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Re: Mathematica as a New Approach to Teaching Maths

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• Subject: [mg127541] Re: Mathematica as a New Approach to Teaching Maths
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Fri, 3 Aug 2012 04:14:40 -0400 (EDT)
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• Reply-to: murray at math.umass.edu

On 8/2/12 4:46 AM, David Bailey wrote:>
> I hesitate to jump into this debate because although I leaned
> mathematics as part of my undergraduate and PhD work in chemistry, I
> have not used it in earnest throughout the rest of my career.
>
> In general, I feel that Conrad's ideas go rather too far. Part of the
> value of obtaining symbolic solutions to integrals by hand (say), is
> that it somehow makes the student more comfortable with the concept of
> an integral. Something similar applies to other mathematical concepts.
> The mechanism is probably more psychological than logical, but no less
> real for that....

Over the course of my nearly 50 years teaching math at university, 
frequently teaching calculus, I seldom if ever found students becoming 
more comfortable with the "concept of an integral" by obtaining symbolic 
solutions to integrals by hand. In fact, doing the by-hand symbolic 
calculations often served to obscure the concept of integral (whether 
indefinite or definite) or at the least distract from what the idea is.

On the other hand, such exercises with Mathematica as asking it for the 
value of Integrate[Exp[-x^2], x] could be eye-openers -- and emphasize 
the (existence) theorem that every continuous function has 
antiderivatives, even though an elementary function need not have an 
elementary antiderivative.

-- 
Murray Eisenberg                     murray at math.umass.edu
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

• References:
  • Re: Mathematica as a New Approach to Teaching Maths
    • From: David Bailey <dave@removedbailey.co.uk>