Date: Oct 20, 2012 12:26 PM
Author: kirby urner
Subject: Re: In favor of teaching "dot notation"

On Fri, Oct 19, 2012 at 2:13 PM, Joe Niederberger
<niederberger@comcast.net>wrote:

> >Because "dot notation" is not a math notation. Says who?
>
> It could simplify a bit traditional math way of indicating composition of
> functions: ln.ln.x instead of ln(ln(x)).
> It even looks a bit like the old composition operator that is a small
> circle.
>
> Perhaps some people already use it that way.
>
> Joe N
>



Yeah, sure:

>>> " the rain in Spain".strip().upper().split()
['THE', 'RAIN', 'IN', 'SPAIN']

Strip the spaces from it, then uppercase it, then split it into string
elements, consuming intervening whitespace.

One could say the first transformation was unnecessary:

>>> " the rain in Spain".upper().split()
['THE', 'RAIN', 'IN', 'SPAIN']

Nor is the order irrelevant (in the sense of giving the same result) e.g.
applying .split() first would make a list, a whole different type of object
that doesn't even have an .upper() method, so the syntax would fail
("nonsense" says the math engine, not required to pass a Turing test for
this job).

Of course we have been flirting with teaching dot notation to K-12 under
the heading of Turtle Graphics / Art / Math or whatever we want to call
it. The choice of the term "turtle" was a happy one, but could have been
"tractor" instead, which might have had more adult connotations in terms of
how adults actually use tractors in the field, whereas interacting with
live turtles is mostly left to Pacific islanders.

Not that the original LISP-based LOGO had turtles as objects with color and
state. Or rather there was only the one turtle, a somewhat environmental
or global presence. The idea you would spawn multiple turtle instances and
control each one separately, using dot notation, would go with moving the
essentials of LOGO to an object-oriented context, more like Smalltalk.

I was at a meeting in London, under the auspices of Mark Shuttleworth, the
"South African Bill Gates" (so who's the American "Bishop Tutu"?), where
Alan Kay of Smalltalk fame said he felt confidant representing Seymour's
views that OO style turtle graphics was just fine with him, i.e. he was
accepting of this leap from LISP based to something a little different,
family tree wise.

Dr. Papert had been invited to this meeting but was feeling frail. Alan
himself was just recovering from something as I recall.

We had a good time over three days in the Kensington area. South Africa
was more the focus i.e. developing new curriculum for that region. I was
invited as another Python guy and sat next to Guido van Rossum, the
inventor of that language.

Our turtle graphics module is part of the standard library (python.org) and
is maintained by Gregor Lingl, a high school teacher in Austria, a man of
considerable mathematical talents.
http://docs.python.org/py3k/library/turtle.html#module-turtle

I don't think we should stop with turtle stuff though; that's an intro and
ongoing tool (might switch to "tractor" at my school -- but only for some
really primitive stuff that uses ASCII art for output).

Once in 9th grade, we're talking about dot notation for more bread and
butter algebra / geometry / calculus.

Specific polyhedrons, e.g. tetrahedron, as subclasses of a generic Poly
class, is where I like to go, with writings starting in the 1990s. Lots of
advances since then.

Again, we're talking free stuff if you have some capable hardware. K-12 is
ridiculously out of date when it comes to what math languages are actually
out there and used, sticking with a distillation of 1800s/1900s typography
that mostly predates Alan Turing. The idea purveyed is that everyone smart
grows up to use calculus daily so lets herd them over Calculus Mountain and
keep the ones that don't fall off. Calculus is treated as synonymous with
adult numeracy in some way. Meanwhile they learn nothing about TCP/IP
unless they're "an engineer" (gimme a break). All math is ethno-math.

Kirby