Lillian C. McDermott
41
History
3/15/10
be compared.
The students determine the instantaneous velocity of a ball at several points
as it rolls down the incline by noting when the ball and a mark on the belt appear to move
together.
(The same criterion is used in David’s speed comparison task.)
Students use a stopwatch to record how long it takes the ball to attain the velocity
of the belt for different speeds.
They plot values of the velocity and corresponding time to
produce a
v
vs
t
graph.
The experiment enables students to make qualitative judgments
about velocity, change in velocity, and acceleration.
It also focuses attention on the
crucial importance of the time interval and brings out the difference between the change in
velocity and its rate of change (the acceleration), a distinction that escapes many students.
Measurement of instantaneous velocity
This experiment is only one of the many instructional strategies incorporated in the
Kinematics
module in
Physics by Inquiry
.
Mark Rosenquist’s conceptual (rather than
formulaic) approach to teaching kinematics provided the foundation for the development
of this module.
His identification and analysis of specific difficulties in connecting graphs
to the concepts of position, velocity, and acceleration and relating graphs to real world
motions also helped guide curriculum development in other contexts.
One encouraging early finding in our development of the
Kinematics
module in
PbI
was the great improvement in performance on Acceleration Comparison Task 1 by
students from the EOP class.
Virtually all began the course unable to distinguish between
position and velocity in comparing two simple motions.
Mark’s contributions to the EOP
course emphasized concept formation along with the development of scientific reasoning
and graphing skills.
The students spent much time on laboratory exercises, class
discussions, individual dialogues with instructors, and on examinations.
They
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).
