## Archive for the ‘Blogs’ Category

domestic arts in the age of digital distribution. RIP, vlorblog. here are some posts mentioning “clean” and “dish”: https://vlorblog.wordpress.com/?s=clean+dish (courtesy of the “search” feature from that blog).

… but i’ve lost control of that one.

so here it is again. with a photo

from “vlorbik unstrung”.

the music isn’t by me, of course. “stealing”

already-well-known tunes was good enough for

joe hill and woody. and dylan. so it’s good

enough for me.

i easily figured out the main “trick” in playing it

but haven’t practiced it enough (even now) for

public performance.

negatively fifth street (2015)

a drifter escaped from a boxcar/ denouncing obviously jive believers/ has a zine about it in the catalog/ but nobody can work the damned randtrievers/ and the cats are praying in the alley/ and the pool shark is chalking up his cue/ an’ i’m out lookin’ for my lady/ down on kirkwood avenue

jesse, he’s round the corner/ buskin in front of the bird/ doesn’t bother him if no-one stops to listen/ doesn’t bother him if they don’t like the words/ and some violence boys might come and beat him down/ and he’ll forgive ’em more than i could ever do/ but that’s nothin compared to what’s goin on/ back on kirkwood avenue

a melancholy cougar/ buys a hoagie from a clown/ there’s a tempest brewing somewhere/ and there’s panthers on the other edge of town/ and the goddess of gloom and the jester/ are doin’, that thing they love to do/ in a video montage/ at the parking garage/ on kirkwood avenue

a cloud of marijuana/ is obscuring the people in the park/ or maybe i’m just losing my eyesight/ or maybe it’s just getting close to dark/ an’ the tournament game was a victory/ so now it’s turnin’ into a zoo/ an’ the riot squad and the thunder god/ are on kirkwood avenue

grading linear algebra again.

so far this quarter, i’ve (1) returned

the text from last quarter (late) and

i’ve (2) gone back and got a different

copy of the same text a week later.

and that’s it… a week and two days

into the semester.

but starting today there’ll be bigfat

envelopes full of homework piling up

in my mailbox. so very likely i’ll be

posting less over in the cooking show

(where i’ve had a pretty good run going

for about a week).

math stood tall: edusolidarity recap at JD’s.

Mathblogging.org looks pretty promising.

(i couldn’t put this in a comment

for this “log laws” post

at *f(t)*; too long.)

it’s the old principles-versus-procedures problem.

students hate general principles.

i’ve had tutees pay me hundreds

to supervise their homework

who very clearly “tune out”

whenever i try to explain

what’s going in in a general way.

it’s worst when it’s about a topic

they’ve been exposed to before…

the famous “math phobia”. panic

sets in when you realize that

you’re going to expose your ignorance

yet again… about fractions, variables, or

vocabulary (“equations” and “expressions”,

for example)… to name some common

weaknesses for *beginning* algebra.

the tendency is to believe that whatever

this “general principle” thing is that

teachers keep wanting to come back to

is secret-math-head *code* for something

that, if we’d only present it in plain english,

then they’d know how to work the problems

on the test (which had darn well better

be *just like the ones we practiced*).

so we give in and show ’em the “procedures”:

FOIL instead of “repeated distributive law”,

for example… and they *pass* the tests

but get *further behind* in the grand scheme.

“i’ve done OK this far by disregarding

all the math-brains-only *theory*…

and now i’m failing. but i’ll *never*

be a math-brain… good heavens,

i’d have to go back and understand

an *awful lot* of stuff i’ve been

given a pass on all these years!…

it’s the pedagogy! it’s my learning

style! it’s my teacher! math sucks!”

the phenomenon persists at all levels

(that i’ve passed through in learning

math up to my published thesis…

when, sure enough, i still felt myself

an imposter compared to the “real

mathematicians” i’d been working

with in grad school).

“logs” are a particularly interesting case:

otherwise-well-prepared calculus students

are often very weak on logs. hell, every

tenth student has decided they’ll just

go ahead and pretend “ln(x)” is to be

replaced with “1/x” somewhere along

the line no matter how many times

it’s marked wrong.

when “should” students learn about

the abstract, proof-heavy style

of math-rightly-so-called?

the typical student will never

*feel* ready for *any* new idea.

(this should be considered in

any discussion of “developmental

barriers”).

do-the-same-thing-on-both-sides.

logs-are-inverse-exponentials.

here’s a common-log equation:

log(4) + log(25) = log(x).

and here’s its solution.

10^[log(4) + log(25)] = 10^[log(x)]

10^[log(4)] * 10^[log(25)] = x

4*25 = x

x=100.

now, kate’s worksheets are great

and i’m not suggesting that anyone

make my approach into their

exhibit A for day-two-of-logs.

so don’t get me wrong.

the point i set out to make when i started…

if i can remember that far back… is that

*no* approach can overcome the simple

fact that our courses are designed to

go *much too quickly* for median-level

students. the good news is that we

can spot talent pretty easily this way:

anybody who can keep up typically

hasn’t “hit the wall” where math

gets *hard*; give ’em an A and

pretend we’ve done something

to be proud of.

my “discrete mathematics” students

last quarter were all calc 2 vets:

future programmers and engineers

and whatnot. and *almost* all of

’em learned quite a bit about

writing proofs. the *easy* thing

here is (of course!) the logic.

(i mean the symbol manipulation;

what all the p’s and q’s have to do

with the “logical structure” of

a given proof is much more obscure

than it appears to non-teachers.)

if *anybody* i’ve ever worked with was

developmentally ready to take on

“show using the definition of logs

that log(a) + log(b) = log(ab)”

as an exercise, it’ll’ve been these

talented hardworking students.

but the resistance was palpable and i folded.

there was… as always… much too much

material (i also had to skip stuff like

“manipulations with sigmas” and

“complete induction”… the class

emerged ready to take on maybe

a third of the exercises in the sections

covered [mostly the easiest ones]).

there *is* no developmental appropriateness

in “real world problem solving”: one needs

a technique that *works* wherever it’s found.

our task as math-teachers-in-schools,

though, is pretty much “preparing students

for yet another class”… and one technique

that “works”, alas, is *hide your weaknesses”.

that idea of “apply some inverse-thingy

on both sides of the equation”? one of

a handful of big ideas in algebra

(along with “variables”, “graphs”,

and “roots of polynomials” and…

well, not much else…)

“look: to undo an *addition*, we do

a *subtraction*… to undo a multiplication,

we do a *division*… and these ideas

were *hard* when we tackled ’em

back in some earlier course.

a little later, we decided that

we wanted to ‘undo’ squares,

and introduced ‘square roots’;

more generally (and about half

the beginning-algebra folks

get lost around the bend in

here somewhere) we’ll need

to undo powers-of-the-variable

like x^K, and introduce Kth roots.

well, then, doggone it, why shouldn’t

the same undo-the-operation

strategy work for K^x?”

i’ve ranted out this mini-lecture

not just to get it out of my system

(for today), but to demonstrate

that one need *not* have any

*formal* understanding of

“inverse function” to use the

never-stop-harping-on-general-principles

method that i’m more or less advocating here.

(indeed, inverses-treated-formally

is a classical crux. “never mind

*why* i solve x = f(y) when i want

a formula for f^{-1}(x)… just show

me *how*!”… one of the most

glaring examples of the

i’ll-never-understand-the-reasons

phenomenon known to me.)

okay. this was fun.

haven’t i got a *job* or something?