[Edu-sig] kids programming: math, robotics, language & learning

[Daryl Anderson]

This is a 'cross-post" of an item I put up on the math-teach forum at which
I was first introduced to this forum by Mr. Kirby Urner. I'm pleased to have
discovered you folks and would be as interested in your perspectives on my
comments as I am in those of math teachers.


	One important strand in this discussion and throughout math-reform
discussion, when it actually takes place, seems to boil down to a "content"
versus "context" debate. I'm sure this is in many ways as false a dichotomy
as nature/nurture. Nevertheless, talking about it as a dichotomy can lead to
interesting discoveries. 

	I, for one, think it is much more important how I and other teachers
structure the context of a math classroom than what is on the "scope and
sequence" chart. By this I don't mean better bulletin boards and seating
charts! (any more than I define "class participation" as the typical waving
of small hands in reply to a carefully leading question from the sage
onstage). I mean, for instance, that how I build habits of real mathematical
discourse into eleven-year-olds approaches to math is more important than
whether I "cover" division of fractions. The former is pretty hard to do.
The latter can often be a decent base upon which to build the context - we
DO "do" division of fractions. My (relatively short) professional experience
is that kids at all "levels" of math benefit from learning to ask and answer
questions about each other's work - that most of them even, somehow (?!) do
better on classic normed arithmetic-based tests at the end of the year. It
is not just important to me because I find the theory and research
compelling, but because of that actual classroom experience with 125 kds a
year. We might disagree on the relative value of this. I'd like to hear
more.

	The reason I mention it (and the reason I have turned what started
out as a private post to a forum one) is that I am interested in your and
others' opinions on the content-context question viz kids programming !

	Personally, I always enjoyed programming for the ultimate
"solvability" of its problems (notwithstanding a CS course I once took which
showed me how hard it was to prove a program correct). With a good debugger
environment and lots of stubborn patience any slapped-together program could
be made to behave. And finding out why it didn't work was great fun.

	Although I hold a professional belief (and a personal one as a
father) that kids and people "naturally" take to problem-solving and gain
some form of true ego-energy from successes in that arena, I DON'T believe
that the p.s. aspect of programming appeals to most kids - or, at least,
that it is the best way to bring p.s. into a math curriculum. And I don't
place it as a foundation for my desire to work more actual programming into
the computer environment of my math (and English) students.

	The foundation for me, is context. I see programming as a
tremendously valuable arena for kids, even young ones, to explore the notion
of an algorithm and to discover how many different algorithms can lead to
correct solutions. Programming also allows kids to explore the notion of
"efficiency" in algorithms in general and the fact that even "efficiency" is
context-based.  (E.g. the notion that computers can process many brute-force
algorithms with negligible loss of efficiency). This, then, allows me to ask
them to reflect on relative efficiencies of paper-pencil arithmetic,
mental-math, calculator usage and estimation. I've asked kids to write short
programs to simulate the processes of paper-pencil arithmetic - e.g. the raw
"symbol manipulation" imbedded in "sum up the ones column, carry the one,
etcetera. Quite revealing for all concerned. 

	Language and natural/artificial language processing viz programming
can feed strongly into pieces of an English curriculum. A "parts of speech"
unit is really cool if built upon a challenge to create an "alien" language.
And exploring artificial languages give the sort of flicker-contrast
discovery that found us Pluto. I think some of the content in the "How to
think Like a Computer Scientist" site makes interesting reference to this
notion of different forms of "language".

	Programs to make some"thing" do something - such as the Lego
Mindstorms robotics control language or Logo (or a free, purely
visual/icon-based "language" called DRAPE that I've found) add an important
element to this mix. I'm not sure what it is, yet. Your thoughts ?

	Moving beyond this we wander into some fascinating areas of
cognitive science and the like. The Python language is accessible IMHO,
because it is interpreted. But the Object-Oriented model may be most
accepted and most useful primarily because it matches the developed
"event-driven" machine architectures of this era... I'm not sure they match
human mode of cognition. maybe they do, though... Certainly discrete,
sequential, "imperative" processing is NOT what goes on in the human mind.
Some "sum-is-greater-than the parts" combinatorial explosion of capability
arises from the neural "nets" that are at work, no ?

	A somewhat related phenomena crops up recently in robotics. The
control code necessary to build a machine that can purposely move through a
natural environment seems to require an immense database of discretely
processable situations and seems to be flattening the curve of developments
in the field. Recent work by has developed extremely simple (electronically)
devices which incorporate seemingly simple analog circuitry that combines to
create complex and lifelike-seeming "behaviors" from very simple machines. I
think these are called "BEAM" robotics.

	Finally, I have the sense that "professional" mathematics has been
transformed in some ways by computer-based access to powerful graphic
modelling tools. I have spent quite a bit of time exploring the utility of
these technologies for younger, non-professionals, Not so much the "Cabri"
gemoetry explorers, and certainly not the flash-n-jazz"software" that is
just drill-n-skill decked out in spangles. In particular, I've tried to
engage younger (10-12 y.o.) kids with the idea of "proof" by exploring
visual proofs using tools like Powerpoint and Flash. 

I'd be very interested in your and other's thoughts on these varied matters.

-regards
-da