Re: [Phys-l] unbiased experiments--inquiry methods

["John Clement" <clement@hal-pc.org>]

> >
One of the decisions that has to be made is whether it is worthwhile to go
into more advanced analysis as to why you get the result based upon other
principles.  In an advanced calculus based course this might be useful.  In
a basic course the pendulum lab can be left as an example of "scientific
method"  Modeling uses it as the first lab purely to get students into the
methods of analysis.  So the students never are acquainted with how Newton's
laws can be used to predict the result.

The decision is made to pare out some of the extraneous material with the
goal of getting basic understanding of force, velocity, acceleration,
momentum, and energy along with motherhood and apple pie.  The pendulum is
just a specific application, and there are many others that are of much
greater importance to building a consistent mental model.

Modeling only uses a simple experiment as a paradigm for the later
development of the model.  As such the pendulum does not serve as a good
clear model for a single concept.  It is way too complex if you wish to get
into the details.

John M. Clement
Houston, TX


> > Actually the students shouldn't "encounter" the equation, they should
> > determine it from the lab.  The Modeling approach has them graph the
> data,
> > and if it is a straight line, just find the equation.  If it is not,
> then
> > they try different ways to make a modified graph by changing the X axis.
> > If
> > they have X vs t and it "looks like a parabola" graph X vs t^2 and see
> if
> > they get a straight line.  This is a fairly old fashioned approach.  Of
> > course the students have to follow some rules for taking the data so
> that
> > the data is analyzable by this approach.  If it is a 1/sqrt(x)
> > relationship
> > they have to first make a graph of 1/x and then by noticing the
> curvature
> > try 1/sqrt(x).  So for most situations all they need is to recognize is
> > linear, inverse, square, and square root relationships.
>
> Fine so far--this is pretty much where we first go with the pendulum
> experiment I described.
> But then what?  You end up with T = 2(L)^.5.  You can deduce that the
> constant (about 2) needs units of seconds/(meters)^.5.  Students can (do)
> see that gravity has something to do with the motion.  I guess if you want
> to spend 3  periods on this you can work on the dimensional analysis, the
> 'guess' that the acceleration of gravity needs to be in there somewhere
> (although why the mass is not is going to be mysterious), and then play
> with
> the experimental constant and the units until you see an unexplained
> constant of about 6 floating around.  That this constant is actually 2 pi
> might be deduced (if the original experiment is accurate enough) but this
> might be a big stretch for HS and gen-ed students.  Connecting all this to
> SHM is yet another HUGE leap.  Now our science/engineering students might
> get there, but with the content requirements of those courses, can one
> really spare the time?  I really can't see the value after a point.
> Somewhere along the line one really needs to jump in with an equation.
> Reinventing the wheel once or twice is fine--but not for a whole
> curriculum.
> Students need to also know how to learn from books, from articles, from
> lectures--that is, from the learning paths that are available to them
> outside the structured classroom.