> On Tue, Dec 13, 2011 at 11:42 AM, Dan Christensen > <email@example.com> 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. >
Fossilized??? I can assure you that these concepts are alive and kicking!
> 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,
It has been said that there is nothing more practical than a good theory.
> 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.