It's been interesting to watch the various conversations on phys-l in the
last ten days or so. Should statistical ideas be explored by experiment? Is
it right to use an accelerometer to measure kinematic acceleration?
I think we'd all do well to remember that teaching and learning are highly
contextual activities. A given question or experiment may, strictly
speaking, have a certain flaw or incompleteness. Does that matter in the
context in which the activity is used? Maybe, or maybe not. The nits that
can be picked are actually quite informative, because it helps us set the
proper context.
For example, in the Newton II lab I described earlier, another contributor
quite rightly pointed out that the accelerometer sensor does not measure
kinematic acceleration (not his words). Instead, the accelerometer is making
a dynamical measurement which actually depends on the second law. In my
opinion, that doesn't disqualify this sensor for use in the Newton II
experiment. Here's why: the measurement I described is very easy to perform,
and takes at most ten minutes, even with multiple masses. Before performing
the experiment, however, I would have my students explore the behavior of
the accelerometer.
It is a fairly simple matter to show, experimentally, that the accelerometer
readings agree with the 2nd derivative of the motion detector distance
readings, when the motion is entirely horizontal. (This step need not be
done with a dynamics cart, but can be done with a hand-held accelerometer,
yielding clean motion data.) That shown, whatever is going on inside the
accelerometer (literally a black box), accelerometer readings agree with
kinematic measurements if the motion is strictly horizontal.
I simply choose to do the NII experiment with an accelerometer rather than a
motion detector because a typical student can actually collect useful data
quickly. It takes a certain amount of time and finesse to set up the
experiment with a motion detector, while the accelerometer setup is quick
and easy.
The kinesthetic part of the NII lab has an impact on some students--just
feeling the force in their fingertips as they wiggle the cart back and forth
and see the associated force and acceleration graphs is an eye-opener to
some. That will matter for students coached to think about this aspect,
while it leaves others (and many instructors) cold.
On the other hand, I can also imagine a different experiment having more
impact on a mathematically inclined class. There is no one best way for all.
Similarly, I know of students who seem to be able to get their minds around
the concepts of a simulation very rapidly. They find simulations quite
illuminating. Then there are students who are left cold by staring at a
computer screen, especially if the only output is in the form of numbers and
graphs. Listening to a Geiger counter and taking data to illustrate the
statistical point may reach those students much more quickly and effectively
than using Excel. It depends on the background and biases of the audience.
Finally, as instructors we need to note that students take on our own biases
very quickly. If we (or a prior instructor) talk up experiment as the
ultimate authority, then students will find experiments striking. If instead
we talk up the mathematics, then elegant presentations may have great
impact.
Let me call your collective attention to the article in the recently arrived
PER supplement to AJP, "Computers in teaching science: To simulate or not to
simulate?" Richard N. Steinberg, Phys. Educ. Res., Am. J. Phys. Suppl. vol
68 number 7, July 2000, page S37-S41.
I'll not reveal the conclusions (I want folks to read the article!), but
will instead point out an interesting observation. It seems the some
students, in viewing an simulation, used the simulation as the authority.
For example, the ball doesn't go as high because the graph doesn't go up as
far. The circularity is obvious to us, but is it to the student?
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John E. Gastineau john@gastineau.org