Re: if using Mathematica to solve an algebraic problem is like copying

*To*: mathgroup at smc.vnet.net*Subject*: [mg108887] Re: if using Mathematica to solve an algebraic problem is like copying*From*: "David Park" <djmpark at comcast.net>*Date*: Tue, 6 Apr 2010 07:23:27 -0400 (EDT)

Why is using Mathematica similar to copying someone else's homework? Putting the question of the motivation and economics of student cheating aside, the question is: how can Mathematica be used to promote learning by students actually interested in learning? How about the following as one possible method? Use an Axiom Set - Problems approach. Give the students the axioms or rules of his subject (with descriptive names) in an active form and then have them solve problems by choosing and applying the axioms step by step. If they could do that, would it satisfy you, even though the computer was doing the dog work? Would you object if the students didn't actually memorize the axioms but worked from a table or palette? Would they sort of memorize them just by repeated use? Or is it your position that students have only learned what they can recall from memory and apply using pencil and paper? More generally, is it your position that Mathematica can't ever be helpful in learning, or that it hasn't been shown to be useful, or that we just haven't learned ourselves how to make it useful. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: Richard Fateman [mailto:fateman at cs.berkeley.edu] from someone else, then consider this article, which suggests that students (at MIT, at least) learn significantly less, in some sense by copying their homework. http://web.mit.edu/newsoffice/2010/homework-copying-0318.html Of course this would be similarly true for other computer systems. While the details of the experimental setup may not match, the results are startling.