Re: More on (Derivations)

[Rick Tarara <rbtarara@SPRYNET.COM>]

I want to voice my agreement with what Joel has said, even though one can
count the number of derivations I formally do in my intro courses on one
hand.   For example, I feel it is important to 'derive' the kinematics
equations, especially for the problem solving classes which will be using
them extensively, but also for my 'liberal arts' class in order to show how
this set of very useful equations DOES NOT come out of thin air.  (And I
have had to memorize that you get the equations starting with the definition
of acceleration and the 'common sense' equation that the distance traveled
is the average speed times time.)  What I try to do often is have the class
'derive' and equation.  Things like the Heat Flow across a boundary (despite
there being no such thing) can easily be determined by the students--both
the quantities involved and the functional dependence.   Working though some
of the Trig when one gets to waves is useful (since nobody seems to take
actual Trigonometry anymore.  There are a couple other places in the intro
sequence where a 15 minute derivation SHOULD be intellectually justified.

I suspect the knee-jerk reaction against derivations really comes from our
shared experiences in higher level undergraduate and most certainly graduate
courses, where reading the book to one's class and slogging through all the
derivations is par for the course.

Rick

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Richard W. Tarara
Associate Professor of Physics
Department of Chemistry & Physics
Saint Mary's College
Notre Dame, IN 46556
219-284-4664
rtarara@saintmarys.edu

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----- Original Message -----
From: "Joel Rauber" <Joel_Rauber@SDSTATE.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Monday, August 21, 2000 2:08 PM
Subject: Re: More on (Derivations)


> I am trouble by a couple of the comments on derivations:
>
> e.g.
>
> > This avoids the need to rely on derivations which are
> > mysterious and tedious to  algebra-challenged students
>
> One of the more important reasons for covering derivations (besides
helping
> in learning where a lot of the stuff comes from, and fits into the scheme
> of
> things, and isn't just a collection of facts), assigning some derivations
> as
> HW and even having them every now and then on tests (not to be memorized,
> because often its a similar but different derivation from the assignment;
> in
> fact as long as there aren't numbers most students view a problem as a
> derivation, or worse as "theory"): is to address the "algebra-challenged"
> nature of the students.  Derivations requires that they try to develope
and
> enhance their skills with algebra and algebraic reasoning to solve
> problems.
> If nothing else, I hope my students develope these kind of skills and the
> cognitive abilities that come from developing them.
>
> > I agree with that. I never do a derivation that I can't complete in a
> > few minutes. If it's longer than that they forget even what we were
> > trying to do.
>
> This means that those students never have to attempt to grapple with a
> longer derivation and develope their skills in dealing with such.  I'd
hope
> that one of the purposes of higher education is to develope these very
> skills.  I know attention spans are such that this is difficult; but its
> for
> that very reason students should be forced to confront such tasks, even as
> a
> freshman, where I believe it should start.
>
> Naturally I don't mean that the bulk of the intro course should be half
> hour
> derivations or any such nonsense; just that every now and then a longer
> than
> few minute derivation should be dealt with (by whatever means); following
> long arguements is an important higher level coginitive skill and the
> developement of that skill should beging sooner than later.
>
> My comments are not necessarily meant to be appropriate in high school
> contexts.
>
> Joel Rauber
> Joel_Rauber@sdstate.edu