[seul-edu] ISO Phase one evals--Advanced Math Apps, Why?

[lep <prevettl@cochise.cc.az.us>]

Mark, Doug, all,

I started a new thread here.

>bc  Calculator  N command line calculator with arbitrary precision is
not needed in classroom
>GAP Abs Algebra N Topic beyond the scope of most (all?) secondary
schools

I've been meaning to talk to the group about the reason
for all the advanced math software packages in the
SEUL database. This may warrant some discussion to
clarify all the fine points, but I'll go ahead and
start with some issues I think people (especially
math instructors) should be aware of.

It is true that bc and GAP are advanced math
packages, and you would not be using GAP to
do abstract algebra at the K-12 level (I think that
was actually tried about 50 years ago and it
was a total failure!) You would only use the
parts of GAP that were appropriate for K-12 education.

For instance, here is an example of how I used GAP to
create some simple web interactive exercises for
factoring numbers. (Sorry, long link, put all 4 lines
as one link in browser without any spaces. Or go to the
highlighted link, search for 'Cochise', click
Cochise 2001, select Factoring Numbers 4 to 100)

http://wims.unice.fr/wims/wims.cgi
?session=new&lang=en&cmd=new
&module=contrib%2FCochise2001.en
&exo=FactoringNumbe4&qnum=1&qcmlevel=3

Unix applications are fantastic for web applications
because they take text input and produce text
output and that makes it easy to pull the results
into web pages. Since the source is available, if
you want to edit the text or layout of some application
to more closely match your textbooks, you can do that.

Here is an actual GAP command for factoring 48:

Factors(48);  <--- command
 [ 2, 2, 2, 3 ] <--- output

So you see it isn't a complicated program at all
to use - if you know how to use it. GAP also has
some nice commands for sets, permutations, and
discrete math type stuff that I haven't seen
elsewhere.

Like many other existing Unix applications, what is
needed are some clear and simple instructions on HOW to
use the resources in a way that is appropriate for
K-12 education, and also resources that simplify the
interface, so that only the parts of the program that
are relevant to K-12 education are visible to the student.

Other programs will factor numbers, but I found that
this particular output of GAP was the most useful
for this particular exercise. In other cases, one of
the other math packages like Pari-GP, Maxima, Gnuplot,
bc, or Octave, etc., had the capabilites I was looking for.

While there are some programming projects underway
specifically for K-12 math education (notably Dr. Genius)
Math is one discipline where there are already is a lot
of high quality existing software available.

Programs like GAP and Maxima have been developed over
the last 20 or 30 years to handle real world research.
They are very robust and stable and have all the
characteristics you would expect for a research tool.
(Except for the fact that they are free!)

It just makes sense to think about using these tools.
Millions (billions?) of dollars have been spent on
programming efforts all over the world to develop these
programs - why not use 'em? Many of them are _still_
being actively developed. There's nothing wrong with
re-inventing the wheel, so to speak, and writing
math routines to factor polynomials or do symbolic math
to use in a Linux version of 'Math for the Orgeon Trail',
for instance (you can learn a lot of math!), but Unix has a
tradition of also building on the work of others.

That's why programs, like WIMS, that do build on the work of
others are so inspired. They take these fantastic programs
and create simple web interfaces that can be used to access
only the parts of the program that are required for a
particular situation.

Why hasn't someone created a scaled down version of these
programs just for K-12 education? Good question. It is
certainly possible. But for someone to have the expertise
necessary to do that, they are probably too busy *using*
GAP or bc to take time to do something like this.

So WIMS takes another direction: don't rewrite the programs,
just use web forms to simplify the interface. (Actually a
scaled down version of WIMS for K-12 education might be
more quickly accomplished than scaling down GAP or Maxima.)

Of course, when the capabilities of the web interfaces run out,
then you have access to the actual programs. And there are
all kinds of reasons to use simple commands in a shell
prompt - like introducing kids to programming, special
projects, etc.

Tcl/Tk could also be used to create simple interfaces for
standalone graphical sessions for GAP, Maxima, etc.,
in the same way that WIMS does for internet sessions.

Regards,

L. Prevett
Mathematics Instructor
Cochise College, Sierra Vista, AZ, US
prevettl@cochise.edu