Date: May 27, 2013 3:15 PM Author: kirby urner Subject: Re: When math makes sense - w/ cooking, consruction I remember a story (true) from my friend Russ, in construction, and an avid

geometer as well (with an eye for its art value -- not unlike George Hart

and his daughter Vi).

This foundation they were building on seemed a bit off and when he asked

the guy who laid it how he made sure it was rectangular, he said he'd

measure the two diagonals, and they were equal. QED.

Of course if you think about it, an isosceles trapezoid has the same

property, and that in fact is what they were building on, although the

distortion was only apparent to the builders (they didn't start over as I

recall).

Per my STEM standards (standards I'd apply versus those handed to me by

authorities I do not recognize as such e.g. "state governors" (snicker)),

the 1, 2, 3 power relationship between linear, areal and volumetric

quantities would be harped on quite a bit.

Here's a simple computer game I sketched for this purpose:

http://worldgame.blogspot.com/2006/03/green-signal.html

This blog demo isn't precisely that issue, but what goes with it is the

topic of "optimizing" and the fact that a sphere encloses the most volume

for the same fixed amount of material.

Volume:Surface ratios would be a core topic. The fact this it's not a

constant as a shape grows and shrinks (scales) is an important fact in

nanotechnology as surface area becomes exponentially more compared to

volumes enclosed (materials used, dose delivered).

I thought when I read the article first that we'd see kernel popcorn, not

popped popcorn, going into the cylinders. That has the potential to get

messier. I've often used beans for comparing volumes.

The beans I've used (e.g. in a Montessori demonstration -- then with

students taking over) came with "mixing bowls" i.e. polyhedron containers

open on one face so that beans might be poured from one to the other.

The same Russ (above) helped me build these things, out of stiff

paperboard.

http://www.flickr.com/photos/kirbyurner/479693617/ (when in primo

condition)

Fill the tetrahedron with beans and pour into the octahedron 1, 2, 3, 4

times and it tops off. The edges are the same length. Now pour from the

tetrahedron into the cube. Here, it's the face diagonals of the cube that

match the tetrahedron's: 1, 2, 3 times and it tops off.

Yes, the ratios are exact, but given these are pre-schoolers and

kindergarteners, we don't dive into the algebra right away.

You could call this a GeometryFirst [tm] curriculum in contrast to

something more Gattegno (AlgebraFirst [tm] was more his trademark, what

with the Cuisenaire Rods, color coded with matching letters for algebraic

expressions).

This idea of using a tetrahedron as a unit of volume helps limber up the

young brain and is a segue to other lesson plans I've already discussed in

this thread, such as this one:

http://mathforum.org/kb/message.jspa?messageID=9125328

Note that current CCS (common core standards) do NOT emphasize 1,2,3 power

relationships twixt linear:areal:volume, nor the 1:2:3 rule for

omni-triangulated spheres, nor V + F == E + 2.

http://learni.st/users/60/boards/1179-area-volume-and-surface-area-common-core-standard-7-g-6

http://www.corestandards.org/Math/Content/7/G

http://www.corestandards.org/Math/Content/7/RP

Students growing up in Wayne's generation learning math the way Wayne did

would probably not be as prepared for the Age of Carbon as my STEM

students, though we will not have data tables ready at hand to prove this.

We'll just keep renormalizing those IQ tests.

Dialing back to Dom Rosa era math texts would be devastating in my view.

A good high school curriculum would be a combination of something like

"Mathematics for the Digital Age" by Litvin & Litvin (I finally met Maria

at the most recent US Pycon), and Edward Popko's "The Divided Sphere" (I

own the electronic version for reading on company computer -- got a note

from him this morning).

Combine these two with more glue readings and exercises, cross-referencing,

and you've got a really promising STEM core.

But we'll never get there if we surrender to the "governors" of the various

US states and act at like they're supposed to tell us what to do, like

slave-monkeys. What a silly / ridiculous notion.

What surprises me is how the teachers seem to be caving to this stultifying

brain rot. I guess they fear for their jobs.

Kirby

Re nanotech in the age of carbon:

http://mybizmo.blogspot.com/2013/05/the-age-of-carbon.html

http://worldgame.blogspot.com/2006/12/nanotech-talk.html

http://worldgame.blogspot.com/2010/03/towards-nanoscience.html

On Mon, May 27, 2013 at 9:56 AM, Robert Hansen <bob@rsccore.com> wrote:

>

> On May 25, 2013, at 1:39 PM, Anna Roys <roys.anna@gmail.com> wrote:

>

> Perhaps. However, one might also consider the value whereby students who

> are not engaged in their studies become engaged due to creative

> presentation of content.

>

>

> We all want that. Now all we need to do is reestablish an oath of teaching

> whereby the policy makers, schools and teachers provide honest and

> reasonable guidance to their students and their prospects. Most of these

> students will be doing something "hands on" when they leave school. It

> won't be algebra. It is about time that school has meaning again, and not

> just for the academically minded.

>

> Bob Hansen

>