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Re: [Phys-L] one variable at a time ... or not



On 07/01/2016 10:37 AM, Larry Smith wrote:

For a simple pendulum I have my beginning students vary the mass,
length, and amplitude, one at a time; make graphs of the dependence
of the period on these; and, along with dimensional analysis, try to
deduce the formula for the period. I can’t see this experiment
being as instructive if they changed all the variables at once

That's a fine example as far as it goes. In the introductory course,
it makes sense to select and collect examples of that ilk, where
there are only a few variables, and the obvious variables are
naturally uncorrelated.

If the problem were not naturally simple we would search for ways
to make it simple.

Alas the real world is not so simple.

Simple examples are 100% fine as a pedagogical starting point, but
they must not be the ending point. Although the "building block
approach" starts by taking each task apart into simple components,
it must not end there. It is essential to put the blocks back
together, two at a time, three at a time, et cetera, to finish
the overall edifice.

Sooner or later (preferably sooner) the students need to
learn to live in the real world.

I suppose I could add a comment at the end that there are many
applications where changing just one variable at a time is not the
best approach, so that OVaaT is not the ending point.

A passing comment is likely to spread confusion, if it is not
ignored entirely. It would be better to provide a specific,
easy-to-understand example. One thing that comes to mind is
changing the tires on your car. If you do it one tire at a
time "to see what happens" you will get dangerously misleading
results.

I see this as somewhat of a Big Deal. I’ve seen too many “Conceptual
Physics” courses where the students learn simplified concepts in
isolation, but never learn to put things together. A pile of
disconnected concepts is not interesting, just as a pile of
disconnected Legos or full-sized building blocks is not interesting.
They only become interesting – and useful – when they are put
together in artful ways.

Concepts without real-world connections will be more-or-less
instantly forgotten. This defeats the point of the whole course.


I collected some of my thoughts on this topic at:
https://www.av8n.com/physics/one-variable-at-a-time.htm