[Date Index]
[Thread Index]
[Author Index]
Re: if using Mathematica to solve an algebraic problem
*To*: mathgroup at smc.vnet.net
*Subject*: [mg109045] Re: if using Mathematica to solve an algebraic problem
*From*: Helen Read <hpr at together.net>
*Date*: Sun, 11 Apr 2010 04:33:15 -0400 (EDT)
*References*: <hpmlcd$9v0$1@smc.vnet.net> <hpplf0$m8t$1@smc.vnet.net>
*Reply-to*: HPR <read at math.uvm.edu>
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
Prev by Date:
**Re: if using Mathematica to solve an algebraic problem**
Next by Date:
**Re: if using Mathematica to solve an algebraic problem**
Previous by thread:
**Re: if using Mathematica to solve an algebraic problem**
Next by thread:
**Re: if using Mathematica to solve an algebraic problem**
| |