Archive for March, 2010
john d. cook on the rule of 3.
online resources list from ncatlab dot org.
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…”