On Fri, Jan 1, 2010 at 5:31 PM, Wayne Bishop <email@example.com> wrote: > As an interesting topic for exceptional math students, sure. As standard > fare for everyone, please stick with the standards and give parents an > opt-out option for their students' participation. Arrogance of education > "experts" is prevalent enough without working at it deliberately. Decimals > first is bad enough but duodecimal or hex, let alone sexagesimal? Please, > folks, get serious. > > Wayne >
Sexagesimal was not a serious proposal from my corner. That was Robert mocking my base-16 standard (requirement), poking fun.
Indeed, I was arguing that "other bases besides base-10" should *not* mean equal time for "anything goes" random bases.
The argument that changing the base actually makes the standard base-10 *more* understandable is sensible, probably why New Math took it on in the 60s (in addition to seeing where computing was heading).
One uses the same abacus as before, but doesn't carry until adding to F. 0F + 01 = 10. The columns stack higher. That's easy to grok.
We don't really understand "base 10" until we understand "not base 10".
Having that contrast answers the question "what's a base"?
Anyway, the solution I've yakked about for Oregon is maybe one you like: a new course that satisfies a 3rd year math requirement, and a special set of standards just for it.
There's some grant funding already in the bag (though I'm not the bag's holder).
So we get a whole separate math course for our hexadecimal topic, if not for elsewhere as well. It's what students signed up for (in part).
This isn't the same as having a computer science elective, because we're talking about getting math credits.
Now, would a precalc-calc student be precluded from taking digital math in addition? Of course not. It'd be like taking an extra course in statistics.
However, given our commitment to spiraling and wanting to give overviews and previews, having this added option will have some ripple effects in earlier grades.
I'm guessing we'll be seeing more hexadecimal numbers in 8th grade if not before. "Anticipating student demand" is a part of the equation. "Wanting to internationalize" is another.
Parents aren't as hostile as you might suppose maybe. They know, just as junior does, how many professions make use of these concepts.
The thought of students trying to divide and multiply numbers in base-16 maybe just sounds tedious and stressful, but not that's not where I was going with my lesson plans.
So far, no one is talking about doing lots of grueling exercises like the four operations by hand, in binary or hex. No one is proposing long division of AA into F18ABCF01.
One has a computer at one's elbow (if lucky, a calculator as runner-up - -- but then we're sort of missing the boat here), for converting in and out of decimal, should the exercise require that.
I was looking at simple mappings, lookup tables, treating hexadecimals as unique indexes, x-values to be paired with y-values.
This is in keeping with the "memory address" motif, for which hexadecimals are standardly used, and in keeping with the Unicode motif.
We're moving closer to "coordinate system" in the sense of "addressing scheme". Computer memory is a "wall of bricks" (like the Great Wall of China) and we use it to store both data and instructions.
The lesson plans help demystify, set the stage, without lots of "make work". We're expecting these spirals to continue on into college, for those that pursue them by this route.
When we get to RSA in senior year (assuming a more advanced class for a 4th year), we'll be glad for this easy way to convert phrases to numbers and back.
>>> import binascii >>> tohex = binascii.hexlify("Able was I ere I saw Elba") >>> tohex '41626c652077617320492065726520492073617720456c6261' >>> fromhex = binascii.unhexlify(tohex) >>> fromhex 'Able was I ere I saw Elba'
We're also hitting the function concept (spiraling), giving 3rd year math students another take on something from algebra 1.
As Robert pointed out, having some Chinese characters in the mix can't be all bad.
I also suggested some logical puzzles where students would need to think about file formats, encoded information. Good stuff to know about. Explaining "How things work" is a goal.
As a rule of thumb, I think it's hard to know, just from a topic's mention (e.g. "hexadecimals") just what it implies in terms of a curriculum.
Teachers definitely need to be in the habit of reviewing one another's work, offering pointers, criticisms, making improvements.
The sharing culture we've already developed around source code will come in handy here.
Teacher buy-in is just as critical as parent buy-in and there's an aspect of green field development to our digital math track (because it's new) that we're hoping will attract some imaginative talents.
As a digital math teacher, you already know how to create web pages, or are learning those ropes in preparation. You also now something about the different Internet protocols and tcp/ip (did you screen 'Warriors of the Net' yet?). You know some of the lore.
Your already knowing all this makes developing curriculum less of a "dictate from on high" operation and more of a "looking for good ideas and adapting them" operation (Wikieducator's subculture has some of this flavor).