In her AERA-C post of 27 Jan 2004 13:42:23+1100 titled "Pedagogical
content knowledge," Catherine Scott wrote: "I am having a brain
freeze . . . and I cannot retrieve the classic book in which content
knowledge, pedagogical knowledge and pedagogical content knowledge
were introduced and discussed."
Nick Noakes responded: I suspect it's either . . .Shulman (1986). . .
or the more often cited Shulman (1987).
Nick has the references right. For a discussion of "Pedagogical
content knowledge" within the context of physics education see Hake
(2002). There I wrote [bracketed by lines "HHHHHHHHHHHH. . . . ." :
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LESSON 7. Teachers who possess BOTH content knowledge and
"pedagogical content knowledge" are more apt to deliver effective
instruction.
"Pedagogical content knowledge" is evidently a term due to Shulman
(1986, 1987), but its importance has long been well known to
effective classroom teachers. The difference between content
knowledge and "pedagogical content knowledge," can be illustrated by
consideration of the Halloun/Hestenes (1998a,b) type question given
in the "Introduction":
A student in a lab holds a brick of weight W in her outstretched
horizontal palm and lifts the brick vertically upward at a constant
speed. While the brick is moving vertically upward at a constant
speed, the magnitude of the force on the brick by the student's hand
is:
A. constant in time and zero.
B. constant in time, greater than zero, but less than W.
C. constant in time and W.
D. constant in time and greater than W.
E. decreasing in time but always greater than W.
CONTENT KNOWLEDGE informs the teacher that, according to Newton's
First Law, while the brick is moving vertically upward at a constant
speed in the inertial reference frame of the lab, the magnitude of
the force on the brick by the student's hand is constant in time and
of magnitude W, so that the
NET force on the brick is zero.
On the other hand, PEDAGOGICAL CONTENT KNOWLEDGE would inform the
teacher that students may think that e.g.:
(a) since a net force is required to produce motion, the force on the
brick by the student's hand is constant in time and greater than W; or
(b) since the weight of the brick diminishes as it moves upward away from the
Earth, the force on the brick by the student's hand decreases in time
but is always greater than W; or
(c) no force is exerted on the brick by the student's hand because as
the students hand moves up the brick must simply move up to stay out
of the hand's way.
In addition, pedagogical content knowledge provides a hard-won
toolkit of strategies (see, e.g., the list of "Popular IE Methods" in
II-C above) for guiding the student away from these misconceptions
and towards the Newtonian interpretation. Unfortunately, such
knowledge may take many years to acquire (Wells et al. 1995).
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REFERENCES
Hake, R.R. 2002. "Lessons from the physics education reform effort,"
Conservation Ecology 5(2): 28; online at
<http://www.consecol.org/vol5/iss2/art28>, Conservation Ecology is a
free "peer-reviewed journal of integrative science and fundamental
policy research" with about 11,000 subscribers in about 108 countries.
Halloun, I. & D. Hestenes. 1985a. "The initial knowledge state of
college physics students." Am. J. Phys. 53:1043-1055; online at
<http://modeling.asu.edu/R&E/Research.html>. Contains the "Mechanics
Diagnostic" test, precursor to the much used "Force Concept
Inventory." This landmark work is regularly ignored by the NRC and
its "expert" science-education committees (which sometimes even
include physicists!), e.g., McCray et al. (2003).
McCray, R.A., R.L. DeHaan, J.A. Schuck, eds. 2003. "Improving
Undergraduate Instruction in Science, Technology, Engineering, and
Mathematics: Report of a Workshop" Committee on Undergraduate STEM
Instruction," National Research Council, National Academy Press;
online at <http://www.nap.edu/catalog/10711.html>. Physicists
attending the workshop were Paula Herron, Priscilla Laws, John
Lehman, Ramon Lopez, Richard McCray, Lillian McDermott, Carl Wieman,
and Jack Wilson.
Shulman, L.S. 1986. "Those who understand: Knowledge growth in teaching."
Educational Researcher 15(2): 4-14.
Shulman, L.S. 1987. "Knowledge and teaching: Foundations of the new
reform." Harvard Educational Review 57(1): 1-22.