The story goes like this: Kids aren't taking gradeschool computer science and fewer are enrolling in the dead-end career path of advanced computer programming, and educators are all in a miffy over it fearing these kids are doomed, I tell ya, doomed. Doom on you, doom on you ...

"Some kids, for whatever reason, are missing the opportunity to at least take a bite out of the class, to see what it's all about ... They would use the skills they learn for the rest of their lives."
[ More Computer Classes Urged for Kids - Yahoo! News ]

Yeah, right, essential life-long skills like maybe How to Write VBasic Macros in Word? First off, let's remember that Bucky Fuller's gradeschool teachers said he would be ipso-likewise damned for all time if he didn't learn how electric motors worked. Doomed and damned and double jeopardy because, listen man, there are electric motors everywhere and the future belongs to those who can fix them.

• Exhibit A: Your refridgerator. Did you even know there was an electric motor in there?

• Exhibit B: Your local Maytag Repair person. Are they the one driving the Lexis?

This is the real crisis in Education: Educators have flunked out, packed it in, and hide from the future, and I have proof, proof in the form of a direct observation of our 5 year old idling some travel time in the back seat of the van, amusing himself by counting to 1000...

Where Educators Go Horribly Wrong

We could feel it coming ... 12, 13, 14 ... ... closing in on that first hurdle, the switch from the 'teen' rule back to decimal digits. We're watching a connectionist machine (if you'll pardon the model, but it will be clearer later). We hit nineteen, and there's a pause .... Twenty said with some degree of pride.

Why? Because he recognized the departure from the increment association rule that says +1 leads to the "next symbol" and moved into the new domain of "digit recycling" and it felt good to remember that rule. So far, educators are all with me because that is what they teach, pride for a trivial rule recall. But let's go on ... 26,27,28 ... ... remember, we're into Domain II, recycling the digits, and the count slows because he's headed for "Twenty-Ten" and he knows he's been there before but he's not totally sure what he did last time because, heck, how often does this come up everyday? and here is where our education model will pratfall: Twenty-Ten!

Classic education? Punish the child by making a fool of them by handing them a grade-token that's less respected than the one their peers got. Maybe do so without using negative words, as if that's better (kids are not stupid y'know), but basically, bzzzzt it's the Game-Show model and the points are tallied at the falls, the winner plays the game of least mistakes in rule recall. But dig, we gave him the rule of digit recycling, and we didn't explain that 'ten' wasn't a single token.

No, dear, that's Thirty. Mama advises

since it's Mama, no question, it goes into the rulebook, Thirty it is, and on we go, and he's clicked on that Tw- and Th- mnemonic so we get to 39 and ... Four-Tee.

It's here where Educators should be pouncing: Right here we have the first evidence of learning, direct observation of the subject taking new information and putting it into practice, adapting it for his own experience.

The fictional Dr. Who fears the Daleks because of their blazing skill in the ability to adapt to new circumstance. Don't tell the folks force-feeding their kids with Italian and Polo lessons, "Intelligence" isn't the smarts to stuff your head with rules to recall. If anything, that's a better definition for stupidity because it doesn't help the creature adapt to changes and unforseen challenges in their environment and any truly 'smart' kid should recognize, adapt and route their way around fact feeding.

This is the great Folly of the Examination: Instead of measuring the pupil's tolerance for brain-stuffing, education should turn to the same rule we use when we want to decide if an octopus or an alien being is actually 'smart':

How fast can they extrapolate and adapt new information?

Throw them a curve, see if they duck; then throw them another. That's where the 'A' grade should go, and it could be measured objectively and directly, and in milliseconds.

But wait, there's more ...

Now we've established a new benchmark for assessments, only we've only just passed 4% of our goal. Patience now, it's a long wait ... 75, 76, 77 ... something else educators don't do very well is wait, but stay with me, there's even bigger goodies ahead ... 97, 98, 99 ... and you guessed it, a pause of hesitation while we exchange the current rule program and grope for another, only we have an edge here because, in our culture at least, this one is a famous rule, it has to do with money ... One Hundred! One hundred and one, one hundred and two ...

Fine, ok, trad tutoring rules say we have a graduate here, hit the bored stead-state requirements or whatever, send the lad on his way, but, dig, those of you with a mathematical bent, you've maybe already guessed:

We have an impending problem called "Orders of Magnitude" that tells us the time now between rule-exceptions is going to get very, very, very, tediously very long.

Here's where the educator should really perk up, grab the clipboard and pen and stand by eagerly awaiting fresh and tangible evidence of intelligence: Repetition fatigue is going to set in, a rare and precious opportunity to observe real problem solving.

I know a math tutor who coaches kids on those inane math-competition exams. Jill has 9 cassette tapes more than Jane, Jane has 6 less than Bobby and the winner is Nobody because Everybody knows that if Jane and Jill and Bobby all know each other like the illustration shows, they trade tapes all the time. It's not just a contrived game-boy problem, it's a non-problem, a farce. Repetition fatigue: Now that is a problem, one we all face. So, watch now, carefully, wait for it ...

Fooour hundRED and FIFty one, fooour hundRED and FIFty two ...

You catch that? He's employed melody and rhythm as a strategy to avoid the effect of repetition fatique on his neural connectionist machine. He has interceded on the rote mechanistic exercise and embelleshed the process to keep himself awake. Clever that, and I'll bet the relative rates and lags of the onset of um fatigue ah mistakes and the appearance of spontaneous playing the wetware against itself strategizing, I will wager you a clear M.Ed. that there's significant intelligence metrics to be had there, far more predictive of the rocket scientist vs short order cook than whether Jill is X or Bobby is Y.

The Artist as a Connectionist Machine

As an aside, a curious phenomenon appears. I notice his skipped-number mistakes have an interesting pattern to them: He tends to skip numbers that have repeated digit sound-tokens.

These are associative errors, totally divested of any inherent appeal to any 'logic' like we ram into their wee ears in gradeschool math; these errors are cognitive illusions, evidence that the creature is using rules of token coincidence transformation rather than any Ptolomaic sense of a symbolic computation. It's as if the associative brain is recognizing the first occurance and generating a deja vu recognition of a "past event" that tricks the 'observer' into thinking the first 'Seven' in "Seven hundred and Seven" is somehow "Already Seen" -- the skipped numbers don't follow any written symbolic-token digital rule, seventy seven is two very different word-sound tokens, but 707, 646 ... we see a lot of those get skipped.

Meanwhile, back on the Road to One Thousand ...

This is a car trip, and I love watching emerging minds so it's no problem at all; we often play tedium-games that would drive most sane adults completely out the windsheild. A few more times we encounter the rule-pattern association shifts, the tell-tale pause for shifting cognitive gears where the rule-sets must be swapped out, very different from your odometer, and very much like how if I ask you if 4 times 9 is 36 or 68, you can answer faster than if I ask you if 7 by 8 is 56 or 54 because your inner "mirror mind" is modelling numbers not by their position in some table or sequence in some pattern, but by their relative weight. But that's a whole other story.

Fractals in Adaptive Learning

Inner representations of learned constructs is interesting, but what interests me more is the learning, and whether we can tell that it is happening with better confidence than by deploying minefields of pop-quizzes. It's a long way to one thousand, with no new rules until the very very end, and sure enough the pause between each something-hundred and ninety-nine and the next clicks along smoothly.

I do notice a very curious fractal effect: as we cross over the ninety-nine marks, there is an initial re-emergence of the somethingty-nine pause as we recycle digits through the tens of the early hundreds, and the rate at which this pause vanishes is another opportunity for educational metricizing. Curious, eh? Again, the rule isn't symbolic, but associative, and there's a pause, a short time-out while we allow the connectionist machine to speculate whether the additional digit has altered the playing field sufficiently to invalidate the rule? Or, maybe it is tied up in memory and experience and the known physiological constraint that short-term memory is just that, while the last time we used this rule is now outside of the short-term range prompting a pause to re-collect the rule, test it for appropriateness, and then proceed?

There is some evidence to support that last proposition, and it's more than the observation that humans never learn from History because the situation always appears different: We have a small quandry to address while he mulls over the possible existance of Ten Hundred but it's retracted immediately as the recognized goal-state number. Once he hits this One Thousand, emboldened by his triumph, like any good human, he presses on. ONE thousand and ONE, ONE thousand and TWO and on we go -- his older brother groans, but dig this, we come to the first critical test. Clipboards and pens ready? Prime your stopwatch ... sure enough, there it is, a pause, a small pause but still a pause longer than the recent nine-rollevers, right at that old friend from a thousand counts ago, one thousand and twenty NINE ...

You can breathe again. He says 'thirty'. The rule has been learned-of, assimilated and accommodated as the cognitivists say, but more than that, the rule has been extrapolated, taken home, put to use in new ways for which it was not previously presented. Not surprisingly, the extra cognitive involvement in all this extra-curricular rule-adapting has made the tedium strategizing vanish, because the excitement of this transition domain is entertainment of itself. As we pass 1040, the melodizing re-emerges and it's clear sailing once again.

Until ... can you guess?

When rules collide

Keep in mind, this is not an odometer, it is a little boy. A little boy who lives in a cultural context. A little boy who has heard people talk and who watches TV. Blasphemy as this may be to consider in the psychological circles, this little boy has a context and a history and a whole little mirror neuron mapped world inside him that has some rules of his own which he's now suspecting may impinge on and even contradict the explicitly provided rules accumulated from this purely academic exercise of getting to two thousand by ones.

Mommy, what comes after one thousand and ninety nine?

What do you think: Pass or fail?