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Topic: Cool Math Lessons: Functions
Replies: 2   Last Post: Mar 26, 2012 11:47 AM

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kirby urner

Posts: 1,635
Registered: 11/29/05
Re: Cool Math Lessons: Functions
Posted: Mar 25, 2012 11:19 PM
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On Thu, Mar 22, 2012 at 7:40 AM, Ken Abbott <abbottsystems@gmail.com> wrote:
> Trying to get students to think about math and not just prep for test taking.
>
> Functions
> http://www.cool-math-lessons.com/2012/03/functions.html


This has its merits, I don't dispute.

Robert and I have gone around on this issue before too.

Where I'm coming from as a Silicon Forest type exec, is from a need to
break away from the stereotype view that algorithms / functions /
processes are exclusively or even primarily about number types.

All your examples are somewhat confined to the integers and reals as
domain / range, whereas in the real world we work in, a function is a
kind of callable object that munches on string literals just as
likely, or on other kinds of objects, such as picture files or movies.
These are domain objects just as surely and work is getting done,
outputs obtained. The "function" concept deserves to persist outside
the narrow K-12 channel.

Why is the K-12 channel so narrow when it comes to what "function"
might mean, in choosing only number types for domains? 'Godel,
Escher, Bach' came out quite a long time ago by now, and typified the
drift towards a more lexical kind of argument associated with DNA
sequencing, pattern matching, text more generally.

Why are ASCII and Unicode not treated much in K-12, except in some
computer science elective for the better endowed? Why isn't there a
digital math track for students who want to indulge their interest in
digital technologies while winning math credit at the same time? No
good / reasonable answer to either question. We're dealing with a
backward civilization pure and simple, a fact any student might tune
in at any point in his / her career -- but we hope sooner rather than
later, in the interests of saving time (theirs as much as ours).

So maybe throw in some functions that add "ed" to a string, e.g.
f("talk") --> "talked"; f("peak") --> "peaked" and so on. Yes, you
might link this to grammar and a discussion of exceptions to rules.
The phrase "the exception that proves the rule" is pretty deep by the
way. The philosophers of mathematics I yak with, groomed in
Wittgensteinian stables, tend to think rather purely in terms of rules
and exceptions, when it comes to thinking / language more generally.

Finally, back to number crunching functions, which I'm not saying
should go away, I'm always looking for lesson plans that (a) relate
1st 2nd and 3rd powering to linear, areal and volumetric grown (of the
same shape, ideally) and (b) do not *necessarily* link 3rd powering to
a cube, 2nd powering to a square. It's (b) that's uncommon, though
it's always surprising how little we see of (a). (b) relates to that
meme re the Pythagorean Theorem, well-developed in Portland's Geek
Hogwarts, Winterhaven PPS: the shapes you erect on the two legs and
hypotenuse such that the sum of the two equals the third, do not have
to be square shapes.

I'm talking bio and nano technology at this point. You know there's a
magazine named 'Tetrahedron' right? What we discovered in the golden
age of ocular microscopy is that the Platonic forms, far from being
only in some Ideal Realm, are at the ultra-small frequencies, in the
form of crystals and microbes. At even smaller scales, the geometry
resolves to where you want students more adept at thinking CCP / HCP
than the current crop. XYZ thinking, so rectilinear, so orthodox, so
wrong, so insecure, still needs to be chipped away at. We do that
every chance we get, in various pilots around town. No wonder
Portland's so weird right?

So along this Digital Track, expected to run all four years
eventually, you'll encounter Regular Expressions, the J language, and
invitations to share your posters at a Pycon. Facebook and Twitter
live here. We know about MongoDB, Cassandra, Voldemort, JQuery, SQL,
GNU, Rails, Django, Drop Box, Spotify, Google, Silicon Valley, Wiki,
LAMP... Redmond, Bangalore, Prineville. All that stuff you might hear
about when geeks talk, but what for some reason never seems to gain much
traction in most TeacherVilles (picture many encampments).

Kirby


Message was edited by: kirby urner



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