THE PARADIGMS PROJECT
National Science Foundation
•DUE-9653250, 0231194
•DUE-0088901, 0231032
http://physics.oregonstate.edu/portfolioswiki
The Paradigms in Physics Project at Oregon State University has reformed
the entire upper-division curriculum for physics and engineering physics
majors. This has involved both a rearrangement of content to better reflect
the way professional physicists think about the field and also the use of a
number of reform pedagogies that place responsibility for learning more
firmly in the hands of the students. The junior year consists of short case
studies of paradigmatic physical situations which span two or more
traditional subdisciplines of physics. The courses are designed explicitly to
help students gradually develop problem-solving skills We have developed
many effective classroo activities that are documented on our wiki. Along
the way we are also learning what it takes to design and implement largescale modifications in curriculum and to institutionalize them.
Cognitive Development
at the Middle-division Level
Corinne A. Manogue
Elizabeth Gire
POTENTIAL OF A POINT CHARGE
Students recall the
formula for the
potential due to a
point charge.
Class discussion
focuses on
strategies to
choose the correct
formula.
STAR TREK
Len Cerny, Tevian Dray, Barbara Edwards, David McIntyre, Janet Tate,
Drew Watson, and Emily van Zee.
THE PROBLEM (TASK ANALYSIS)
Pedagogical Content Knowledge is the teacher knowledge
associated with how the students interact with the content.
Listed in this column are VERY common student problems
that come up as students are working on the activity.
Recognize that the superposition principle applies.
4 0

i
(x,0,0)
D
POWER SERIES
Students use a computer
algebra package to plot the
first several terms of a power
series expansion
And visually compare their
approximation with a plot of
the function
RESEARCH LENSES
BEHAVIORISM – describes learning by focusing on the behaviors of
students. Anything that a student does is described in terms of behaviors,
including thinking and learning. Behaviorists do not consider abstract
constructs (such as the mind) in their analyses.
COGNITIVISM – describes thinking by positing the existence of mental
states that are manipulated during thinking. Cognitivists infer the structure
of cognitive entities from experiments and observations of students.
SITUATIVISM – describes knowing by considering that the actions of
students are affected by the context (social, cultural, physical) in which the
students' perceive themselves to be. Situativists view knowing as
determined by both the person and the context. Learning is identified by
students' increasingly effective performance across situations, rather than
by the accumulation of knowledge.
Reference
Greeno, J. G., Collins, A. M., & Resnick, L. B. (1996). Cognition and
learning. In D. Berliner and R. Calfee (Eds.), Handbook of
Educational Psychology (pp. 15-41). New York: MacMillian.
Q
Q
Using a computer algebra system, students explore different ways of
visualizing a scalar field in three dimensions.
POTENTIAL OF A RING OF CHARGE
Evaluate the distances in the denominator for this
specific case.

1 
V  x 
4 0 

VISUALIZING POTENTIALS
Students place themselves
around the classroom to model
various charge density
distributions (linear, surface,
and volume) while building
their conceptual understanding
of the idealizations involved in
going between discrete and
continuous representations of
charge.
qi
r  ri
Choose a coordinate system and draw
a diagram.
Students are asked to draw
equipotential surfaces on
whiteboards for various
charge distributions.
ACTING OUT CHARGE DENSITIES
Recognize that the r in the iconic equation is the distance between the source
and observation points r  r '
V r  
DRAWING EQUIPOTENTIAL SURFACES
Students often claim not to know how to get started.
Often, the difficulty lies somewhere in the process of
translating an abstract, coordinate-independent, algebraic
representation, through a geometric representation, to a
coordinate-dependent, algebraic representation on which
the students can “do math.”
kq
V
r
1
FOLLOW-UP ACTIVITIES
PCK
Two charges + Q and – Q are placed on a line at x=+D and x=-D,
respectively. What is the fourth order approximation of the
electrostatic potential, V, valid on the x-axis, for |x|>>D?
Choose a coordinate label (x, 0, 0) for
the point at which the potential will be
evaluated.
Using a Star Trek scenario
as a premise, students
discuss how to specify the
distance between two
objects (Captain Kirk and
Mr. Spock)
•Department of Physics
•College of Science
•Academic Affairs
We would like to thank members of the Paradigms team, especially
Start with an “iconic” equation – the potential due to a point charge.
PREPARATORY ACTIVITIES
Oregon State University
Q
 x  D

2
Q
 x  D
2




Recognize from the geometry that the denominators should be
expressed with absolute values, especially when x is negative.
1  Q
Q 
V  x 



4 0  x  D x  D 
Students working in small groups
calculate the electrostatic potential
due to a ring of charge. Sums go to
integrals.
Most students do not know what to do with the absolute
value signs, especially when x is negative. Many just
drop the absolute values. This topic can be a source of
rich class discussion during the whole-class wrap-up.
MODES OF COGNITION
We have used the following icons to classify the tasks and problems
according to a mode of cognition required to successfully complete that
portion of the task or that fails when students have a particular problem.
Recognize that the denominators have something to do with known series.
recognizing patterns
Decide what to factor out to put the denominators in the form of “one plus
something small and dimensionless”.
fleshing out formulas
1 Q
D
V  x 
 1 
4 0 x 
x
1
D
 1
x
1



Implement known mathematics from a memorized power series.
Simplify, group terms.
1 2Q   D 
V  x 
 1   
4 0 x   x 
2



WRAP-UP (WHOLE CLASS DISCUSSION)
In the whole class wrap-up discussion, students:
•practice presenting their ideas,
•compare with examples from other parts of space,
•compare with limiting examples,
•explore symmetry.
applying learned mathematics
Believing that the only way to find a power series is
using successive differentiations.
1
1
 xD
The failure to recognize that
xD
p
Not recognizing that 1  x  is a common power
series.
1
Not knowing how to do the algebra to put
xD
p
in the form of 1  x 
choosing foothold ideas, choosing a principle/iconic formula
restricting the scope
applying a principle to a specific case
sense making
translating representations, harmonic reasoning
seeking coherence
shopping for ideas
probing and refining intuitions
playing the implications game
employing a safety net
Many of these cognitive modes and icons were first introduced in:
Reference
Reinventing College Physics for Biologists: Explicating an Epistemological
Curriculum , E. F. Redish and D. Hammer, Am. J. Phys., 77, 629-642
(2009).