## Archive for the ‘“=”’ Category

*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.

this i vow. i believe in the power of symbolic-objects-carefully-defined. in the power of “math”, in other words. and the holiest-of-all-math-holies i swear i will keep most sacred.

oh, equal sign! great in perfection!

none are like thee in the power to reveal!

no not “continuity” nor “magnitude”…

nor even “quantity”… nay, *nothingness*!…

not even “infinity”…

how are we to speak

how are we to write

how are we to think…

& who’ll understand *any* parable

that won’t understand that there

even *are* any parables…

it depends what the meaning of “is” is.

and the meaning of “is”, is, dammit, “is”.

otherwise, fuck it. what is *wrong*

with these undergraduates? happy christmas.

or whatever.

and a very new year.

… … .

any luck? three different symbols, right?

an equal-sign-that-didn’t-know-when-to-stop;

a “left-and-right-arrow”; and a *double* leftrightarrow.

right?

okay. it appears to work on *this* set-up;

no telling what *your* mileage looks like

(just be sure that it *will* vary).

these symbols, then.

these symbols *all* stand for versions of

“two things have the same interpretation”.

there’s already a great deal of confusion

about (what i take to be) the *best-known*

symbol in this class: the *sign of equality*, “=”.

i’ve remarked on this phenomenon before.

but at the “math 366” level–my current class–

it becomes very important to be very careful to

*distinguish* between various notions of

“means the same thing as”.

but… how?