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Re: Error Analysis



Hi all-
I would go further than Gary in avoiding error analysis, as I
discuss in the appended posting from last year. I much prefer that
the labs be devoted to conceptual matters, as in Hake's SDI labs
or the High School Mechanical Universe project.
I'll bet that many of your AP students don't really have a "feel"
for acceleration. And I'll be amazed if some of these students wouln't
name the "top of the trajectory" as the place where the vertical
acceleration of a projectile is zero.
****************************************************************
What error analysis should Academic and AP Physics high school students
be doing? Thanks for any imput.
Roger,
I sometimes wonder if college freshman are mature enough to understand
error analysis, and feel very lucky if I can get them to record answers plus or
minus some error after my course. For some it seems obvious and others I think
still don't get the point, but do it to get me off their backs. With this
background I wonder if you can teach students a year younger and with a lot more
unbridled energy anything about error. If I were in your shoes I would probably
try to show them how an average of many measurements gets better results and
tell them that the standard devition key on their calculator give them an
indication of size of the error.
I think the most valuable thing that students can learn in the
limited time available in high school labs is the connection between what
they calculate in problems and what happens in the real world.
Gary
***********************
From: ANLHEP::JLU "Jack Uretsky, Internet:"JLU@HEP.ANL.GOV", HEP Division, Argonne National Lab, Argonne, IL 60439" 8-FEB-1995 13:45:04.22
To: GATEWAY::"HERR@CATSEQ.CATLIN.EDU"
CC: @PHYS-L,JLU
Subj: Re: Teaching "error analysis"

Hi all-
Lowell Herr says:
********************************************************************
We start working with uncertainty at the 8th grade level (not to the
degree you would in college) and then continue to expand on this base in
the ninth grade. For example, when students
are working with electrical energy they have a 3% uncertainty on both our
volt and ammeters and a numerical value for the thermometer depending on
what type they use. When the variables are multiplied, students need to
convert to % uncertainty and add the percentages. I think you get the
idea. I don't require uncertainty analysis in every experiment but I
generally require it on about 1/2 of the 22 - 25 labs we do each year.
Juniors and seniors receive a 'stepped-up' version including some
statistical analysis of the data.

I think it is important that students be exposed to this at the high
school level so that when they are really pushed in college this will not
hit them as a totally new concept.
**************************************************************************
This was in response to a message from Jon Bell.
I certainly agree that if one is going to teach "uncertainty",
the concept needs to be introduced early, and must pretty well permeate
the educational process. I think, however, that there is another requisite;
there needs to be a practival payoff for thinking about uncertainty. I'll
try and explain what I mean.
I spent about four years teaching a non-calculus physics sequence
with a very traditional lab. The students measured "g" three or four
different ways, and other physical quantities, and were required to make
uncertainty estimates. It was clear from reviewing the lab reports, however,
that the concept was not taking hold. The uncertainty estimates were often
part of a "mickey mouse" ritual that the students had to go through to get
a satisfactory grade on a lab report. Deep understanding was not an element
of the ritual.
Well, I'm not one to spit upwind more than 4 times in succession
before the message begins to seep through, so I began to ask myself, "Why
am I doing this?" "Where in my own life did I begin to get a grasp of the
importance of uncertainty estimates?" My answer was that uncertainty
became important when I was an upper-class aero engineering student. In that
context, one has to find a compromise between two alternatives: structural
safety, on the one hand, and aircraft performance, on the other. Excessive
structural safety adds unnecessary weight to the aircraft, which is detrimental
to performance. But adequate structural safety requires compensation for
uncertainties in the predicted strength of the structures. The smaller the
uncertainties, the less excess strength is needed for compensation.
I think that it was at that point that the issue of uncertainty
became very real for me, and I began to learn about uncertainty for the
first time. I'd had the usual previous acquaintance with the subject in
physics labs (and, more to the point, machine shop), but that acquaintance-
ship was inellectually unstimulating. It was, in my opinion, a wasted
effort.
My conclusion, as far as the teaching of elementary physics was
concerned? Don't bother with it. It's a distraction from the main show,
and the cost/benefit ratio is huge.
Regards,
Jack