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Re: simplify a trig expression

  • To: mathgroup at
  • Subject: [mg65494] Re: simplify a trig expression
  • From: Murray Eisenberg <murray at>
  • Date: Wed, 5 Apr 2006 06:55:38 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <> <> <> <> <e0r0c9$mt$> <>
  • Reply-to: murray at
  • Sender: owner-wri-mathgroup at

I am totally in sympathy with your comment, "And the result of this 
exercise is to question _why_ we continue to set such exercises!" 
Unfortunately, I am in a distinct minority among my colleagues in 
thinking that there are better things for humans to do than such exercises.

Actually, in some years past I've taught an alternative version of 
calculus where students relegated to Mathematica most such computations. 
(They still had to demonstrate, through really simple examples, that 
they understood the ideas of very basic methods such as substitution and 
integration by parts.)  And since we relegated most of the symbolic 
manipulation to the computer, it meant we could concentrate 
upon...thinking.  Some students really like that.  Unfortunately, many 
of the students were not of a mind to think instead of blindly pushing 
symbols around.  So over several years, as word spread that using the 
computer made things harder -- more thinkng! -- students voted with 
their feet to take the old-fashioned course instead of the alternative 
one.  Enrollments went too low in the alternative course just as my 
department faced a huge personnel shortage during a period of 
Massachusetts budgetary crisis.

Paul Abbott wrote:
> In article <e0r0c9$mt$1 at>,
>  Murray Eisenberg <murray at> 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:
> 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                     

Murray Eisenberg                     murray at
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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