Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

[Phys-L] Re: student mathematical capability



----- Original Message -----
From: "John Denker" <jsd@AV8N.COM>

What is the point of trying to teach relativity to kids who cannot solve
one
linear equation in one unknown? It seems like a misapplication of
resources.

I've been expecting this question from JD.

In my case, the course (for Gen-Ed students--we have a 2 semester,
laboratory science requirement of all students) is in two parts. In the
first semester the primary goal is to look at science (physics in
particular) as a way of knowing. What does science tell us about ourselves
and our world and how does it go about doing that? To approach this, I
concentrate the entire first semester on MOTION and try to superimpose an
historical perspective upon a reasonably standard, conceptual curriculum.
We trace the development of ideas on motion from Aristotle to Newton and
ultimately to Einstein. We try to describe motion first then try to
understand the causes. Mostly we are working with the Newtonian models.
However, near the end of the semester we will consider that modern
observations demand that we move beyond Newton to the more sophisticated
models of Einstein et. al. To that end, Special Relativity is introduced in
the form of Einstein's Postulates and the consequences of those postulates
as summarized in 'moving clocks run slow', 'moving masses increase', and
'moving lengths contract'. I use the light clock to show how such a clock
would 'run slow' as viewed from the fixed observer and then we speculate
that in order for the postulates to hold, the moving observer must perceive
this clock as running normally. This leads to the _all_ moving clocks run
slow conclusion. Students, of course, don't really buy this so then I
present the experimental evidence. We then look at the twins with the
primary 'useful' consequence of all this being that (at least in theory)
time dilation makes interstellar travel a (far) distant possibility--other
serious factors being ignored. The mass effect is discussed in terms of
particle physics phenomena--my electrostatic accelerator days has me use
bending magnets and high speed protons as the example. What I actually
present is what classical physics would predict for the magnetic strength
needed to bend the particles, the path they actually take, the relativistic
prediction (based on mass increase), and the success of using such settings.
I know of no experimental evidence for the length contraction other than it
is necessary for the consistency of the theory. We do look at a whimsical
consequence--my version of the 'barn paradox'--which of course is not a
paradox at all.

Anyway, in this kind of course, we try to keep the math to a minimum--but
not zero--I am not hesitant to show them where the Calculus ends up being
useful (and why Newton developed it), to do some algebra to show how some
relationships are developed (deriving the kinematics equations from the
definition of acceleration for example), to have the class develop equations
just by considering all the pertinent factors, and to expect the students to
actually do calculations IN THE LABS where they have partners and an
instructor to help if they get stuck. Still, we are limited by the overall
math skill level and many of the finer points attempted clearly go over the
heads of many students. Hopefully (and seemingly so from my assessments)
they do understand enough of what we do to make the course worthwhile. The
second semester of the course delves fairly deeply into the Energy
problem--national and global.

Rick

*********************************************************
Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, Indiana
rtarara@saintmarys.edu
********************************************************
Free Physics Educational Software (Win & Mac)
Animations for Lectures
Photo-realistic Lab simulations
Energy management simulations
www.saintmarys.edu/~rtarara/software.html
Energy 2100--class project
www.saintmarys.edu/~rtarara/ENERGY_PROJECT/ENERGY2100.htm
********************************************************
_______________________________________________
Phys-L mailing list
Phys-L@electron.physics.buffalo.edu
https://www.physics.buffalo.edu/mailman/listinfo/phys-l