> > And yes, I think it would help some students to understand what a
> > group or ring is if it is programmable in sage - but I say only some,
> > others might be confused or more happy with another approach! I think
> > there is no golden way that fits for all students, but more
> > opportunities and more representations of the same idea help to
> > abstract it.
>
> Groups and rings have been around over a hundred years, are one of the
> most basic ideas in mathematics, and the basic definitions can be
> learned by any math undergrad in a few hours. They should all learn
> what groups and rings are. This remark really has nothing to do with
> Sage.
Some of this thread is sage-edu material as well...
It's worth pointing out that using technology, whether log tables,
calculators, tablet computers, or Sage, in the classroom is only going
to be worthwhile if done well, and with an eye toward enhancing what
is already being taught, not as yet another thing to learn per se
(which is some of what rjf is getting at, perhaps).
That said, multiple representations of things definitely does help
some students learn the point of the object and to internalize it - so
e.g. a Newton-Raphson interact (Sagelet?) on basins of attraction
might help contextualize it (and drive home the point that math does
not always have cookie-cutter answers, as it is portrayed), or the
PascGalois project might, via visual cues, really get students to
really start understanding how small changes in a group or in which
elements one chooses could affect things.
However, as rjf points out, without this being valued in the course as
more than some extra work, one needs to integrate this in some way.
There are lots of ways that can happen - not just with a final exam
done on a computer, though I am sure there are more where Minh's
example came from! But certainly there are successful examples (and
terrible ones) out there. I've found that it takes several attempts
to make it seem really worthwhile for students - which one could
probably say about any other pedagogical strategy!
Anyway, with regard to this thread, I like Robert's point:
Whether or not to use computers in teaching is a huge, open-ended
question... however, if a professor/department/university decides
to
do so (or at least offer the option) the technical question is how
easy can it be set up and administered. This is where the "sage in
a
box" idea could be very appealing.
- kcrisman
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to sage-devel@googlegroups.com
To unsubscribe from this group, send email to
sage-devel-unsubscr...@googlegroups.com
For more options, visit this group at http://groups.google.com/group/sage-devel
URLs: http://www.sagemath.org
-~----------~----~----~----~------~----~------~--~---
