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Math for GnuBees
Posted:
Apr 21, 2007 11:14 AM
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I've been having an interesting chat with a community
college prof over on mathedcc, somewhere in Philly.
We're comparing east versus west coast early math
teaching, with regard to 1-ary and 2-ary operators
especially (unary and binary -- operators that take one
or two arguments respectively).[1]
I've been using the opportunity to talk of "dot notation"
which is pretty intrinsic in several OO languages, or
math notations if you will (Iverson). So when our
students see 2 + 2, they might internally reflect that
two "animals" (nouns, objects, things with features)
have met in the forest, and one has called a well known
operation on the other, made it "plus" for example, with
self as the object of said verb. Put another way, as:
2.+(2), 2.add(2) or finally, in legal Python notation,
as 2 .__add__(2) -- and note that space, so as not to
confuse a dot with a decimal point.
What does it all matter?
Well, it tends to change your way of looking to think of
every number you meet on the street knowing "internally"
how to add and multiply, subtract and divide. We're used
to thinking of that knowledge as somehow "over the heads"
of these stupid numbers like 2, that are just names of
any sets of n members or whatever the formal Bertrand
Russell style definition. Nowadays, in OO, it's like the
numbers have "swallowed" all that operational knowledge,
which persist as "methods" within a shared "class" or
blueprint.
As gnu math teachers, we don't shy away from putting this
very definite OO spin on basic math ops quite early in
math student careers, just as we don't shy away from
sharing about Fuller's concentric hierarchy of
polyhedra, their whole and fractional volume ratios,
transformations among.[2] It's a part of our ethnicity
(subculture) to share these materials.
We know other math teachers, like Rosa, Renfro and
Talman, Bishop and Goodnight, Shelley and Pam, will
perpetuate their traditional spins, whatever these may
be or look like in practice. It's not up to us to set
the agenda for the entire nation all by our wee little
lonesomes.
But within Python Nation, for example, we have our young
to look after, to nurture, to show the ropes. Public
schools serve *us* too (we too pay taxes, slave for the
government on occasion). So let's not pretend the OO
approach doesn't even exist. It does, and we teach it.
Kirby
[1] thread head on mathedcc:
http://mathforum.org/kb/message.jspa?messageID=5657989&tstart=0
[2] http://www.grunch.net/synergetics/volumes.html
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