OTOH--Scientist and Engineers use equations all the time. Sometimes we have
not derived these, but rather understand them at some level (well the
scientists do) and trust that they have been thoroughly tested. I fit all
the equations needed for my first semester, Calculus level class on one side
of a standard piece of paper--and didn't use particularly small fonts. That
same sheet includes some math stuff, like basic Trig and the quadratic
formula (although they all have that function on their calculators these
days.) Many of the formulae were derived--kinematics from the definition of
acceleration, KE and grav PE from Work--but the work formula given through
the definition. Newtonian gravitation given--not derived, but then used to
derive Kepler's Third Law. While the derivation of centripetal acceleration
is given in all the books--I usually just use it. Likewise, we need the
velocity of a wave on a string formula in order to setup standing waves, and
it can be derived, but it is not worth the time and effort (IMO)--happy to
give and use the formula and reference the book derivation.
So--I would suggest a reasonable mix of derived and given equations is not
too bad. It is the way we all (well almost all, I suspect some do derive
everything from first principles) operate. I used statistics equations for
some time before sitting down and figuring out where they came from and I
fitted a lot of my thesis data (eons ago) using Distorted Wave Born
Approximations which I only vaguely understood--but had a program that would
do the calculations (yes on punch cards!)
;-)
Rick
Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, Indiana
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----- Original Message -----
From: "Paul Lulai" <plulai@stanthony.k12.mn.us>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Monday, January 31, 2011 2:35 PM
Subject: Re: [Phys-l] Any teaching tips
"an equation should be acceptable if the student can derive it."
High school freshman are not very good at deriving. The rearranging of a
single equation with 3 variables is a challenge for 1/2 of them (seemingly
insurmountable for 1/10 of them).
I plan to try the graphical analysis approach and find the relationships in
that manner this semester (don't often teach freshman). I suppose this
would count as deriving. I don't know how much success (or time would be
required) to derive a relationship from multiple other relationships.