On Tue, Dec 13, 2011 at 11:42 AM, Dan Christensen <firstname.lastname@example.org> wrote:
<< snip >>
>> >> That's right - and from there one can go on and muse >> about how and why the math meaning of the word >> "function" has become so abstract and inert.
This abstract meaning was part of the conventional Dolciani presentation. The concept fossilized a long time ago, along with surjective, injective, bijective or whatever synonyms.
However, when it comes to scripting logical agents to get work done (manage baggage handling, run a supermarket), there's a strong bias towards rules we might both write and follow (aka "encode").
The practice of law is similar: fine to have your castle-in-the-sky definitions, but lets not pretend lawyers earn their keep by governing in Plato's Realm.
> > For most students, a "black-box-input-output" model of functions will suffice. I am, however, focusing more on students tending to proof-based mathematics in their immediate futures. It would be nice if everyone could master these "abstractions" and the basic methods of proof, but few are motivated to do so. I hope my little video and my software will help a bit in this regard. >
I'm a little leery of this "for most students" as it consigns them to a proprietary "black box" or "none of your business" view of internal workings, whereas our students are encouraged to dig into banking, insurance, real estate, with gusto, to discover all the business rules involved. Transparency is a public value, we would argue, starting with the voting process itself (a first place to start looking at functions and mappings, in conjunction with SQL).
As long-time readers here know, I'm into a "virtual presidents" model of public schooling, i.e. the aim of public school in a democracy is to groom students for effective participation in the relevant roles. If you want a military hierarchy (like Sparta) train towards that instead. Or incorporate elements of both as I do, given our democracy is under siege, is surrounded by idiocracies, plutocracies... oligarchies (whatever anti-democracies).
The kinds of construction we do in geometry require more spatial awareness than the planar people provide. To counter the imbalance, we start with polyhedrons right out of the box (but not a black box -- you can see what makes it tick).