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Re: if using Mathematica to solve an algebraic problem

On 4/10/2010 6:55 AM, Richard Fateman wrote:
> It may work for you, since you have a certain level of curiosity about
> the subject and about Mathematica.  For students who have no curiosity
> about either, they will learn as little as possible. Perhaps in college
> you encountered subjects for which you wanted to get a passing grade,
> but you did not have any interest in learning. Now imagine that subject
> is calculus.

I don't have to imagine. I teach calculus every day, and deal with 
students ranging widely in ability and motivation. The fears expressed 
by some people about the supposed "dangers" of using Mathematica in 
calculus classes just aren't borne out in my 13+ years of using 
Mathematica in the classroom.

As an example, I teach my students all the usual techniques of 
integration, including integration by parts, trigonometric substitution, 
partial fractions, and so forth. I assign homework that students know 
full well they are to do by hand for practice. This homework is not 
collected or graded, so there is absolutely no motivation to "cheat" and 
use Mathematica for it. The less motivated students will do little or 
none of the homework, with obvious consequences when it comes to quizzes 
and tests; Mathematica doesn't change that. The more motivated students 
will work on the homework diligently, and many of them will use 
Mathematica to check their work. Often times students will e-mail me 
when they are working on even numbered problems (with no answer in the 
back of the book), and ask for help reconciling one of their answers 
with the result they got from Mathematica. Having Mathematica at their 
disposal isn't hurting any of these students, and it's helping some of them.

Meanwhile, we do applications of integration (for example, finding the 
volume when a region is revolved around, say, the line x=5). We will do 
a some examples by hand, and use Mathematica to help with others. We'll 
often put up a plot in Mathematica, set up the integral -- which is 
where the thinking comes in -- and use Mathematica to finish. This 
allows the students to practice the important part, which is the thought 
process involved in setting up the integral -- and which Mathematica 
isn't going to do for them. If they have to do every single one of these 
integrals and all of the associated algebra etc. by hand, they are not 
going to get nearly as much practice at the setting up part. They get 
integration practice separately. The students understand exactly what 
they need to practice doing by hand, and when it is appropriate to use 
Mathematica. Nobody complains that it's pointless to learn to integrate 
(or whatever) since Mathematica can do it all for them. *Nobody*.

Helen Read
University of Vermont

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