Re: Recommended learning exercises for beginners?
- To: mathgroup at smc.vnet.net
- Subject: [mg63794] Re: [mg63756] Recommended learning exercises for beginners?
- From: "David Park" <djmp at earthlink.net>
- Date: Sat, 14 Jan 2006 02:33:04 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Gareth,
I'm absolutely convinced that the use of Mathematica in technical courses in
universities can revolutionize the teaching and learning of technical
material. Nevertheless, I think there are some real roadblocks to
implementing this. It is almost impossible to obtain anything near the full
potential with the present approach. However, the problems can be solved.
I'm writing basically as a student using Mathematica. I don't have
experience as a teacher. But I've had a fair amount of communication with
students and teachers and believe I have a reasonable view of the problem.
I'm interested in hearing as much comment as possible, pro or con, on what I
have to say.
There are three principal problems. 1) Students do not have enough
preparation in Mathematica before being asked to use it in technical
courses. 2) There is a gap between Mathematica and what is needed in
specific fields. 3) Mathematica is often approached with the wrong paradigm.
It is not fair to ask students to learn Mathematica and difficult technical
material at the same time. Nor is it fair to ask professors and instructors
to teach Mathematica in the introduction to their own courses. Students
couldn't obtain a working knowledge of Mathematica in the first class, or
maybe not even in the first two weeks of a course. Universities should offer
first term Freshman courses in Mathematica and they might even make them
required for all students entering technical fields. Or professors could
make completion of such a course a requirement for their particular course.
Universities just have to bite the bullet on this, otherwise students will
simply resist Mathematica as too time consuming or fumble with it. It would
be best if students were to learn Mathematica in high school.
Mathematica by itself is not ideally suited to teaching various subjects.
Mathematica is actually a metatool for making the tools needed in any field.
It will almost always require additional routines to provide the necessary
convenience and flexibility and to fill the many annoying little gaps.
Students should be encouraged to write definitions, rules and routines but
it is unreasonable to expect each student to write all the routines needed.
This means there must be good packages for each field. There aren't really a
lot of good packages around; most of them are far too special purpose. Good
packages will be natural, follow the regular Mathematica paradigm and be
'broad and dense' in the sense that they provide the needed routines to
manipulate the subject matter at every level. The student should be able to
derive results, step by step, in whatever detail is required for
understanding, all using Mathematica and the associated packages. The
student should think he is 'doing mathematics', applying mathematical
principles, axioms and propositions to his material. He should be thinking
in terms of his subject matter and not about computer science and
programming. We paid good prices for all those hard working guys at WRI to
do the computer science. The student and professor need to concentrate on
the subject at hand.
For teaching, Mathematica comes with a very good paradigm. Unfortunately,
many users fail to appreciate it, or veer off from it. I don't think of
Mathematica as a 'calculator' nor do I think of it as a 'programming
language' ("I'm from computer science and I'm here to help you.") I think of
Mathematica and the Mathematica notebook as 'pencil and paper'. It's a very
magical piece of paper because it will remember what I have written, execute
commands, and make diagrams come alive with animation. It is the paradigm of
text-equations-diagrams (TED) but fantastically improved. It is the standard
style of textbooks and research papers. It certainly goes back as far as
Euclid. The TED style is pervasive and persistent because it is completely
flexible and open. Theodore Gray has provided us with a nearly perfect GUI
that follows this style. Most efforts to provide alternative GUI's are
misguided and probably counterproductive.
Students need to learn literary and graphical skills as well as calculation.
They need to learn how to organize the material, to write textual
explanations (The Text cells are as important as the Input cells!) and to
use diagrams to illustrate their material. Rather than working a number of
throw-away exercises, students could write notebooks on particular topics.
When they have finished they will actually have something that they can keep
and that might be useful to them in the future. It would be more interesting
for everybody. In the time that they have, students could do MORE examples
and MORE DIFFICULT examples. It would be a revolution.
Mathematica and Mathematica notebooks are significant teaching tools - but
it is a mistake to think that we have learned how to use them to anywhere
near maximum effectiveness.
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
From: Gareth Russell [mailto:russell at njit.edu]
To: mathgroup at smc.vnet.net
Hi Group,
I am teaching a course (for the third time) using Mathematica to
explore Theoretical Ecology. Students mostly have no prior experience
with Mathematica, so in the first class we look mainly at Mathematica
itself, and I give the students homework designed to get them using it
and learning some of the basics. Do date, I have used a mish-mash of my
own material, but it could certainly be more coherent. So I am
wondering...
Do any of you have recommendations for 'Introduction to Mathematica'
notebooks that have worked well for you (or your students)? I'm
thinking of practice exercises, as well material to study.
If I get a number of responses I'll collate them and repost as a
resource for the group.
Gareth Russell
NJIT