```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 avidgeometer as well (with an eye for its art value -- not unlike George Hartand his daughter Vi).This foundation they were building on seemed a bit off and when he askedthe guy who laid it how he made sure it was rectangular, he said he'dmeasure the two diagonals, and they were equal.  QED.Of course if you think about it, an isosceles trapezoid has the sameproperty, and that in fact is what they were building on, although thedistortion was only apparent to the builders (they didn't start over as Irecall).Per my STEM standards (standards I'd apply versus those handed to me byauthorities I do not recognize as such e.g. "state governors" (snicker)),the 1, 2, 3 power relationship between linear, areal and volumetricquantities 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.htmlThis blog demo isn't precisely that issue, but what goes with it is thetopic of "optimizing" and the fact that a sphere encloses the most volumefor the same fixed amount of material.Volume:Surface ratios would be a core topic.  The fact this it's not aconstant as a shape grows and shrinks (scales) is an important fact innanotechnology as surface area becomes exponentially more compared tovolumes enclosed (materials used, dose delivered).I thought when I read the article first that we'd see kernel popcorn, notpopped popcorn, going into the cylinders.  That has the potential to getmessier.  I've often used beans for comparing volumes.The beans I've used (e.g. in a Montessori demonstration -- then withstudents taking over) came with "mixing bowls" i.e. polyhedron containersopen 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 stiffpaperboard.http://www.flickr.com/photos/kirbyurner/479693617/  (when in primocondition)Fill the tetrahedron with beans and pour into the octahedron 1, 2, 3, 4times and it tops off.  The edges are the same length.  Now pour from thetetrahedron into the cube.  Here, it's the face diagonals of the cube thatmatch the tetrahedron's:  1, 2, 3 times and it tops off.Yes, the ratios are exact, but given these are pre-schoolers andkindergarteners, we don't dive into the algebra right away.You could call this a GeometryFirst [tm] curriculum in contrast tosomething more Gattegno (AlgebraFirst [tm] was more his trademark, whatwith the Cuisenaire Rods, color coded with matching letters for algebraicexpressions).This idea of using a tetrahedron as a unit of volume helps limber up theyoung brain and is a segue to other lesson plans I've already discussed inthis thread, such as this one:http://mathforum.org/kb/message.jspa?messageID=9125328Note that current CCS (common core standards) do NOT emphasize 1,2,3 powerrelationships twixt linear:areal:volume, nor the 1:2:3 rule foromni-triangulated spheres, nor V + F == E + 2.http://learni.st/users/60/boards/1179-area-volume-and-surface-area-common-core-standard-7-g-6http://www.corestandards.org/Math/Content/7/Ghttp://www.corestandards.org/Math/Content/7/RPStudents growing up in Wayne's generation learning math the way Wayne didwould probably not be as prepared for the Age of Carbon as my STEMstudents, 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 Mariaat the most recent US Pycon), and Edward Popko's "The Divided Sphere" (Iown the electronic version for reading on company computer -- got a notefrom 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 variousUS states and act at like they're supposed to tell us what to do, likeslave-monkeys.  What a silly / ridiculous notion.What surprises me is how the teachers seem to be caving to this stultifyingbrain rot.  I guess they fear for their jobs.KirbyRe nanotech in the age of carbon:http://mybizmo.blogspot.com/2013/05/the-age-of-carbon.htmlhttp://worldgame.blogspot.com/2006/12/nanotech-talk.htmlhttp://worldgame.blogspot.com/2010/03/towards-nanoscience.htmlOn 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>
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