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Topic: What math is – or was!
Replies: 37   Last Post: Aug 21, 2011 1:52 AM

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kirby urner

Posts: 3,198
Registered: 11/29/05
Re: What math is – or was!
Posted: May 14, 2010 2:08 PM
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On Fri, May 14, 2010 at 9:04 AM, Haim <hpipik@netzero.com> wrote:
> Jonathan Groves Posted: May 14, 2010 8:19 AM
>

>>It is ironic that K-12 science education at least makes
>>some attempt to show students how science is discovered
>>and how scientists work.  But why not mathematics as
>>well?

>
> Jonathan,
>
>   Science, almost by definition, is "hands on".  If you have any reason to believe that science education in our public schools is especially effective, please share it with us.  If it is not especially effective, why should we consider "hands on" pedagogy in the teaching of mathematics?
>
>   I have given a similar challenge to Kirby Urner.  In the past, he has made a big deal of the role of "narrative" in education.  I have pointed out to him that there are disciplines, like literature and history, that are nothing but narrative.  I am not aware that they are especially effective, either, in teaching K-12 students, and I have asked him for evidence to the contrary.  (Kirby has not even acknowledged the question.)
>


Note that your above paragraph does not contain a question. When the
premise is your "awareness" of this or that, we're somewhat at a
disadvantage, unless our "awareness" also counts for something. Some
free ranging argument over whether history teaching is effective or
not could consume miles of bytes to no avail.

Conjuring the picture of a bored distracted student, tuned out, not
engaged, is not a difficult trick.

Anyway, yes, I believe in weaving history and mathematics together,
also some philosophy, in general working to integrate across the
compartments to improve students' mnemonic access to various
timelines, as well as to past, contemporary and possible future
concepts.

Anchoring these concepts and developing skills around them requires
hands-on exercise and mathematics has always been hands-on in that
respect. The nature of the exercises may change, but not the need for
interactivity.

When looking at SQL, for example, I talk about "keeping tabs" with
tabulation machines. Plenty of history, a lot of it dark and ugly,
worth exploring here (I'm out there on BlipTV doing just that, in a
talk for math teachers (3 hr workshop) recorded in some Hyatt Regency
near O'Hare in 2009).

There's a "how things work" aspect to teaching about tabulation and
record keeping, but also a hands on aspect, e.g. import sqlite3 is
enough to give cursory access to a simple SQL engine in Python.

Of course SQL isn't part of the Underwood Duddley sequence, or is it?
What if we access a store of polyhedra in some relational structure?
Venn diagrams, boolean filters... it's all here, both free and open
source, just need a teacher with relevant training, perhaps from South
Africa or the Philippines. For home schoolers, or just to give the
flavor: http://showmedo.com/videotutorials/video?name=1510240&fromSeriesID=151

My detractors say I'm just relabeling "computer science" as
"mathematics" and then giving out math credits for what amounts to a
shop class. That's sort of right, but then it's an
over-specializing bureaucracy that electrifies the fences between
disciplines in this way. If you have no access to historical time
lines you might not see this.

A graphical novel, tracing recent history of mathematics through
Russell, Frege, Wittgenstein, Peano, Cantor, Godel etc., and ending up
in computers (Von Neumann) is 'Logicomix: An Epic Search for Truth'
by Apostolos Doxiadis and Christos H. Papadimitriou (Bloomsbury, NY:
2009). There's some fictional material in terms of who met whom and
how things unfolded, so I wouldn't call this literal history. I like
the Athena connection though, given Python (if you know some Greek
mythology, you know these icons go together).

Note that I'm no champion of the "reform" tomes routinely trashed by
Mathematically Correct. For one thing, those have no mention of the
simple whole number volume ratios you might get when using a
tetrahedron as unit volume.

This segment needn't dominate but it *does* need to be included, along
with ideas about sphere packing. This is just basic training for the
imagination, low level like mental arithmetic (call it "mental
geometry" if you like).

The payoff, in terms of having stronger spatial geometry concepts, is
obvious so I use the presence or absence of this content as a litmus
test to rank curricula (one of several).

It's easy to supplement with the missing ingredients of course, so I
don't throw away a perfectly good curriculum just because of this one
glaring omission (gaping hole).

>>So many students little idea of many of the modern
>>applications and modern ideas in mathematics.

>
>   Were you not persuaded by Underwood Duddley,
> http://www.ams.org/notices/201005/rtx100500608p.pdf
> that there are very few real-world applications of mathematics?
>


Underwood Duddley makes the case that the current curriculum is
outmoded. He says right at the top that he's talking about the status
quo, not the more intelligently designed stuff that I'm talking about.

>   Perhaps you and some of your colleagues are confused between "many" and "important".  There are certainly important applications of mathematics, but how many such applications are there and, more to the point, how many scientists and engineers are there?  Numbers are hard to come by, but I doubt there are even one million scientists and engineers in the U.S.  World-wide, 10 million is a pretty comfortable upper bound, I bet.  The other 6.5 BBBillion people in the world have, as their highest mathematical aspiration, to be left alone by people like you.
>
> Haim
> Keep The Change
>


I think we're all aware of your particular psychology and what makes you tick.

You wish to speak for the worlds billions, have them say "leave me
alone, we don't want any of your math education".

That's a self appointed position.

It's just as easy for me to step in and speak for them too: "give us
the luxury of being able to study some of this stuff as any lifestyle
that makes room for such study is likely not a life of pure toil and
drudgery, which is what so many of us experience today -- and we're
all the more exploitable given we don't get clued in (and our
exploiters would just as soon keep it that way)."

I would take the opposite view of yours for debating purposes: there
is only mathematics and nothing but, as every breath, step, utterance,
blink of an eye, is a mathematical phenomenon in a mathematical
terrain. Those who play lots of computer games (e.g. Sims) already
have this sensibility: it's ALL math. Or if you wanna break it into
two subjects: Geometry + Geography. The former is everything
abstract (including algebra) and the latter is everything physical
(including astronomical and subatomic phenomena).

That being said, I'm sympathetic to Duddley's idea that a lot of math
learning occurs "on the job". If you look at Spaceship Earth as one
Global University (easy to do), then sure, life-long learning is the
name of the game (or call it "world game").

We're all perpetually engaged in work / study, no matter what our walk
of life. If there's less sitting in rows and columns day in and day
out, less of the standard pattern we call "school", that might be a
good thing. Less passive staring at screens.

I've been urging an "off your duff" kind of math, with slogans like
"math is an outdoor sport" and such.

You could see where I might even sound like a military or
para-military recruiter in that respect (National Guard?), as these
services are always advertising the technological skills you might get
if you sign up with 'em (cryptography etc.).

Again though, I'm concerned about over-specialization and
over-emphasis on mass murder as a way of life, especially where North
Americans are concerned (it's getting harder to go overseas without
receiving stern lectures about so-called "American" corporations).
I'd prefer to be seen as a recruiter for the health professions,
likewise math intensive (cite Andy McKay's talk about using Python to
sort through SMS messages from field clinicians in Kenya).

Kirby


Date Subject Author
5/10/10
Read What math is – or was!
Bill Marsh
5/10/10
Read Re: What math is – or was!
Robert Hansen
5/10/10
Read Re: What math is – or was!
Haim
5/10/10
Read Re: What math is – or was!
Bill Marsh
5/10/10
Read Re: What math is – or was!
Robert Hansen
5/10/10
Read Re: What math is – or was!
Bill Marsh
5/10/10
Read Re: What math is – or was!
Bill Marsh
5/11/10
Read Re: What math is – or was!
Haim
5/14/10
Read Re: What math is – or was!
Jonathan Groves
5/14/10
Read Re: What math is – or was!
Robert Hansen
5/14/10
Read Re: What math is – or was!
Haim
8/21/11
Read Re: What math is – or was!
kirby urner
5/14/10
Read Re: What math is – or was!
Richard Strausz
5/14/10
Read Re: What math is – or was!
Jonathan Groves
5/14/10
Read Re: What math is – or was!
Haim
5/15/10
Read Re: What math is – or was!
kirby urner
5/15/10
Read Re: What math is – or was!
Haim
5/16/10
Read Re: What math is – or was - or ought to be!
- Haim's latest Challenge
Gary Tupper
5/16/10
Read Re: What math is – or was!
kirby urner
5/17/10
Read Re: What math is – or was!
kirby urner
5/16/10
Read Re: What math is – or was!
Jonathan Groves
5/17/10
Read Re: What math is – or was!
Robert Hansen
5/17/10
Read Re: What math is – or was!
Jonathan Groves
5/17/10
Read Re: What math is – or was!
Robert Hansen
5/17/10
Read Re: What math is – or was!
Haim
5/17/10
Read Re: What math is – or was!
Louis Talman
5/17/10
Read Re: What math is – or was!
Jonathan Groves
5/17/10
Read Re: What math is – or was!
Haim
5/18/10
Read Re: What math is – or was!
Louis Talman
5/17/10
Read Re: What math is – or was!
Robert Hansen
5/17/10
Read Re: What math is – or was!
GS Chandy
5/18/10
Read Re: What math is – or was!
GS Chandy
5/19/10
Read Re: What math is – or was!
kirby urner
5/19/10
Read Re: What math is – or was!
GS Chandy
5/19/10
Read Re: What math is – or was!
kirby urner
5/19/10
Read Re: What math is – or was!
GS Chandy
5/19/10
Read Re: What math is – or was!
kirby urner
5/19/10
Read Re: What math is – or was!
GS Chandy

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