Lillian C. McDermott
42
History
3/15/10
encountered many situations designed to help them distinguish kinematical concepts from
one another.
As a result, the EOP students demonstrated a qualitative understanding of
acceleration on post-tests that matched that of students in calculus-based physics.
Many students struggle over the same hurdles in the same sequence.
Although
students who are well prepared may progress faster than those who are not, our research
has shown that many do not acquire a useful understanding of the concept of acceleration
in the short time allotted.
It would be desirable, especially for K-12 teachers, to devote
greater attention to basic concepts, even if some advanced topics must be omitted.
B.
Dynamics:
Right Answers for the Wrong Reasons
87
Two investigations (one in the 1980s, the other in the 1990s) included the tasks
designed by Ron Lawson for the individual demonstration interviews on student
understanding of the impulse-momentum and work-energy theorems.
The tasks later
became part of a tutorial on changes in energy and momentum.
(See the diagrams.)
Apparatus for momentum and energy comparison tasks.
87
See Ref. 32 and T. O’Brien Pride, S. Vokos, and L.C. McDermott, “The challenge of matching
learning assessments to teaching goals: An example from the work-energy and impulse-momentum
theorems,”
Am. J.Phys.
66
(2), 147, (1998).
Lillian C. McDermott
43
History
3/15/10
First mark
Second mark
Top view
Frictionless table
m
B
> m
A
F
o
A
F
o
B
Momentum and energy comparison experiment.
During the interview, students are asked to compare the final kinetic energies and
momenta of two dry-ice pucks (one brass and one plastic) that move on a glass table, as
shown in the accompanying figure.
A constant force
(F)
is applied by a steady stream of
compressed air in a direction perpendicular to two parallel lines.
The pucks start from rest
at line A and move in a straight line, not rotating and essentially without friction, to line B.
A correct explanation was necessary for a correct response.
The comparisons can
be made by direct application of the work-energy and impulse-momentum theorems.
Since the force is constant and parallel to the displacement
(
Δ
x)
, the theorems reduce to
F
Δ
x
=
Δ
K
and
F
Δ
t
=
Δ
p
.
The change in kinetic energy of the blocks (considered as point
particles) equals the work done by the external force and is the same for both pucks.
Since the same force is applied to both, the brass puck acquires a smaller acceleration
(F =
ma)
.
During the longer time the brass puck spends between the lines, it receives a greater
impulse and hence experiences a greater change in momentum than the plastic puck.
(A
correct comparison of the final momenta of the pucks also follows from the equality of the
kinetic energies and the algebraic relationship between kinetic energy and momentum.)
The 28 students who participated in the interviews were volunteers from two
introductory physics courses at UW.
There were 16 from the algebra-based course and 12
from the honors section of the calculus-based course.
The average of their final grades
was higher than the average for the classes in which they were enrolled.
Only about half
the students in the honors section gave correct responses with correct explanations.
None
from the other course did.
Following is an example from one of the interviews.
I:
What ideas do you have about the term work?
