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Re: Mathematica as a New Approach to Teaching Maths

On 7/27/2012 11:43 PM, Ralph Dratman wrote:
> David,
> I agree that Mathematica is quite difficult to learn, but I also think
> a good teacher could make the learning process significantly easier by
> going carefully over certain key points which are not emphasized in
> the documentation.

I think the point that is easy for enthusiasts to miss  (and this 
pertains not only to Mathematica but its competitors) is that students,
by and large, will (mostly correctly) view the introduction of 
Mathematica into their courses as "extra work", "more homework" and
irrelevant to testing  (will there be a computer on exams?).

In point of fact, the difficulties of Mathematica are orthogonal to the 
material in courses in numerical analysis, calculus, and probably other
topics.  I have, for a number of years, been the "go-to" person for
instructors teaching calculus at UC Berkeley, when students using a
computer algebra system get what appear to be wrong answers from such
systems. While the number of such instances has decreased, they have
not disappeared, and some are "features".

It is also important for enthusiasts to realize that many students do
not want their classes to be "enriched" by the introduction of a 
peculiar computer program which they are forced to learn. Many students
simply want to get a passing grade so they never have to take another 
math class.

There are, of course, some set of students who are interested and 
curious and enthusiastic.  For example, students who ask, "How do
you write a computer program that does integrals?"  These are perhaps
the same students who realize that the calculus textbook fails to
describe an algorithm for doing integrals, and may even understand
that there are some integrals whose closed form does not exist.

Publications which address the question of "how does the introduction
of computer labs (etc) affect the student learning level"  rather
consistently come up with a conclusion that is roughly, "they learn
about the same."
> For example, one of the most fascinating features of the language --
> its ability to mix symbolic and numeric quantities -- can also be a
> source of great confusion for the neophyte.

This is confusing only because they have learned another, more 
restricted, language first.  Ab initio, why can't
the mixture of symbolic and numeric calculations work?  To a
mathematical sophisticate totally unaware of programming, it is
a big disappointment that BASIC (etc) cannot deal with uninitialized
variable x  by computing   x+x   resulting in 2*x.

> I would also go very carefully over what one must do to keep the front
> end and/or kernel from going out of control, and how to recover when
> that does happen.

This is of course totally irrelevant to the subject matter at hand, and
disappointing in the extreme that one must spend any time on this.

> I have a number of related ideas to help students get the feel of the
> Mathematica environment before plunging in to accomplish serious work.

Unfortunately, serious work encounters, fairly often, serious barriers.
> I would love an opportunity to teach Mathematica to a small group of
> smart high schoolers or beginning undergraduates.

Tell us when you figure out how to market such a course.

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