The best tool is one which the student can "live with". Maple is hugely powerful, but suffers from a lack of portability - you have to be near a computer when you use it. Whereas a CAS calculator is something the student can take anywhere, throw into a backpack, uses very little power, and can be always available. Such a tool can have huge pedagogical value, if used well.
I use Maple for teaching, which covers most undergraduate mathematics (for my research, which is mostly in image processing, I find Matlab more appropriate). However, one problem with Maple as a teaching tool is that it is very expensive. Even with the cheaper student versions and other ways of getting Maple to students, the costs are still too high for most of my students. I'd like my students to be able to use whatever software I choose at home as well, but that's not practical with Maple.
This means that they can only use Maple on campus, in the designated labs. I'd like Maple to be an integral part of our teaching and my students' learning, but the students more often see it as an unnecessary (albeit powerful) adjunct. If anybody knows how to overcome this particular difficulty, I'd like to know! I've looked at other (free) CAS's but none, as far as I know, combines Maple's ease of use with its breadth and depth.
Thanks, Doug, for your reply - I will contact you privately soon.
Part of the problem, it seems to me, is untangling the educational aims and objectives from the syllabus. For example, if we are teaching solution of linear equations - what is it that we really want the students to know? Familiarity with techniques (row operations, Gaussian and Gauss-Jordan elimination, possibly determinants, Cramer's rule, inverses...) or do we want them to have a higher-order understanding, of a matrix as an operator? And whichever we choose, how can we best use Maple to enhance the learning of that objective?
For my students, any possible understanding of a higher order is swamped by the numerical and algebraic methods of its implementation. So matrix arithmetic, for them, is seen as a mass of many fiddly calculations. And so they set their teeth against it right from the start. And of course we do (or at least, I do) want them to have some familiarity with technique - and so pencil-and-paper exercises are an important part of their learning experience.
I haven't yet got all this sorted out to my satisfaction.