Re: [Phys-L] Curve Fitting

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

Even students in the calculus based physics courses do not understand curve
fitting, and 25% lack proportional reasoning.  In the general physics course
75% lack proportional reasoning.  For these reasons the old fashioned
linearization procedure is used by Modeling.  You may recall that if you
have a parabola in X vs t you plot a test graph X vs t^2 and then use a
simple hand straight line fit to get the equation.  Of course you have to
arrange that the test curves will have an intercept at zero.  This may be
helpful in promoting proportional reasoning and it is less opaque than the
black box fitting.

Unfortunately many students do not understand algebra so they tend to think
the equation derived from the straight line test graph only applies to that
graph.  But the procedure at least is understandable and doable.  Of course
it doesn't give the uncertainty on the coefficient.  Leaning how to figure
out an equation from a simple graph is far more important than solving the
same equation.  Students need to learn how to create equations because that
is a skill which at present is not fully computerized, while solving them is
computerized.

This problem has been with us since Newton.  He fully understook algebra,
but distrusted it because it hid understanding.

Incidentally understanding minimization may require statistical reasoning
which only about 1% of graduating HS seniors grasp.

John M. Clement
Houston, TX

> The problem is that the "user-friendly" packages that are available
> are black boxes that can be
> (nearly) worse useless in terms of the students' actually grasping
> what's going on, if they
> haven't been instructed in the basics of curve fitting.   The same
> phenomenon that we see with
> students who can't distinguish between sine, cosine and tangent, or
> what to do with an inverse sine
> because they have only used their suped-up TI-XYZn graphinc
> calculators is happening with physics
> students whose experience with curve fitting is limited to using the
> black box.  So... I'd fully agree with
> the statement to which you're responding, Jim - it really is important
> to teach students what it is that a
> curve fitting program is trying to minimize, and how it's 
> done in basic terms.
>
> Todd
>
> On Wed, Aug 29, 2012 at 12:22 PM, Jim Deane 
> <jim.deane@gmail.com> wrote:
> > > I mention it in this forum because anybody who wants to do 
> physics needs
> > > to be proficient with least-squares fitting.
> >
> > Hmm.  Do you think this holds true even with the extensive 
> user-friendly
> > curve-fitting software packages available now?
> >
> > I can understand needing to understand how it is done, but 
> I don't know
> > that proficiency is required any longer.
> >
> > Jim
> >
> >
> > --
> > -- --- ----- ------- -----------
> > James K. Deane
> > jim.deane@gmail.com
> > -- ------- - -------- -- --------
> > _______________________________________________
> > Forum for Physics Educators
> > Phys-l@phys-l.org
> > http://www.phys-l.org/mailman/listinfo/phys-l
>
>
>
> -- 
> Todd K. Pedlar
> Associate Professor of Physics
> Luther College, Decorah, IA
> todd.pedlar@luther.edu
> or pedlto01@luther.edu
> _______________________________________________
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