> Kirby, you're killing me.:) But regarding your > 2^10000. Back in 78 or 79 I remember when I got a > TI-58 and a friend of mine had a SR-56 and we spent > countless hours programming big math. We would scroll > display 10 digits at a time. I can't believe how much > programming we did on those things and couldn't save > any of it, just had to retype it in all over again. >
Yeah, I was programming an HP65 somewhat earlier, and some of these calculators could store programs on a strip of magnetized plastic, like a piece of credit card. I learned a lot about "the stack" as HPs were RPN as you know, i.e. 2 enter 2 plus to get 4. Never needed parentheses if you understood about the stack. TIs always seemed dumber. Remember those days?
> As far as your "engagement" example. Engagement in > what? There are two parts to engaging, the engaging > itself and concepts that you are trying to engage the > student in. Showing a student 2^10000 might be good > if you are trying to show a student the number > significance of the exponent operation. Personally, I > like the grains of wheat on a chessboard example. One > on the first, two on the second, and so on. >
That example was simply to blow calculators and their wee little screens out of the water. We call them "hamster brained", use other epithets, maybe show Youtubes of running them over in a car, get that aggression creatively channeled. Scrolling doesn't hack it. You need Unicode and the ability to change fonts. Like yesterday I was doing Bernoulli Numbers in Akbar font, just to celebrate Ada Byron some more.
> But in the context of any higher math that stuff has > no applicability to teaching the symbolic nature of > exponents and how it factors into or out of > polynomial expressions. >
Well sure it has applicability, as once you get how to symbolize exponentiation in a language, then you can start writing polynomial expressions and evaluating them, graphing them. Figure out what they're good for, learn more about the Binomial Theorem etc. I'm really big on Pascal's Triangle. The graphs are cool because even if XY flat, we have the Z axis and full rotatability, so you don't develop that mind-numbing prejudice that "positive numbers always go off to the right" (depends on where you put the camera silly!).
Hey, you should study my curriculum more. I've got videos, essays, working source code galore. The legislators see this, next to my thesis that most academics can't add 2 and 2, especially PhDs, because once you step outside a narrow range, they glaze over, filter out, don't see what the U2 has to do with it or whatever.
Math Forum sort of makes that point for me. I yammer for years about A&B modules, the primitive dissection of the space-filling MITE, a discovery from the 1940s, memorialized in a book dedicated to H.S.M. Coxeter by someone with 42 college degrees and a Medal of Freedom (not me, just have the Princeton thing so far), and only Haim ever bothers to call me on it, says they're irrelevant or whatever (nice try). In the meantime, we do an all-6th-grade assembly in a Portland Public School, show slides about the octet-truss (AG Bell), sphere packing (JH Conway), and build a tetrahedron out of 24 A modules (12 left, 12 right).
Haim takes on GRUNCH as well, as does MPG a little. But mostly, if you're an over-specialist, a Dr. Precious, you can't be bothered with "connecting the dots" as every other one won't be "higher math" so who give a $#!% right? We actually seem to reward that kind of willful selfishness in universities -- partly why I encourage my students to look elsewhere for higher learning, like maybe Google or PSF. OK, OK, Princeton still has some credibility -- they've got me and Walter Kaufmann as alums :)
> I don't know how many hours, days, months and years I > have spent with APL, Forth, Fortran, SAS, C, C++, C# > and a several other less interesting languages. Let > alone all of the work with assembler and machine > code, past and current with embedded systems. But it > is substantial. And I never called it "math". I think > you are killing whatever your message is by doing > that. >
You might not have read much Iverson, designer of APL, but he called APL an executable math notation, i.e. here's another math language, with its own typography and every- thing, that happens to *run* on machine, what Leibniz used to dream about. How is it *not* a math notation? He went on to design J with Roger Hui & Co. Now *there* are some real mathematicians! Tim Peters haunts our Python Nation, some others. We're well endowed too.
> If you are saying that there are career opportunities > available that are mostly just CS centric then why > not just say that? I will say that if you are math > orientated then you can probably be CS orientated and > vica versa. But one doesn't replace the other.
I'm saying the academic division into CS and "higher math" is a figment of the university system, starts after K-12, and we don't want that kind of mental corruption to infect our young, at least not in Portland. Keep your hyper-specialized blinders *off* our kids, thank you very much, and unless you know what A&B modules are, don't even think about pretending to be a gnu math teacher. Stay low on the pole, with those university people and their sorry sad warez, mostly rip offs that needed to be "formalized" by someone less ept. Sorry to get all invectivey here, but we have a Rad Math meeting tomorrow evening, Silicon Forest a sponsor, and we're just not in the mood to kowtow to analog math teachers, an inferior breed. Forgive my impatience.