Archive for July, 2015

*At least when I was at school we were correct in writing “Answer = “, even though the teachers hated it!*/— howardat58, upthread.

i’m more likely to’ve encouraged this behavior
than to’ve “hated” it.

but “Answer” is a pretty awkward variable-name
so, given a chance, i’m also likely to’ve made it
as plain as i could find a way to do that what i’d
*really* like to see is a clear

A = …. messy expression to be simplified

right at the beginning and *then* the

A = Simplified-Version-i.e.-“Answer”

bit at the end. which gives a presentation
clearer than one is likely to find on the
blackboards unerased by the previous
class. alas.

because “define variables (with units) precisely”
is a *major* sticking point for *many* students
and i’m not just talking about Remedial Algebra.
one of my favorite-ever calculus tutees
refused my excellent advice on this subject
*many* times.

but without it, we simply *cannot* organize
our presentations coherently.

she finally… same calc ii student here…
couldn’t endure my continual insistence
on keeping equations balanced as she
wrote out her calculations. we broke up
over it.

the attitude seems to be “it’s all just
ritual-process calculation anyway
until i can get the Answer”, whereas
of course one seeks to instill instead
something like “the Answer is itself
a collection of equivalent statements
(leading to the value of a variable)”.

“scratch” work is *obviously* the enemy of clarity
once one is made to *grade* the work.
and not just clarity of *presentation*.
having calculated out some expression,
let’s say correctly, one is in the position
of having to *do something* with the result.

but without the whole A = Answer format…
a “proof”, if you will… one is left with a
bunch of area-on-the-page with certain
code-strings (and scattered english)
bearing no particular *stated* relation
to one another at all.

and if Answer = “the thing i want to see”
i’m very likely to give ’em full credit.
but that won’t make it good work.

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I have briefly mentioned that the alternative to explicit instruction may be described as ‘constructivist’ teaching. I don’t want to become bogged-down in this – I am aware that constructivism is actually [a] theory of learning and not of teaching and I have no problem with it in this regard; we link new knowledge to old etc. If it is true then, no matter how we teach, our students will learn constructively. However, some educationalists clearly do see implications for how we should teach.

i don’t want to become bogged-down in this either.
and yet i have been, deeply, many times, for years.
not so much these days. i just, you know, despair
of anything useful being said or done and check out.

all educational philosophies are useless in practice
until particular special cases are to be discussed
in carefully constructed contexts… so all we readers
ever seem to get is atrocity stories and suchlike
ill-disguised partisan politics.

“carefully constructed contexts” would include, for
example, a lot more attention than i’m usually able
to find about who the heck “we” are supposed to be.
this annoying pronoun is used as if it’ll mean all things
to all people. but it usually means nothing to me.

(in the passage at hand, i take “we teachers”
readily enough, so this isn’t a good example of
what bothers me… but hints at it. in electoral
politics, “we” can mean we-voters, we-americans,
we-patriots… and, often enough, two or three meanings
must be inferred to make any sense out certain
passages at all.)

angels dance on pinheads and owen leaves the room.