Path: utzoo!utgpu!water!watmath!clyde!rutgers!sri-unix!quintus!ok
From: ok@quintus.UUCP (Richard A. O'Keefe)
Newsgroups: comp.edu
Subject: Re: Becoming CAI literate
Summary: on teaching mathematics at an early age
Message-ID: <660@cresswell.quintus.UUCP>
Date: 18 Feb 88 01:33:18 GMT
References: <26@dogie.edu> <3340@killer.UUCP>
Organization: Quintus Computer Systems, Mountain View, CA
Lines: 46

{I read this in comp.ai, but am following up in comp.edu, because
 the discussion seems to have very little to do with AI.
}
In article <3340@killer.UUCP>, Eric Green writes
> Spending hours and hours improving your speed of computing numbers was
> worthwhile before the advent of $5 calculators. But I would much rather that
> our school children be taught MATHEMATICS for those multitude of hours. Sure,
> teach them computation skills. But don't make mere arithmetic computation the
> only thing taught to our students, like it is today (at least in this state...
> from grades 1 through 6, adding, subtraction, multiplication, and division,
> day after day... blech!). Is it any wonder that the majority of the students
> in the local "gifted and talented" program despise "math" class, calling it
> boring and repetitive?
> 
> Hey, has anybody read Heinlein's novel "Tunnel in the Sky" anytime in the last
> 30 years? Gosh, if only the future of math education had been so sparkling!
> Instead, we're still stuck in the 19th century....

I read "Tunnel in the Sky".  I don't remember anything particularly
sparkling about it; Panshin's "Rite of Passage" handled the theme
rather better, and had more to say about education generally.

I don't know how it's done here, but back home we picked up the
"New Mathematics" where children are taught all about sets and converting
to different bases and how Egyptians wrote numbers and what a commutative
operator is.  Talk about *boring*.  Talk about *remote* from the interests
of the children.  Fortunately I just missed it.  I don't remember finding
arithmetic drills boring, but then, the teachers kept giving me harder
examples to do.  I suspect this is a general phenomenon: *solving* puzzles
that are hard enough to require some work but not so hard that you can't
do them isn't boring.  My experience of University-level mathematics was
that I was constantly appealing to my understanding of ordinary arithmetic
for analogies.  Telling me that '+' was a commutative operator didn't
help me understand '+'; telling me that the operation of an Abelian
group acts like '+' *did* help me understand Abelian groups.  My mathematical
and computational "intuitions" are rooted in the *experience* of arithmetic.

I think we need three things in elementary arithmetic teaching:
	principles:	"This is WHY the addition algorithm works."
			"Look: multiplication is based on divide-and-
			 conquer just like addition."
	relevance:	Accounting/shopping/planning examples.
			How to read newspaper figures sceptically.
			"How to lie with statistics."
	drills!		In computation.  In comparison.  In estimation.
			In checking the plausibility of answers.