mel bay upside down: 7 major chords

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ABCDEFG
(seven chords seven ways, part mercury)

ten for maria.

1 – There isn’t enough user-generated content or “making your own math artifacts.”

equations, most likely, first.

but wait. zero-th.
by-hand copies of the *symbols*
for the material at hand.
“the student learns essentially
nothing until the student’s
pencil makes marks on the page”
is a pretty good first approximation
a lot of the time… or anyhow,
i’m far from the only teacher
given to *saying* stuff like this.

i’ve got plenty to say, too, *about*
this but i’m hoping for a list of ten
in under 2^12 characters (for a little
longer; i’ve begun to despair already
at least a little though if you want
to know the truth).
“unions” should look different from “u” ‘s
as an example more or less at random.

*our medium is handwriting.*

first-and-a-half.
out-loud discussion of and…

second.
…written sentences *about*
those equations. written
at leisure without the
instructor (or fellow student).

third.
similar or exact versions of such equations,
repeated, or, much better of course,
improvised, in a “public” setting
with small or, slightly better i
suppose, large *groups* of fellow
students. oral presentation of
the sentences themselves is not
only okay here but much to be
preferred (the board should not
be littered with sentences).
the “correctness” of the sentences
should nonetheless be at issue
throughout the presentation.
said “correctness” is to refer
explicitly to “code”…
utilizing (hey! ed jargon!)
the symbols from our step zero.

it does not escape my attention
that the “artifacts” created by
the student presentations i here
imagine are scribbles of chalk
on a board, soon erased. so be it.


leaving some out…

sixth
yick, computer code.

seventh
student-designed exercises,
exam templates, lesson plans…

eighth
songs and other verse, games,
comics and other graphics,
something to astonish even me.

ninth
blogs.

tenth
fanzines.

Reply

Sue VanHattumMarch 7, 2010 at 7:08 PM
Maria, I loved your list.

Owen wrote:
>”the student learns essentially
nothing until the student’s
pencil makes marks on the page”

Maybe for higher math, but not at all for young kids. The mathematical issues they’re working on don’t usually require pen(cil) and paper.

My son is thinking so much about what I’d call place value these days. “60 and 60 is 120, right?” “Yep.” No writing – at home, anyway. Lots of mathematical thought.

I’ve long been puzzled by your emphasis on “the code”. Maybe someday I’ll get it… :^)

Reply

AnonymousMarch 8, 2010 at 6:57 PM
My son is thinking so much about what I’d call place value these days. “60 and 60 is 120, right?” “Yep.” No writing – at home, anyway. Lots of mathematical thought.

I’ve long been puzzled by your emphasis on “the code”. Maybe someday I’ll get it… :^)
—sue v.

maybe today!

the “places” of “place value” are
places *in* certain symbol strings!
it sure doesn’t matter that you
*speak* of such strings without
having actual *written* code
in front of your actual eyes…
that’s not what i’m always
going on about at all…

60+60=120
presumably gets its interest
from 6+6=12,
together with, right,
the “place value” concept…
*as it manifests in base ten*.

now of course you and your kid
don’t have to have spoken of
bases-other-than-ten for
the essential *role* of “ten”
in discussions of place value
to have become quite clear
all around.

“what’s so special about ten?”
i can now imagine asking
some kid of the same age
if i were lucky enough to
know any…
and i’d sure enough expect
(maybe with a *little*
stack-the-deck prompting
from me) pretty soon to
start hearing about the
role of *zero* (in, again,
certain symbol-strings).

and when our conversations
*without* written work begin
to break down… and if we
still *care*… why then,
we’ll break out some *pencils*
and take a look:
“what do you mean, *precisely*?”.

we’ve been talking about code all along.

tangent.
calculating with numbers
is the very *model* of
one-right-answer-ism:
3*4=13
is just flat-out wrong.
and this is our greatest strength.

in principle, anything worth
talking about passionately
in a math class should have
the *same* character:
there *is* a right answer
if we could only find it.

in order to have this happen,
we have to agree on things.
we *can’t* agree… and be
*sure* we agree… and be *right*…
without certain so-called “rigorous
definitions”: marks on paper
(generally; otherwise
*verbatim verbal formulas*
memorized syllable-for-syllable
[mostly… i don’t seek a
“rigorous” definition of “rigor”…
“one is *this* many”
and its ilk (so-called “ostensive
definitions”) are all the rigor
we can *get* sometimes]).

generally the “rigor” one speaks of
is… i think… pretty *close* to the
being-able-to-calculate-it-out-like-a-computer
thing i spoke of (with reference to
elementary arithmetic) a moment ago.
and this comes from “code”.

again. our power in mathematics
comes to an amazing extent from
being-able-in-principle to emulate
some doesn’t-know-anything-*but*-code
*machine*.

now i’m as much of a luddite as the next
guy, if the next guy figures the wrong turn
was somewhere around “domesticated animals”.
but one *glaring* benefit of computers
in math ed is that students will work
for *hours* on getting code letter-perfect
(if they know no human being can see
their failures happening), that wouldn’t put
in five *minutes* of homework on paper
without getting so frantic about each
“move” that they fall apart before even
getting started. it’s that “interactivity”.
this used to break my heart but it’s true.

if schools were for clarity,
command-line programming
would begin in about first grade.
it’s much *easier* than almost
any other thing you can do
with a computer (which is why
it emerged much *earlier*
than the hugely-user-unfriendly
[from a “code” point of view]
*graphical* interfaces that
erased it from the national
consciousness in around 1984).

(somebody mention “logo”.)

math *is* hard.
but it’s much easier than anything else.
because we’ve got *all* the certainty.
(programming on this model
is of course a subset of math).

ot

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  1. i fucked up the very first one.
    this was a good idea just the same.
    the real upside-down A-chord goes
    0
    0
    2
    2
    2
    0
    (rather than, what is shown here)
    0
    2
    2
    2
    0
    0
    .
    or maybe *that’s* backwards.

    recently somebody corrected me
    in some many-year-old detail of
    a long-forgotten post. so there.

    go and do likewise.

  2. RIP “fisto”.
    the second macbook
    destroyed by me; with
    luck the last. i’ll sure
    as hell never pay full
    retail for another.

    a cry for help.
    when there is
    no help. peace,
    peace. when
    there is no peace.




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