On Sat, Jun 14, 2014 at 8:53 AM, Joe Niederberger <email@example.com> wrote:
> Just a discussion starter: > http://anniemurphypaul.com/2013/06/why-do-so-many-of-us-hate-math/# > > I'll quickly add that if one just googles this topic, you will find many > many answers, almost all of which have some ring of truth about them. An > obvious question is therefore, what, if anything, can be done to improve > people's opinion of math (or at least their experience of it,) and would > such remediation have any wider benefits for society? > > Cheers, > Joe N >
Lets define two modes of learning: recall and recog (short for recognition).
Watching a movie like Donald Duck in Mathmagic Land is recog in that one passively takes it in and on 2nd or 3rd viewing maybe one starts to connect the dots, to reflect. E.g. Donald meets the Pythogoreans in one section (4 mins 15 secs), and the student starts thinking about the Pythagorean Theorem and the proofs, including the one by president Garfield. Recog is curled up with a good book, watching a film, going to an art museum, listening to a lecture.
Recall is where you're on the spot to do it yourself (DIY), working out with so-called "exercises" (answers in the back sometimes, but you have to show your work). Recall is building a fire, speaking a foreign language (not just listening to it), hiking, solving puzzles (crosswords, sudoku, treasure hunts, geo-caching... ), programming a computer or VCR or other device, acting in a theater, working with clay.
The learning process is an oscillation between recall and recog, hiking and setting up camp (recall), and campfire stories (recog).
One reason people hate math pedagogy, which they hate more than math (math is "unhatable" and to make it the target is an adroit / sneaky move on the part of the pedagogues to deflect attention from themselves): too much emphasis on recall with poorly developed recog tools.
When I say Donald Duck in Mathmagic Land in first or second grade at Markham Elementary (Annex, Capital Highway and Barbur Blvd), I realized didactic cartoons like this would vastly accelerate the appreciation for cultural context, history, and I'd be able to connect more dots in a hurry. Gimme more!
But alas, they were stingy with such overview and keen to rub our faces in the DIY stuff with no attention to dot connection. No timelines or bios, little history, hardly any bothering to connect anything to anything. "What lazy slobs, these adults" I could hear myself thinking.
Evidence: when adults try to restore or repair their miss-diagnosed "hate for math" (what they really hate how it's taught), they go for dot-connecting trade books e.g. Mario Livio about Phi, or Steve Devlin or Ivars Peterson, or some author who writes a fine coherent prose and tells a story.
DIY / recall textbooks have "story problems" but they never deign to tell you a story unless they're a Disney, some independent guy with money and a dream. They want a "heads down, just focus / concentrate, don't ask for big picture overview, attend to authority, let the adults make you" mode. Oppressive. Tyrannical. Math sucks. No kidding.
But things have improved vastly since I was a kid (e.g. Sesame Street, Electric Company, Big History, Myth Busters etc.) to where at this point I'm not so worried about it.
The recog stuff has developed a lot and nowadays all you need is a skilled teacher who understands its importance.
Youtubes, that database of clips I used to call the Videogrammatron in the 1980s, is here and thriving. I add to it myself, a few grains of sand here and there (dots).
When I teach Martian Math (for Saturday Academy, for whomever), I make full use of Youtube, flying through Mandelbulbs or whatever, telling history, e.g. how Mandelbrot was a swing of the pendulum away from Bourbaki. Anyone can recognize a simple story like that. I tell them tales, like about that time Orson Wells scared 'em on the radio (AM or FM?) by making 'em think the ETs were really here. That's baked in to Martian Math.
I'm like Donald Duck in Mathmagic Land, leading a tour group. They slurp up the recog and exult in the fact that my recall (lots of Visual Python, already written so just change some colors or speeds or something) is not monopolizing. Vectors, complex numbers, rates of change, polyhedrons.... (Martians measure volume with tetrahedrons dontcha know).
They get to sit back and relax and also connect dots and reflect. Math and meditation go together, should not always feature these frantic exercise hunger games "on the clock" (labor force training, Taylorism, typical US disdain for its so-called working-immigrant class, a holdover from Anglo classism, intensely suffocating, partly why the Founders broke off in favor of more liberal less top down management principles -- connect those dots why don't ya?).
Once I read Fuller's Operating Manual for Spaceship Earth it all made more sense. *Of course* they want to compartmentalize and track us early, pigeon-hole (keep tabs, administer). The oppressive adults are mostly conditioned-reflex robot-like zombies passing on the memes of their ancestors without much self knowledge or self questioning. Leave everything to them and it's all over. You need fresh minds (yay kids).
Adults are mostly morons, I realized that early (like "walking dead" one might say). But I was biased as I was locked up in a school, which is where this low IQ approach to cultural transmission is still most in vogue. Outside school, you'll find more adults with imagination (e.g. Disney), praise Allah. At least they exist, these dream-weaver recog-assisting types. And they come into schools like Overseas School of Rome and International School, Manila because they have the imaginations for it, the chutzpah, the charisma, so on the whole I had a great schooling experience compared to 98% of my US-imprisoned peers. Lots of Shakespeare, history and art.
Yes, schools are still a bastion for failed pedagogical techniques and when people think of "learning math" they still think of brick and mortar school buildings full of misguided if well intentioned individuals (called "teachers" in popular culture -- really more day care / baby sitters). That's all going away though, in the way we remember and some get nostalgic about. All that one room schoolhouse nonsense. We're at home in Cyberia now.
Again, I'm not too worried about it (all this change). This is 2014, not 1944. Lets try, really hard, to remember that and not try to fix what doesn't need to be fixed (e.g. brick and mortar "schooling" as we know it). Just let it die.