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