Re: if using Mathematica to solve an algebraic problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg109010] Re: if using Mathematica to solve an algebraic problem*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Sat, 10 Apr 2010 06:53:26 -0400 (EDT)

I quote, third-hand, what a student at my university said a few years ago to his chemistry instructor: "Professor, I know what you're trying to do: you're trying to get us to think. And we don't like that!" On 4/9/2010 3:32 AM, Richard Fateman wrote: > David Park wrote: >> Sometimes I find it difficult to understand these discussions. >> >> For example, Richard's: "There is of course the possibility that something >> really useful >> will be developed that will make it possible to teach all students >> everything they need to know." What kind of something would that be, and in >> what way would it make it possible? It seems like a rather vague but >> expansive goal. >> > Something like "No child left behind" :) > Maybe better teaching technology. Or > Perhaps something like an injection with "smartDNA". > Or surgery. ("I spoke excellent French, as soon as I recovered from the > surgery..") > > > > > .... > >> But another way to use Mathematica is to try to set up the rules or axioms >> for some subject matter and then practice using them to carry out various >> derivations or prove various theorems. Mathematica may do the dog work but >> you have to decide the steps and see why various axioms are necessary. > Sorry, you are expecting students to think. Unless you can teach them > to think, some of them won't be able to > do this. (Seriously, I have encountered students who have done very well > in school whose skills include > excellent memorization, rote substitution into examples, neatness and > courtesy. But they have never been > expected to show any independent thought.) Will using Mathematica > change something here? > >> There >> might be various ways to do this for teaching. Should the teacher provide >> the axioms and the student just uses them? Or should you start with a vague >> discussion of some subject and have the students and teacher together >> develop the axioms, something like the Math Circles? >> > Look at textbooks and you will find piles of examples. Generally NOT > algorithms to follow. > How is it that something like the (complete!) description of a > programming language like Pascal can take > 20 pages, but "Pascal for Dummies" can be 20X larger? > > > > > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305