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
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:
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
http://www.flickr.com/photos/kirbyurner/479693617/ (when in primo
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
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:
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.
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.
Re nanotech in the age of carbon:
On Mon, May 27, 2013 at 9:56 AM, Robert Hansen <email@example.com> wrote:
> On May 25, 2013, at 1:39 PM, Anna Roys <firstname.lastname@example.org> 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