Dear GAP Forum subscribers --
Recent letters to the Forum have asked about the existence of teaching
materials that use GAP. The answers have not been completely
satisfactory, for various reasons. Over the years, some people have been
privately collecting examples, exercises and the like that use GAP for
instruction, but there has been no major effort to collect all of these
components together or to generate more, nor has there been any good way
to recognize the efforts of those who have developed pedagogical materials.
I am hopeful that this situation will change soon, especially if you are
willing to help.
Right now we are in the process of revising the main GAP web site, and
one of the new pages will be devoted to the instructional use of GAP.
The plan is to try to organize the existing materials and to solicit
more, even those that are not yet perfect. In addition, I hope it will
be possible to expand upon our present refereeing process for
computational GAP packages to designate "accepted" pedagogical packages
of a certified high standard whose authors would get recognition for
their work. I am aware of several people who have a current interest in
such projects and have already made varying degrees of progress, so this
year should be a good one.
As I see it, possible reasons for introducing a computational algebra
system into a course include the following. (1) The software can act as
a fancy calculator to let the students accurately run a variety of
experiments that would take prohibitive amounts of hand calculation. (2)
Learning how to communicate with the software can give students a clear
picture of what one would want to know about a group or a ring or a
field--what would be most useful, what less so. For example, just
thinking about how to describe a group as input or to construct it from
other groups already raises questions students may not have thought of
from reading a textbook. (3) Students can see some programming models
and get opportunities to think algorithmically themselves. (4) And
students can begin to ask how the software actually works, which can
lead them to ask good questions about the mathematics as well as about
programming. As a simplest example, students could look at the different
methods Order can select, depending upon the type of group involved.
In my view, whenever we build an example or an exercise that asks
students for some kind of interaction with the software, it's essential
that we ask ourselves which of these, or other, goals we are aiming at.
Just the fact that the software CAN do something is not, by itself, a
justification for asking students to use it for that. But if we know why
we're asking the questions, then it's amazing how much the students can learn.
You can see, I think, the sorts of things I'd like to be able to make
available to the GAP community and to our students. Let me ask all
interested Forum subscribers to think seriously about instructional
materials that we can put on the GAP site. We can continue to use the
Forum itself as a place for brief questions and answers on the subject,
but it may be best to write directly to me or to Professors Neubueser or
Robertson with detailed questions or suggestions.
Chairman, the GAP Council