[Edu-sig] Integration of Math + IT: a "good thing"

[Kirby Urner]

Originally posted to math-teach at the Math Forum.  One 
typo fixed.  This thread got its start in quotes from the
Singapore math curriculum docs (Singaporeans score relatively
high on global math surveys), which advocates integration 
of math with IT (Information Technology) -- although, in 
practice, this seems to have more to do with learning biz
apps, than with CP4E.

Kirby

=====================

Subject:      Integration of Math + IT: a "good thing"
Author:       Kirby Urner <urner@alumni.princeton.edu>
Date:         5 Apr 01 00:18:37 -0400 (EDT)

Ronald D. Ferguson wrote:
> With the "perfection" of CASE tools, computer algebra systems, 
> and "natural language" interfaces, perhaps the day will arrive 
> when we are all programmers, and all mathematicians.  If this 
> is indeed the future, how would we describe the level of 
> abstraction of the resulting knowledge base?

As AP comp sci course pop up at the high school level, and take
control of the bulk of the computers, I think the opportunity is
to boost the math content on this already-computerized side of 
the fence, versus waging the uphill battle to phase programming
into the graphing calculator ghetto, where the necessary tools 
are simply absent, and where teachers are often professionally 
proud of their chalkboard-only approach -- downright disdainful 
of other technologies.

Phasing more math into comp sci is not an uphill battle at all,
because the core syllabus at the highest levels is comprised of 
such as 'The Art of Computer Programming' by Donald Knuth, a 
multi-volume work packed to the gills with mathematical concepts 
and notations, as are the "on ramp" texts (more accessible) such 
as 'Concrete Mathematics' (Knuth a co-author).  

'The Art of...' as you must know, is built around a very low level 
language, MMIX (updated from MIX, to include a RISC-based instruction 
set), in order not to lose site of the hardware underpinnings:  
registers and such.  For this reason, we might consider 'The Art 
of...' to be "hard core", i.e. for comp sci majors, whereas at the 
secondary school level we're content to ramp up using a VHLL (very 
high level language) such as [fill in the blank with your favorite].

Over on the Python e-list, it's already a given for a lot of posters
that they'll be teaching a comp sci course next year.  A lot of them
are looking for arguments to justify the switch to Python from C++ 
or Java -- the same thing goes on in the workplace, where pointy 
haired bosses are skeptical of Dilbert's idea to use Python for some
next big thing.  Anyway, all questions of "which language?" aside,
it remains an open question for many a faculty members what to use 
for content.  Do we dive into GUI programming right away?  There's 
a lot you can do interactively at the command line, with programs 
writing directly to the console.  But what's relevant to program.  
The game of Hang Man?  The Tower of Hanoi?   OK, maybe, but then
what?

Enter mathematics -- all that stuff you've been learning in math 
class must be relevant, or at least gives us a lot of ready-made 
grist for the mill.  Probability, permutations, bases, functions, 
factorial, binomial coefficients, vectors, matrices... yeah, there's
a lot here, and we can get into it without spending a lot of time 
prettifying a GUI, getting lost in the aesthetics of an interface
at the cost of not learning any nuts and bolts.  Because at this 
intro level we need to be learning about data structures, 
conditional execution, namespaces, objects, bits and bytes.  We 
can overlay it with pretty GUI gizmos later -- but before we 
apply the frosting, we at least need some cake.

What I'm hoping is that as comp sci teachers start racing ahead in
linear algebra, showing students how to rotate tetrahedra and so on,
math teachers will think:  hey, this is the kind of stuff _we_ were 
supposed to be teaching.  Why should we have to "make do" with 
these graphing calculators, while the programmers get to play with 
VRML plug-ins and ray tracers?  Good question.

Kirby

PS: For more along these lines, you might want to pull up my post to
the mathchina list, where people are sharing their two cents with the 
visiting professor and delegation:

http://mathforum.com/epigone/mathchina/yoyehwal