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MathGroup Archive 2006

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Re: simplify a trig expression

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65489] Re: simplify a trig expression
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Wed, 5 Apr 2006 06:55:29 -0400 (EDT)
  • Organization: The University of Western Australia
  • References: <200603311109.GAA15029@smc.vnet.net> <200604011038.FAA07301@smc.vnet.net> <200604020900.FAA01612@smc.vnet.net> <11D40ADD-9EC9-4DCE-B685-1CA00605B9B2@mimuw.edu.pl> <e0r0c9$mt$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <e0r0c9$mt$1 at smc.vnet.net>,
 Murray Eisenberg <murray at math.umass.edu> wrote:

> Actually, what I was trying to do is this:  To obtain in Mathematica, 
> the answers to a ten-question integration exam that would be of the form 
> students would obtain with standard paper-and-pencil techniques.  And 
> the purpose of that was to to provide to the graders, whom I supervise, 
> answers that are unquestionably correct -- and, again, in that form.

And the result of this exercise is to question _why_ we continue to set 
such exercises! Surely the graders should be able to check the 
equivalence of the Mathematica expression -- which is equally valid, 
though not "simplest" -- to that obtained by student. But what if the 
student did not get the correct answer. What should the grader do then? 
How are part marks to be assigned?

The easiest way to get Mathematica to get the same answer as standard 
paper-and-pencil techniques is to _emulate_ those techniques in 
Mathematica, not to use high-level built-in functions such as Integrate.

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 pattern-matching 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 paper-and-pencil 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.

Cheers,
Paul

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)    
AUSTRALIA                               http://physics.uwa.edu.au/~paul


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