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Re: Interesting problem looking for a solution.
*To*: mathgroup at smc.vnet.net
*Subject*: [mg122074] Re: Interesting problem looking for a solution.
*From*: "David Park" <djmpark at comcast.net>
*Date*: Wed, 12 Oct 2011 03:43:12 -0400 (EDT)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*References*: <3419157.43225.1318144358445.JavaMail.root@m06> <201110100826.EAA15289@smc.vnet.net> <3523611.7537.1318321009823.JavaMail.root@m06>
Which brings up the question of how do you get students to actually DO
mathematics? If you have to hide the answer from the student one has to
wonder if they are doing mathematics rather than repeating what they have
memorized or applying a technique they learned to a problem guaranteed to be
adapted to the technique.
Can Mathematica be used to broaden the domain of students who can start
doing some real mathematics? It seems intuitive that Mathematica can play an
important role here just because of the ease of doing the drudge work and
exploring various cases. (Could one be a good mathematician without being an
accurate paper and pencil calculator?) Just using Mathematica to automate
old techniques is not going to achieve this aim. So some suggestions:
How about giving students packages that have hierarchical depth so they can
calculate everything, at all levels, while doing derivations, proofs or
calculations? How about providing convenience routines that are adapted to
the area of interest? WRI is not great at this, and they don't have the time
for it, but they have provided the underlying capabilities for it. There is
plenty of room for people to add capability here. A requirement is that
students must be reasonably capable with Mathematica when they come to it.
How about getting away from standardized tests and having students write
mathematical essays on topics small or large? Mathematica is great at this
kind of thing. There may be no fixed answer and students may go in different
directions and even run into insurmountable problems.
How about letting students rediscover existing mathematics? Of course, they
may rediscover it on the internet so there is a different option. How about
letting students clarify existing proofs or topics? Perhaps they could
expand on difficult steps in a proof. Perhaps they could correlate a visual
proof with a formal proof. Given Mathematica's graphics, active calculation,
dynamics and control structures they might find whole new ways to present
and clarify established mathematical ideas. They can't do this without
understanding the mathematics. It requires innovation and it is definitely
value added.
How about letting students pick their own subject related topic? How about
letting groups of students work on a notebook together?
Maybe all this does not fit in with modern automated mass produced
education. I'm not an expert on it, having never taught anyone anything in
my whole life. I just comment from the perspective of a poor student.
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/
From: Murray Eisenberg [mailto:murray at math.umass.edu]
Back when I was doing such things with student projects in Mathematica,
I sure wish I had had use of David Park's HiddenNotebookData function
from his Presentations application: it would have simplified doing a lot
of things.
(But not all, probably: if you want to test a students definition of a
function on-the-fly against randomized input data, you need to hide a
"correct" definition of that function as well as generation of the test
data. At that point it may be just simpler to use a separate encoded
package of the sort I described in another post on this topic. Doing
this with a whole suite of student functions, each tested against a
series of test data, would likely create so many strings from
HiddenNotebokData that one would want to keep all that separate from the
student's own notebook where she was developing and testing the functions.)
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