## Archive for March, 2010

john d. cook on the rule of 3.

online resources list from ncatlab dot org.

antiquated math word of the day: “sagitta” at *mathrecreation* (“dan m”).

ladies and gentlemen, wearmath dot com.

a perspective on higher category theory, by tom leinster.

Math Teachers at Play #24. *Lots* of stuff here!

*Walking Randomly* about math carnivals.

easy, fun, and free: dan meyer.

VLORBIK ON “MASTERY”

in my world all serious players

understand that math facts must

be learned from infancy along

with the mother tongue. more-

over, i believe it’s still

pretty widely understood even

at the level of popular culture

that math is the very *model*

academic subject. debating

the importance of “math facts”–

early and often–looks to me

like sheer lunacy.

of *course* everybody should be able

to recall (or quickly compute), say,

single-digit “multiplication facts”…

the “times table”… skilled teachers

working with trusting students can

make this pretty painless… though

presumably the “army we’ve got”

would have to resort to some

“drill and kill”…

*everybody knows* that computational power

leads to personal power. trouble is, they

can’t guess how hard or easy it is

to get how much.

“math is hard” sez barbie. and many others

including me. math *is* hard. but everything

else is harder still. i trust no living being

as much as a computation, for example…

and i trust committees even less than *that*…

but committees are the *level of debate*

for math ed…

anyway, who cares, hard, easy.

love your neighbor. hardest thing

in the world. still you’ve gotta

*do* it or you’re no good to anybody.

one learns faith in maths, in some sense,

because *faith plays no role*. atheiests

and the devout agree on all the same theorems

(once they’ve agreed on definitions and

computations); likewise anarchists and

republicans. i’ll even say that,

for the same reason, faith in mathematical

truth is the *strongest* faith: we have

*very few* heretics, anyhow. almost everybody

quits *learning* math at some point; sure.

some of us are even lucky enough to *forget*

massive amounts. but nobody denies that

the *doctrines* are sound…

*[the document at hand…
personal correspondence from
early summer… goes on with
some discussion of tough versus
tender teaching styles (both
can be done well or badly;
let a thousand flowers bloom).
that stuff depends too much
the give-and-take it was written for.
when we return, we find me ranting
or rambling or whatever this is
on the related… but certainly
not the same(!)… question]*

“SPIRAL” LEARNING versus MASTERY

a little of each and a lot of both;

unask the question. should we read

for the sentences or the paragraphs?

there must always be *something* you’re working on

or you’re not even doing math: problems.

each living one *of* ’em is an exercise in mastery.

every calculation is a proof: you flatten it

right down to the ground and you *win*.

if it was a *hard* calculation, you win big.

otherwise: spiralling. reinforcing “skills”.

why try to figure out how to write *all* books?

just let some one person that cares and can write

try to produce *one* book as clearly as they can

and get all the capitalists out of the picture

and it’ll be hugely better than any current text

in intro-level math: shiny unreadable page-splatter

uglier even than most (other) advertisments.

some’ll spiral more; some’ll shoot at early mastery.

good. true math is scribbled on blackboards anyway.

random pieces of paper. those weird computo-pads.

by humans not committees.

this is what all the singapore-saxon stuff is about:

*everybody knows* it would be a whole lot easier to do it

on the cheap. but then how are all these fine people

over *here* gonna get *paid*? an army of no-talent

bureaucrats with nothing better to do than tell *us*

what to do, alas, but whatta ya gonna do: state-mandated

standards that you need a building full of lawyers

even to *pretend* to qualify for. it’s no *mystery*.

if we could afford a small fraction of the enemy’s pocket change

for counterpropaganda, textbook publishers would be as despised

all up and down the internet as teacher unions already are.

esquith is surprisingly frank on this. my new hero.

are you actually still *reading* this?

ON TEACHER “TRAINING”

doom. the real thing is just amazingly well-known;

the *real* training is called “doing the math”

(and “doing the reading”); there’s nothing like it.

a program that requires special “training” strikes me

as an attempt to hijack teachers into selling some product.

and always will. and i am *not* alone.

there *is* an academy and business doesn’t get to change

its rules around at random to sell more crudware any more

than they get to change the rules of football so the

hometeam can always win.

no dice, baby. if *i* can’t read your damn book,

what good can it possibly *be*?

in a well-regulated universe, the sharper *kids*

could be leading the ones right behind them.

no telling how much i learned from the one guy

who stayed ahead of me in math the whole way up

through public school… one heck of a lot though.

how do you *get this to happen*?

hint: never in a million years by government mandate.

meanwhile talent begs in the street.

or, as the late great bukowski has it,

“great poets die in steaming vats of shit”.

*my* saying has the virtue of being literally true

(though of course it’s buk’s you’ll repeat);

you’ll have seen some astonishing street musicians

playing for cigarettes and pocket change i bet.

math-heads are the same way: we’ll *give* it away

if we can; just show me somebody that *cares*

and i’ll work on a problem with ’em.

it’s what i’m here to do.

i never was all that good a learner, really.

this doesn’t keep me from trying to become one.

and i *do* seem to be pretty good at

“passing it forward”… such, indeed,

is my almost unwavering belief if i’m

allowed on bad days to omit classroom

work from consideration…

once it’s *really* academic, interesting people

are working together on interesting problems

and the rest is easy. i’ve seen it done.

(of course by “easy” i mean heartbreakingly

frustrating… but also richly satisfying…)

but we’ve got this assembly line over here

just for the *buttons* on those calculators…

and all these *prisons* and *jails* and *wars*…

and *so what* if their teachers never *did* quite “get” fractions…

never cared much for *reading* either if the truth is told…

maybe they’re just as scared as the kids… maybe worse…

and getting up *out* of this mess just looks *impossible*…

and the government has fulfilled its duty to its masters

if the students are all quietly under their surveillance.

and the *last* thing anybody at that level wants is mass literacy.

it was supposed to’ve been the other way around:

humans using government to control corporations.

with any luck i can die fighting for this

instead of giving up The Art. scary as hell.

and right in here, i’m loving it.

“… the riot squad is restless… they need somewhere to go…”

math for the street: enumerating the rationals explicitly.

one never tires of encountering novelties:the sophomore’s dream at w’edia via the squared circle (RIP ’09 evidently).