this will all make sense later

whenever you’re teaching, say,
“intermediate algebra” and talking about,
say, adding fractions… whatever,
sooner or later somebody will say
“my *old* teacher showed me…[this]”,
where [this] is, typically a sketch of,
some very-likely-flat-out-wrong or
in-any-case-insufficiently-general or
*would*-work-if-not-radically-misapprehended
other way to go.

and we’ve got, as it were, a new
stumbling block. because, although
it’s easy enough to learn to rein in
one’s initial reaction
(“well, first of all i don’t believe you;
*no* math teacher would’ve told you *that*…
but more to the point, so what?
it obviously hasn’t been working out
for you since you’re still being
“remediated”. maybe *this* time
you’ll take it *seriously*”)…
the student isn’t getting “buy-in”.

because this “new” thing that *you’re*
presenting is *felt by the student*
as an *attack* on the “trusted source”
that they remember as having taught them
*something*… something that will have,
at least, made some sense to them at one time.

so they’ve circled their mental wagons
around their wrong idea hoping to keep
your good idea out as some kind of
*act of faith* (in their trusted source).

or so i conjecture.

i was telling essentially this story
one day in the barracks and was overheard.
“i like the way you put things”
said i-forget-who (a near-stranger)
gladdening my heart and giving me
some confidence that here was,
anyway, some blog fodder.

because we teachers need to talk about
issues like this and i’m just the guy
to jump right in and participate
whenever i can. i’ve *always* felt
this way. i’ve *also* felt that
formalizing such discussions,
say under the heading of
pedagogical content knowlege,
is in vain and a grasping for wind.

because why? because there’ll be
*no* “right answer”… anyway no
right answers of the kind we encounter
in, well, say, adding fractions.
where certain very precise claims like

can be displayed as it were
like a “text of our sermon”,
an anchor to insure that our discussion
never drifts off into mere opinion;
a way to get our *feelings about*
the material off to the side
and compare *our* ideas to
what i’ll go ahead and here call
“the truth” or “the fact of the matter”
or something like that.

nope; it’ll always, like in *most*
academic subjects, be about *words*…
and *opinions* about them…
things that flat-out *don’t have*
“literal meanings” in the sense
that equations do. what’s weird
is that we usually like to pretend
that words *can* and even usually *do*
have strict, this-and-only-this
“meanings” in ordinarly conversational speech.

i was kidding around yesterday
with some funny-when-taken-too-literally prose.
typical math-major stuff, really.
people say “always”, for example,
to mean “sometimes”… and are clearly
understood in their context.
this happens all the time (see?).

along comes a math major who thinks
(or pretends to) that “one non-example
refutes any claim to universality”
and expects (or pretends to) that
*displaying* a counterexample will
cause whoever is making the sweeping assertion
to *modify* their claim rather than,
say, reply with, “oh, you’re being
too literal” or some variant.

“acceptance is the answer to all my problems”.
all? really?
you’re just being too literal.
well, maybe *you’re* not being literal *enough*.

we keep wanting to be able to say things that
are *true*, as it were universally, and moreover
we keep wanting these things to be *believed*.
but because we’re working with ill-defined concepts
(not mathematical symbols), this is,
strictly speaking, impossible.

there’s *always* (okay, i don’t mean this)
some man-behind-the-curtain “hidden assumptions”
preventing us from settling arguments
in, say, religion and politics:
we *say* we’re talking about *school* classes,
for example, when maybe we’re “really”
talking about *social* classes
(but are prevented by blindspots and taboos
[in this case, by generations of redbaiting]).

math-heads keep noticing this; it annoys the others.

oh, and we saw _revolutionary_road_ a little bit ago.
good picture. but did the cinema really need another
madman mathmajor? couldn’t he have just been a philospher
or something? geez.