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Topic: "dot notation" on a math track?
Replies: 10   Last Post: Jan 12, 2010 5:24 PM

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kirby urner

Posts: 3,690
Registered: 11/29/05
Re: "dot notation" on a math track?
Posted: Jan 7, 2010 11:18 PM
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On Thu, Jan 7, 2010 at 7:02 AM, Robert Hansen <> wrote:
> Who agreed with hexadecimals? Let alone ASCII? Where are we heading with this? HTML? Are you hoping to improve the god awful state of MySpace page design?

Lets back up here.

You were saying above that this Litvins text I ran by you (Mathematics
for the Digital Age and Programming in Python), a conservative
discrete math offering, could easily go on your shelf next to some

Now I'm not sure if what you meant by that is that it would be OK to
use it in the classroom, but that decision is out of your hands and

Some are already using it, including at the high school level.

So over on math-thinking-l, another list that I frequent, we find out
that the 2nd edition is hot out of the oven, and all the Python in
that book has been migrated to Python 3.

< lore source="python nation" >

Now Python 3 is a milestone in the history of Python's development
because it's the one Guido, the inventor, used to somewhat mockingly
refer to as PY3K (thinking how Y2K had been such a "crisis").

At least he was putting it off to 3000 it sounded like -- but of
course that was the joke, as he was hard at work on making the leap
way back in 1999 such that by now, in 2010, we're already looking at
3.1 and plan on entering a tunnel of no more changes to the language,
mission accomplished. [0]

The thing about the Python 2 versions is they each bent over backwards
to stay compatible with the previous ones. However, Guido felt he had
made a few fixable mistakes in the primitive design, such as around
how to handle division.

Then there was Unicode, now really the standard, with ASCII a subset
(in UTF-8, ASCII is bit identical to itself, so the changeover has
seemed somewhat invisible to ordinary Americans perhaps).

Many language designers would simply regret their errors and give up
on starting over. If you have a huge installed base, that's a real
disincentive against making serious changes. This is how most
languages go to the computer language graveyard.

But snakes shed their skins, have this reputation. Guido's title,
Benevolent Dictator for Life, suggested he hadn't lost control of his
creation, might be able to pull it off.

And indeed the guy chose to deliberately insert a chasm of "no going
back" that would "break everything" (except we have some nifty
migration tools and an army of coders, so some of us are already
switched over, chugging along happily on these shiny new tracks).


So here's the equation: reasonable math book, covers lots of great
topics, uses the latest Python.

That implies learning some Python and that implies learning about Unicode.

Unicode doesn't make nearly as much sense if you don't know about
ASCII, and ASCII is all about hexadecimals.

So we want to bring all that in, basically allow this hybrid of
traditional math and this new brand of discrete math.

It doesn't look like Dolciani, nor Everyday Math, nor Saxon. It's not
attempting to do so. There's still a lot of spiraling though.

Think of it as a 3rd year math course, satisfying your 3rd year
requirement in Oregon. You did algebra and geometry and now feel too
burned out to try algebra 2.

You're ready for something completely different and jump on this new

The lab looks like fun (lots of LCDs) and the teacher is all hot to
trot having taken some digital age math training at some summer camp
in Colorado c/o Google or Yahoo or one of those.

So again, it's not like a hostile takeover, just a wedging in of
something new, consistent with state standards.

We've got a green light, even funding, or so they tell me.

I'm in the process of proposing an OSCON talk for July, where I'll
provide some insider perspective.

Thing is, I'm not sure exactly what the game plan is. Were we
supposed to read something in the paper about it? Since when did that
ever happen? Math Wars is all about calculators and whether we should
memorize the multiplication tables right? That's the only debate in
the newspapers. Oh yeah, and we need vouchers.

I'll keep checking those blogs then, lots more going there.

Like, I've got some stuff scheduled, but there's got to be more. Is
there some secret government program we don't know about?

> You haven't really made the case for adding programming to the 3 R's. And even if you did, why not simply offer an elective programming class? In Python if you wish.

It's not so much programming if you don't write these long scripts
(which you might, I don't know).

But Python may be used interactively at the console.

You go 2**38 and that's what you get back. It's a nice big display,
gets all the right answers (the the Decimal type you can get PI to a
thousand places, just like Weird Al in 'White & Nerdy' ( )).

So all we're really doing is swapping out the Texas Instruments or
Casio for something Intel or AMD. One electronic circuit board for

Should math have any electronics going? Isn't that engineering?
Well, if it's engineering, then lets teach that instead? There's
still a lot of math, if you read between the lines. :)

Now you might counter that calculators are programmable and some
curricula have taken advantage of those features. No problem then. I
bet your teacher might help you with that.

Then when you come back tomorrow, your work will still be there.

When the lesson moves on, from Fibonacci numbers to their convergence
to Phi, you'll already have most of the three or four lines of code
that you'll need. [1]

I know I'm writing all this in the future tense, as if I haven't been
doing this for years in my classrooms. [2]

Well, for many teachers, this *is* still future tense, and they've
never heard of Python, nor Litvins, nor any of what I'm talking about
("what's unicode?").

I'd say Portland area teachers have a lot of fun enrichment classes to
look forward to. If Intel wants to release a few managers to the
effort, I'd be happy to manage 'em, or join 'em at gigs. PCC could be
the venue? Dang if I know all the ins and outs. Lew?

> I don't have time right now to show you why regular expressions have almost nothing to do with natural language which includes grammar. In fact, remember your statement that polyhedra are chemistry? Well, regular expressions are grammar as much as polyhedra are chemistry.

That's a somewhat cute analogy but not necessarily a good one, because
in reading Linus Pauling about twinning in the fcc, you'll actually
come across words like "cuboctahedron" and "icosahedron" a lot. I'm
not making this up.

Ordinary materials science, which includes nanotechnology, is all
about polyhedra and if you've done your A, B and T modules, folded
them from plane nets like we do in Kirby's classes, then we're
accustomed to certain angles, kind of know when we're seeing 'em. LCD
triangles and all of that. (gives the flavor,
if you're curious)

We get more practiced at spatial geometry through practice (!), and
that actually has applications, when it comes to looking for work.
I've got my resume on line, and there are jobs there where my knowing
something about polyhedra actually helped me put food on the table,
imagine that!

Regular expressions, on the other hand, are a clever way to search
through text looking for matching patterns.

They're ubiquitous in some areas and have infiltrated the more recent
web frameworks as dispatchers for URLs, i.e. when you send one of
those http strings through your browser, the first piece of code to
take a good look is a regular expressions pattern matcher looking to
forward your request to some kind of handler (Google App Engine and
Django both work this way).

"So what?" asks the analog math teacher, "why should I care?".
"Because in this class we explain 'how things work'" comes the answer,
from some off camera source.

> You would think that if you really cared about turning more kids onto programming you would clean up these serious flaws in your message.

My message inherits from a rather long lineage at this point: that
"executable math notations" have a place in the classroom, even
pre-college (Mathematica is one a lot of people use).

This was more of a pipe dream when hardware and software were both
expensive, but now that costs have come down, we have this golden
opportunity to galvanize a languishing economy and education system by
bringing some of its core content into the modern age.

Investing the the future by improving education: that tends to work
where it's tried, provided the improvements are real, not just
cosmetic or window dressing.

Proposal: lets introduce a sober contemporary industrial grade
interactive interpreter, put it in a "chat window" (named IDLE) on
more student desk tops.

What impact will this have?

The chicken-egg people say you can't use students as guinea pigs and
until we have guinea pigs we won't have data and until we have data we
shouldn't have guinea pigs and...

But some schools take risks, including with parental consent, and
allow such tomes as Litvins to be used in the classroom.

I'm not saying all of Portland Public Schools is switching to this
text. I'm not saying this text is the only resource using Python.

You've accused me of lying in the past and I don't want to leave
myself wide open to that charge. I'm just saying that we're free to
experiment out here in the Wild West, and plan to keep doing that.

Stanford isn't the only school able to try out new stuff, MIT either.

> One big problem with more programming is that the art has matured to such a high level that it has lost much of its amature appeal. Sadly this happens a lot, such as with electronics, and maybe there should be more emphasis on "hobby" like electives in school to make things fun. The LEGO and First clubs seem to help with that, but they are hardly something someone can take with them into adulthood.

The same is true for mathematics of course. You're implying that
professional grade programming is out of reach so it'll just be toy
stuff of no real relevance?

But we might use all those same arguments to denigrate these weak
attempts to teach calculus, which never amounts to a hill of beans and
so on.

School just never works, does it, no matter what we try?

However, if not in a defeatist mood, I think you'll see why some
teachers share my excitement about getting more interesting equipment
in the classroom. That alone would have a cheering effect in some
high schools. Wow, adults even care? That hasn't been much in
evidence of late. And they're actually going to teach us how things
work? What planet is this?

"I went to math class and came away understanding about ASCII and
Unicode, about hexadecimals, plus we went on this whole tour of
polyhedra, as generated by this thing called VPython (works with
Python), and learned what a VRML browser is -- and this stuff is all
free so I can download it on my computer at home at play with it"
(privileged kid, has a home computer).

You think parents are disappointed when they hear their kids talking
this way? Most parents would be amazed.

That sounds more like a Saturday Academy class, not like one of
Portland Public's.

But things could reach a tipping point here. We have some dynamite
teachers. They're not slow or unteachable.

Do you think they'd enjoy learning Python, professionally and on the job?

Can you imagine at least two or three saying "yes"?

Here are some pictures from our Aug 7 summit meeting. Note there's a
picture of the state standards we'll be meeting with this new course,
in case anyone asks.
(says "digital")
(a strategy)
(says "discrete")


[0] (temporary moratorium
- - -- give librarians a chance to catch up).

[1] why do we care if Fib[n+1]/Fib[n] converges to Phi as n
increases? Because Phi is not verboten in our geometry classes, even
though Haim might think it should be. You joined us recently, but
during the Bush Adminstration I was all gaga for NCLB, pushing these
curriculum elements I was positive you'd need to know about if you
didn't want to be left behind. I had the NCLB Polynomial and the NCLB
Polyhedron. Once Obama took power, I sort of slacked off on pushing
those. NCLB is not so popular in the current political climate ( I
also had NALB for adults, as they shouldn't be left behind either ). (for those three lines of code)

[2] electives, self selected, nonprofit Silicon Forest storefront,
not Portland Public, though I did do Python at Winterhaven PPS for the
8th grade for awhile, also LEP High, both times as a guest manager on
loan from my company (which also sponsors Oregon Curriculum Network,
as I may have mentioned).

- - --
>>> from mars import math

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