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Re: What's in an expression?

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  • Subject: [mg132435] Re: What's in an expression?
  • From: Richard Fateman <fateman at>
  • Date: Sat, 15 Mar 2014 03:46:05 -0400 (EDT)
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  • Reply-to: fateman at

On 3/13/2014 8:02 AM, Louis Talman wrote:
> On Wed, 12 Mar 2014 01:29:00 -0600, Richard Fateman 
> <fateman at> wrote:
>> Namely, it requires students to (a) derive the correct answer and then
>> (b) understand the computer syntax and type the answer into the computer
>> correctly.
> While (b) is a source of student complaints, it isn't really the 
> problem you seem to think.  The students who have trouble with it are 
> precisely the ones who have trouble with algebra in the first place.  
> The machine merely enforces good syntax, whereas a human reader is 
> likely to be (inappropriately) forgiving.
> --Louis A. Talman
>   Department of Mathematical and Computer Sciences
>   Metropolitan State University of Denver
>   <>

Those darn students who are forced to pass calculus to graduate, but
hope never to use it (because they didn't really learn it), may be
the majority of the class. For them, you are burdening them with some
other apparently useless task.  Sad to say.  The good students are
not the problem.

I corresponded with Murray E off this list -- he contends (and I agree)
that it is possible to relax the rigidity of the syntax somewhat.
(for example, Wolfram Alpha is kind of loosey-goosey, as was Tilu,
a project of my own circa 2000)
  Whether this truly changes the dynamic for students, I am less sure.

It's been my feeling that the original motivation to force students to take
calculus is that it is nearly impossible to pass without knowing
algebra (as you say).  Similarly, it is possible that the motivation
to force people (usually engineering students) to take "sophomore
differential equations"  is to force them to know calculus, without
which it is hard to solve ODEs.
And what forces you to learn sophomore DE?  (The 13 recipes for ODEs,
10 of which types of ODEs you will never encounter again)?  So far
as I can tell, the only people who really learn this are the ones
who are forced to be teaching assistants or teachers.

Anyway, tying the learning of some math subject to use of some
computer program has been appealing to enthusiasts for over 40
years.  I wonder if anyone can point to a case where a student
has really been turned around by some computer adjunct to a math
course.  (e.g. a student evaluation that said,  "I came into this
course unprepared and expected to really hate it, but I have to
take it to graduate. The instructor was uninspiring. But the computer
lab was wonderful and I learned so much and I'm getting high grades
and now I want to be a math major..."  )

Reports on human factors experiments that I've seen
tend to show statistically that computer labs don't make much
difference, pro or con. So they may benefit instructors primarily,
who would like to use neat programs for the fun of it.

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