Re: FAST: exemplary middle school science

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

> One small difference of opinion with Hugh,
>
> >  The other quibble has to do with the idea of "expected results." I
> >  have a running battle with our chemistry teachers who seem to have
> >  the idea that their students can do error analysis in their labs by
> >  simply calculating the difference between the answers they obtain and
> >  the "correct" answer--that is, the answer in the text. This is to
> >  error analysis as "paint by numbers" is to art.
>
> I believe that when measuring a known quantity, where there exists a
> nominally correct value, that calculating per cent error is a legitimate
> part of the error analysis.  It provides a good quick reality check on what
> you are measuring and can often quickly reveal calculational mistakes.
>
> I hasten to add that this isn't and should never be the complete error
> analysis!  Consideration of the error bars, both in a qualitative and
> quantitative manner should be viewed as mandatory for interpreting a per
> cent error calculation. (I note that quantitative estimation of error bars
> is not always easy for students to estimate for labs where  the result is
> the end of relatively long chain of calculation).
>
> Joel Rauber

Agreed, and for this reason I don't always require an error analysis.
And of course we use the "real" value for a reality check--if they
get 100 or 1 instead of 10, clearly there is a computational or
scaling error, so this does get them back into the right ballpark,
but, as you say, they then better do a proper error analysis.

I suspect that at least part of this problem (comparing their answer
to the "correct" one and calling that the error) comes from the
horrendous misnomer that we have given the whole procedure. It should
be called "uncertainty" analysis, or something akin to that, since,
when we don't know the "correct" answer, we don't know what our error
is, only the uncertainty in our measurements. And of course, the
statistical uncertainty analysis is only the easy part of the
process. The much more important and much more difficult part is to
figure out what the systematic uncertainties are. While statistical
analysis can be taught in a formal way, systematic uncertainties can
only be found by careful analysis of the experimental setup and long
experience. Some experimenters get very good at it, and become
renowned for their experimental ability, others never get it so good,
and often learn to stay away from the lab, becoming either
theoreticians or administrators.

Hugh
--

Hugh Haskell
<mailto://haskell@ncssm.edu>
<mailto://hhaskell@mindspring.com>

(919) 467-7610

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