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Re: simplify a trig expression
 To: mathgroup at smc.vnet.net
 Subject: [mg65495] Re: simplify a trig expression
 From: Murray Eisenberg <murray at math.umass.edu>
 Date: Wed, 5 Apr 2006 06:55:38 0400 (EDT)
 Organization: Mathematics & Statistics, Univ. of Mass./Amherst
 References: <200603311109.GAA15029@smc.vnet.net> <200604011038.FAA07301@smc.vnet.net> <200604020900.FAA01612@smc.vnet.net> <11D40ADD9EC94DCEB6851CA00605B9B2@mimuw.edu.pl> <e0r0c9$mt$1@smc.vnet.net> <paulC4EC13.21302303042006@news.uwa.edu.au>
 Replyto: murray at math.umass.edu
 Sender: ownerwrimathgroup at wolfram.com
Actually, we have a system here called OWL that is similar to CalMaeth
and employs Mathematica and MathLink as its backend engine. We use it
in a calculus course aimed at students in biological sciences, social
sciences, and business; several units are on methods of integration.
Curiously, in our mainstream course (for students in math, computer
science, physical sciences, and engineerings) we cannot currently employ
that system mainly for logistical reasons (no lab space available) and
partly because we'd need to develop a richer set of exercises.
So I completely agree that using a CAS behind an online learning
management system is a sensible thing to do. So is using CAS in a
different way, as a tool directly employed by students, to do more
interesting things (as I explained in another message). As I originally
said, all I wanted to do was produce a demonstrably correct set of
answers to a handful of integration exercises that would be in a form
similar to what students would get by hand. And although I have no
doubt that each and every one of the graduate teaching assistants who
will be grading our symbolic integration exam is capable of converting,
say, a student's answer of Cos[x]/(Sin[x] + 1) to Mathematica's result
of 2 Log[Cos[x/2] + Sin[x/2]], and vice versa, I did not want them to
have to waste time doing so: each grader has to read a question on 366
papers! Hence my little exercise in trying to coerce Mathematica's form
into the paperandpencil form.
Paul Abbott wrote:
>
> There is another aspect to this exercise: at my University there is a
> project called CalMaeth:
>
> https://calmaeth.maths.uwa.edu.au/
>
> This uses Mathematica (via patternmatching and other tricks behind the
> scenes) to compare exact answers to those obtained by students with the
> goal being to attempt to automatically determine exactly which step (or
> at least the first one) in the "standard paperandpencil technique"
> that the student got wrong, and giving appropriate feedback. To me, this
> is particularly sensible use of CAS and better than "forcing"
> Mathematica and the student to get the "same" answer.

Murray Eisenberg murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower phone 413 5491020 (H)
University of Massachusetts 413 5452859 (W)
710 North Pleasant Street fax 413 5451801
Amherst, MA 010039305
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