[Edu-sig] "dot notation" (in favor of sharing it)

[kirby urner]

On Fri, Oct 26, 2012 at 7:08 AM, michel paul <mpaul213 at gmail.com> wrote:

> Hey Kirby,
>
> I've enjoyed the discussion, and of course I completely agree that dot
> notation deserves attention in current math education. However, getting
> that discussion going? Wow, from what I've seen ... it would be nearly
> impossible. It would pretty much just get ignored.
>
>
Well, at least we're talking here.

My mom's theory is you can't get anyone's attention about anything anymore
because we're all high on sugar.

She grew up overseas a lot where they don't have so much sugar in
everything.  She thinks US kids might as well be on meth, that's how far
gone.  No wonder they're out there shooting it up like no other culture.
Sugar Pops!


> Yesterday I was involved in a math education group at my school where an
> example suggested for introducing 'function' was 'toast'. Basically, you
> put bread into the toaster, and <magic/technology happens> out comes toast!
> So 'toasting' is a function. Seems to make sense, right?
>
>
Hah.  "Toast" is interesting as in English it's both a verb and a noun.
"To toast", "make toast", "was toasted".

I do like linking "functions" to "verb things that do stuff" i.e. they're
active, though another picture of a function is "a map", which is more
static, like a dict.

What might confuse some students is how Python in particular uses builtin
"range" to create what we would typically call a "domain" in Algebra 1.

f = lambda x:  x * x + 2
mapping = dict ((x, f(x)) for x in range(10))

One could toggle the namespace and just go:

domain = range  # assignment of a synonym i.e. mapping = dict ((x, f(x))
for x in domain(10))



> Well, sure, so long as you're allowing for mutation!  A slice of bread is
> an object, and, like most objects, it can change its state. Makes total
> sense.
>
> However, is that really what they're thinking about? in traditional
> mathematics, the kind they think they want to teach in school, variables
> aren't supposed to change their values once assigned. That's a huge deal. The
> discussion went on from the toaster to use an example like f(x) = x + 2,
> let's say. You put in x, and out comes y. OK ... however, x is still x. x
> did not become y. If you say x=5 then a little while later say x=7, well,
> it sounds like you're running for office! So the analogy actually breaks
> down. A math teacher would not want their students to develop the
> misunderstanding that x turned into y. If you actually want to say that,
> that's OK, we have developed ways to express that.
>
>
Probably where you'll get a lot of overlap is in geometry.  A tetrahedron
of vertexes P,Q,R,S rotating in space, will have changing (x,y,z)
coordinates for each of its vertexes.  We can speak of P.x, P.y, P.z
without too much fear of ridicule by the snoots (math heads -- they tend to
be snooty, whereas engineers are maybe more snarky).


> So it seems to me there are unrecognized conflicts in schoolish
> mathematical thinking, and I believe discussion of dot notation and other
> aspects of computational thinking could help shed light on them, could make
> the unconscious conscious.
>
> -- Michel
>
>
I support these deep dives into what might be cognitive dissonance issues.

Right off the bat, the Python types.FunctionType is not some classic
Dolciani type thing, guaranteed not not be a relation.

It's a related namespace (Python's is, to Dolciani's) but not identical.

However, contrast is information, which is why the Lex Institute for
teaching languages (of 'Who is Fourier?' fame) recommends learning more
than one language at once.  The brain learns from differences, contrasts,
and having these little deltas all over the place, separating namespaces
that are clearly close on some level (like the Latin-based languages) is
highly informative and conducive to learning.  So goes the theory.

Ergo:  teaching schoolish math in tandem with something a little different,
call it industrial math, or aerospace math, or STEM math, could be just the
ticket.

Unless of course your high on sugar (e.g. had Sugar Pops for breakfast),
then just forgeddaboutit.

Kirby
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://mail.python.org/pipermail/edu-sig/attachments/20121026/4fdd7d74/attachment.html>