I love teaching modulo! There are countless ways to create exploratory learning opportunities in which students discover the need for modulo. And once a student starts programming, modulo really starts to feel like the lost operator. This is a situation in which programming yields a new perspective on mathematics. In the same way that we learn the inadequacy of doubles for representing non-terminating decimal values, the modulo gives new depth to the usefulness of division. Most students in the US remember doing division with a remainder ("R = "). I've employed their nostalgia and sense of mastery over this procedure to help them step into modulo. Kevin On 9/29/06, kirby urner <kirby.urner@gmail.com> wrote:

I've been brainstorming with other math teachers on the relevance of the Python modulo operator, a primitive right down there with + * / and -, but which doesn't get a lot of focus in traditional K-12 textbooks these days. Why not?

The old answer was: Modulo Arithmetic belongs to something called Number Theory, which although a have for math purists, has precious little to do with the real world, and so we should focus on basic arithmetic (the "big four" operations) and leave the modulo stuff for college (and even then, only if they choose to become math majors).

The old answer is full of holes of course. We have Modulo Arithmetic devices all over the place in every day life. Clocks, for example. Indeed, the individual columns of our positional notation, are simply Modulo Stacks with carry (hit the Modulus, pop the stack, carry 1, restore 0). Furthermore, we now have RSA running in just about every web client, ready to frame your secure session with a web server authorized to accept your Visa charge (what out for phishing!).

I think the new answer is closer to the mark: there's no excuse for avoiding Modulo Arithmetic, and if your school does so, that's a sure sign of mediocrity and you might want to pass that back to your parents ("mom, our math teacher said we we won't study Modulo Anything this year, but Bugs Bunny said it's important" (or was it Mighty Mouse?)).

So once your school buys onto this bandwagon, maybe your teacher will deign to project a good shell. Python's is excellent, but not the only game in town. J's is wildly powerful by design (hyperdimensional arrays a favorite breakfast food), worth poking around in.

Then there's GameMaker.

Nothing wrong with playing in a Game Engine, though I think Gerald's Darwin @ Home is more impressive: he rolls his own, using the most minimalist Physics Rules, and starting with the earliest Java AWT, then moving to JOGL. Any EIG VPython killer app has yet to be started, let alone offered in beta AFAIK. Please update me if I'm wrong about that.

For more on Darwin @ Home, watch Gerald's excellent Google Video, hosted in the left margin of Myspace.com/4Dstudios.

In sum, I think RSA *will* be making inroads as a curriculum standard in many good schools, right up there with "differentiation by parts" as a relevant algorithm to know about. And one of the benefits is cryptography opens History, both fictionally and nonfictionally. Neal Stephenson has trailblazed extensively in this direction.

One thread: RSA was stumbled upon in slightly different form by some British cryptologists, but classified immediately as "too dangerous" for the general public.

MIT, with the push of needing a business class solution to an emerging real world challenge (i.e. the need to encrypt on the fly, based on any two parties making random contact through the Internet), had no incentive to classify (quite the reverse).

Plus when the cyberpunks discovered the NSA was offering resistence (in part because of the British example -- her dutiful civil servants inspire respect in many corners), the lid simply blew off, with PGP coming out of New Zealand and paranoid geeks teaching their own mothers how to generate public keys (better protection than tin foil).

Given this turgid history, it's somewhat understandable why high schools might choose to stay in the bleechers, leaving RSA to the big boyz 'n girlz to kick around. But that's not an optimum way to leave it, especially now that the patent has run out, and rolling one's own is not in violation of anyone's legal rights. At Saturday Academy, I like projecting that website where you're promised big Reward Money, if you're able to crack some of their Modulo Ns (i.e. public keys) into two constituent Probable Primes (an even bigger reward if p and/or q turn out Improbably Composite?).

"Python: It's Not Just for War Colleges Anymore" -- probably won't fly as a bumper sticker, but I do find it funny (it alludes to its dark DARPA past). Put a goofy little snake with rolling eyes in the corner, with this funny Revolutionary War hat, a Blunderbuss in its coils. Reminds of Don't Tread on Me.

Kirby _______________________________________________ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig