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Re: The Soapbox




I am tempted to show simple transversal, longitudinal and torsional =
waves, to discuss the meaning of y(x,t) as displacement of the disturbed =
medium as a function of position and instants, and mention only =
theta(x,t) for torsion, or E(x,t) and B(x,t) and even mention the =
Psi(x,t) as the density probability.

_Show_ these waves, with a slinky (best for longitudinal waves, but good for
transverse, too) and with a more tightly coiled spring. In preparation for
an explanation of refraction and varying wave velocities in different media,
attach the two securely and show them the change in the wave as it moves
from one medium to another. If you intend to show them how waves reflect,
attach the spring to a post and show them reflection with an end (almost)
free to slide up and down as you send a transverse wave down the spring to
reflect. I usually tell them simply to observe, then after each brief
demonstration, I ask them if they need to see it some more, or can they
describe what they just saw. Then they use their own words to state their
observations. I try to prompt them to observe & describe the phenomena we
will later formalize. In the first intro, I avoid introducing terminology
they are not familiar with. (The students' background of course will vary my
vocabulary. I take my cue from the vocabulary they use.)

After the observations are finished, I move to a more formal discussion. 30
minutes of detailed observation and description usually leaves only a little
time for a formal discussion, but I feel it provides such a good foundation
for the concepts, I make sure the class has it. I also try to connect it to
their experience in math class. I prepare for the class by talking to a few
students and their math teachers about the introduction they got to periodic
functions, so I know how to help them make the connections. But since not
all of my students get the same background, I try to avoid introducing the
concepts with terms. I hold the correct terminology until _after_ they
observe. My informal trial and error research says only two or three terms
should be introduced the day they first see the demonstration. Other days,
they do okay with more terminology and notation, but the first day, they
seem to need the time to absorb the concepts.

Also, I am tempted to get into the aspect of relating the velocity of =
the "news" to the velocity of the material particles and the =
instantaneous slope, and in a smooth way to introduce the all the first =
and second order derivatives with respect with time and postions =
culminating with the wave equation...

I'd hold most of this until they have had time to think about (and possibly
write a description of) the observations for a day.