Re: precision?

[Robert A Cohen <bbq@ESU.EDU>]

On Wed, 1 Sep 1999, Ed Eckel wrote:

> At any rate, the original post to the thread asked if the concepts of
> precision and accuracy were essential to a HS introductory course.  The
> discussion quickly moved into a debate on what each word meant.  I still
> want to know, what is gained/lost by inclusion/elimination of the issues
> of precision and accuracy in an introductory course?

A rather long story...please bear with me...

I teach a course for students majoring in secondary science education.  As
part of the course, they present lessons to the other students in the
class.  One time, a student presents a lesson on conservation of energy.
He has the students roll a ball off an inclined ruler, which then rolls
off the table and onto the floor.  Using cons. of energy,

      (1/2) m v^2 = mgh (h is distance fallen on ruler)

and other relevant relationships, the student solves for x (distance from
table to target) in terms of h and has the students place their target at
x.

What do you think happens?  Well, I'm watching this, knowing full well
that the balls will not hit the target because of several invalid
assumptions.  Most importantly, the cons. of energy relationship doesn't
consider that gravity does some work to rotate the ball.

Not surprisingly, everyone's ball falls short of their target.  They
aren't even close. (Well, one group gets it pretty close but they made a
mistake in their measurement).

To my surprise, however, everyone determines that conservation of energy
has been validated, which was the presenter's purpose of the activity!
When I inquired as to why the balls missed their targets, the students
attributed the differences to imprecise measurements, air resistance, and
(gasp!) human error.

I feel the problem was that the participants (who were going to be high
school science teachers) had little idea of error analysis.  If every
"experiment" validates the theory, no matter what one's results, then what
is the purpose of the experiment?  Every experiment produces results that
don't agree exactly with theory.  The key is to determine whether the
problem is with the theory, assumptions, measurement precision,
measurement resolution, biases, mistakes, etc.

To answer your question, I don't think it matters so much *what* your
students call the reasons for the descrepancy; but it does matter that
your students can reasonably identify the probable reasons by estimating
their effect.

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| Robert Cohen               Department of Physics       |
|                            East Stroudsburg University |
| bbq@esu.edu                East Stroudsburg, PA  18301 |
| http://www.esu.edu/~bbq/   (570) 422-3428              |
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