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Re: if using Mathematica to solve an algebraic problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg109040] Re: if using Mathematica to solve an algebraic problem
  • From: Richard Fateman <fateman at cs.berkeley.edu>
  • Date: Sun, 11 Apr 2010 04:32:21 -0400 (EDT)
  • References: <hpml5n$9nu$1@smc.vnet.net> <hppl95$m08$1@smc.vnet.net>

1. You are asking your students to engage in some "experimental 
mathematics" in which a computer helps advance the understanding of 
students by providing useful approximations or examples.  This is just 
fine. A simpler example typical of calculus is to ask students to use 
graphing calculators to graph a function like a quadratic or cubic 
polynomial and observe how the curve changes as you modify the 
coefficients.  Nothing wrong with this.

2. I think that many calculus instructors would claim that if you spend 
time teaching how to use Mathematica, then you must naturally spend less 
time teaching something else.  When calc instructors tell me that their 
curriculum is full, and they would have to omit something and ask me 
facetiously what they should leave out, I simply tell them. 
"logarithmic differentiation".

3. There is, I think, a concern that computers would be used to 
substitute for something they should learn to do without computers.
I doubt that anyone would object to your particular example, but what if
students learned that there were programs written in Mathematica that 
tested for convergence of series, and used them for their homework, not 
knowing how they worked?  There are lots of things that can be done with 
series, like accelerating convergence, not taught in calculus, but which 
might be done (mysteriously) by computer, so there is a choice.

But if the students make the choice, not the instructor, maybe there is 
a problem.  Say you were teaching how to extract square-roots by hand, 
you might be disappointed by a student who decided to extract 
square-roots by (say) typing into his telephone, and did not learn what 
you were teaching.  We have, apparently, mostly decided not to teach 
this topic anymore, so acceptable behavior changes over time.

RJF




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