.
As discussed by D.C. Phillips (2000) and Phillips & Burbules (2000),
operational definitions retain their crucial role in science (and
thinking generally), despite specious attacks from the
"antipositivist vigilantes."
REFERENCES
Arons, A.B. 1990. "A Guide to Introductory Physics Teaching," see
especially pages 2, 15, 50, 52ff, 60, 94, 159, 289, 315. Wiley;
reprinted with minor updates in "Teaching Introductory Physics"
(Wiley, 1997).
Hake, R.R. 1987. "Promoting student crossover to the Newtonian
world." Am J. Phys. 55(10):878-884.
Hake, R.R. 1991. "My Conversion To The Arons-Advocated Method Of
Science Education,"Teaching Education" 3(2), 109-111 (1991); online
as ref. 8 at <http://www.physics.indiana.edu/~hake>.
Hake, R.R. 1992. "Socratic pedagogy in the introductory physics lab.
Phys. Teach. 30:546-552; updated version (4/27/98) online as ref. 3
at <http://physics.indiana.edu/~sdi/>.
Holton G. and S.G. Brush. 2001. "Physics, the Human Adventure: From
Copernicus to Einstein and Beyond" (Rutgers Univ. Press), esp. pages 161-164.
Mahajan, S., and R. R. Hake. 2000. Is it finally time for a physics
counterpart of the Benezet/Berman math experiment of the 1930's?
Available online as ref. 6 at the Benezet Centre
<http://wol.ra.phy.cam.ac.uk/sanjoy/benezet/>.
Phillips, D.C. 2000. "Expanded social scientist's bestiary: a guide
to fabled threats to, and defenses of, naturalistic social science."
Rowman & Littlefield.