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Re: Mathematica-assisted learning was .. Re: Speak errors

On 4/25/2013 6:46 AM, Murray Eisenberg wrote:
> On Apr 25, 2013, at 2:51 AM, Richard Fateman <fateman at> wrote:
>> I think the comparisons are generally with control groups that were being taught
>> the same material but without "benefit" of computers.  It
>> seems to me that comparing the two groups of students on their ability
>> to write programs would not be pertinent to the question of whether the
>> two groups learned (say) calculus equally well."
> If you think that what I'm suggesting is to "write programs" then you simply don't understand the issues here. It's learning mathematical ideas vs. learning to do (largely mindless) mechanical manipulations of symbols.
I was being somewhat facetious in describing  the other benefits of 
introducing computers as
learning to write programs.  Certainly there is a prospect that students 
would learn, as a consequence
of the computer-related stuff to have a higher appreciation of (say) 
algorithmic / procedural
thought processes, even  "ideas"  (however defined by you)   vs rote 
repetition.  I am not aware
of any peer-reviewed research papers  validating such a hypothesis. 
Occasional anecdotes

You might or might not recall that the standard methods in calculus 
courses (and I suspect in
physics/ etc courses)  consist largely in teaching mindless mechanical 
manipulations. Worse,
they are taught by repeated examples, not as fixed algorithms by which 
any of the problems
can be done by following those algorithms. Then students are graded on 
their ability to
perform the mindless manipulations.

It is my own cynical view that the real value in compulsory calculus is 
that it is mighty tough
to do those manipulations without a firm grasp of the (mindless) 
manipulations of algebra and
perhaps trigonometry.  Therefore the calculus, which is itself vital to 
10% of the students and
useless to 90%, has the effect of reinforcing knowledge of algebra, 
which is somewhat more
relevant to people. (e.g. financial matters...)

Perhaps somewhere there is a calculus course that does not depend on 
such an approach.
One time I taught part of a calculus course at MIT  (circa 1972) -- an 
added computer "lab"
in which I explained the fundamentals of the Risch integration procedure 
to students in course 18.001,
which was a more "applied" calculus.  The students seemed to like that.
   The main instructional themes and senior faculty lecturers were 
unaffected by it. In that
year, or so far as I know, in any future year.

I note that the MIT regular calculus, 18.01
apparently uses a computer algebra system, but not Mathematica.
I do not see how it is used or how it could be used on the exams.

In the previous century (1987 ish)  there were reform efforts regarding
"Calculus for the New Century"
which is presumably THIS century.  Big news.  Graphing calculators..

It occurs to me that we have had a similar conversation previously.
Indeed ...  21 Jan 2010..


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