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Re: Mathematica as a New Approach to Teaching Maths

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• Subject: [mg127554] Re: Mathematica as a New Approach to Teaching Maths
• From: David Bailey <dave at removedbailey.co.uk>
• Date: Sat, 4 Aug 2012 05:59:05 -0400 (EDT)
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On 03/08/2012 09:15, Murray Eisenberg wrote:

>
> 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.
>

I was, of course, reporting on my personal experience, and I still 
wonder if I am so unusual in that respect. Perhaps for me, abstract 
ideas gel best when they are associated with some well defined procedure.

They also permit calculations in the head. To take perhaps an extreme 
case, suppose that a student can't integrate x^n without a computer. 
Such a student can't mentally integrate a formula like dx/dt =a t to get 
the expression for the distance traveled after time t under constant 
acceleration. If an integral is a black box that can only be eliminated 
by a computer, that must surely inhibit creative thought in mathematical 
subjects.

Also, the techniques you might use to solve an integral - change of 
variables, for example - tend to crop up over and over again - they 
aren't just used to solve integrals!

If Conrad's ideas were tried on an experimental basis, or if they formed 
the basis for a new subject - applied computation (taken as well as 
maths) - I'd be happy, but if we see a whole generation of people who 
can only do maths on a computer, I think that will be a bad mistake.

It is almost inevitable that an innovator will tend to exaggerate a new 
idea - perhaps not meaning it to be adopted wholesale and literally - 
but Conrad's ideas do concern me in their present form.

That does not detract from your example. Realising that many integrals 
don't exist in closed form - and that some special functions have been 
designed specifically to represent integrals, is obviously important, 
and Mathematica can help a lot. I am certainly not arguing that 
Mathematica is not useful in education!

David Bailey
http://www.dbaileyconsultancy.co.uk

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