a (pretty commonplace) math-ed
BC nurtured by me at various times:
be calculated out from first
principles.”

(particular examples:

i’ve elaborated somewhere
in here.

*values of trig functions
[for “basic” angles (i.e.,
\pi times 0, 1/6, 1/4, 1/3, & 1/2)];
i now (mildly) urge beginners to develop
a routine of *charting* these
values for the “sin” function
when faced with several exercises
calling for trig calculations.
the other charts are easily
devloped as needed from there.
but heck, i’d’ve just done better
myself to admit that sin(\pi/6) = 1/2
is a *darn useful thing to know*
even without drawing some big ol’
equalateral triangle in my mind’s
eye every time just to “see” it.

*various “infinite series”
like e^x = 1 + 1/[1!]x + 1/[2!]x^2 + 1/[3!]x^3…
[one is utterly puzzled at some point
can have such easy-&-useful tricks
associated to it; too many unfamiliar
notations (or unfamiliar properties
of [somewhat] *familiar* notations)
are floating around. one is waiting
for the “aha” when “differentiates
to itself” will be able to work itself
out *vividly*… anyhow, it’s nice
a nice simple *target* set up for
certain suchlike gropings-in-the-dark…]

*many others

)

but, of course, “figuring out from first
principles” is *hugely important* and
widely under-rated in the imagination
of our typical students… so, just
rephrase it as “*seldom* memorize…”
and you’ve got a *winning attitute*
rather than a BC.

it’s that *totalizing* thing: “never”.

again: “accentuate the positive”
is a winning attitude (dammit).
but “eliminate the negative” is
a bullshit commitment
(as is “don’t mess with mister
in-between”, i suppose).

it’s just no use *talking* with a
hardened hear-no, see-no, speak-no
evilist. or anybody else that already
knows the answer before the question
arises. be it jesus or allah or
more teachers or younger teachers
or more training (or less) or acceptance is
the answer to all my problems today.