
Re: Math Wars Philosophizing in the NY Times
Posted:
Jun 18, 2013 12:45 PM



Clyde Greeno rightly observes that a far too small percentage of students > 'survive' school math to enter STEMspecific higher education programs. My > question: why haven't the 'math progressives' done something (however > small) about increasing that percentage? >
I did not understand his reference to "Kcalculus" out of the blue. I looked it up, but no light was shed thereby.
http://mathforum.org/kb/message.jspa?messageID=9138177 http://arxiv.org/abs/physics/0201002
> > I've not yet read "Wars in American mathematical education" by Andre' Toom > (recommended by Domenico Rosa). > > One is delighted to observe that Professor Wayne Bishop gives the article > broad approval as "not bad". > > Kirby Urner's objection that the article 'overimplifies' quite a bit is > (more or less) justified  but I also believe that such oversimplification > is inevitable given that the authors are discussing quite complex issues in > 'pure prose'. Had they used the 'prose + structural graphics' (p+sg) that > I recommend for the effective discussion of complex issues, I believe this > objection would have had less force. > > Kirby Urner: > > We were also doing Venn Diagrams a lot back then. Do > > people want to tell me which "algorithms" they mean > > when we talk about union and intersection, set > > difference? I don't think most nonSTEMinformed > > imaginations extend to the set object, nor the > > multidimensional array object when thinking of > > algorithms (nor where algorithms come from: Algebra > > City). > > I observe that KU's comments above would have considerable import for an > argument between Joe Niederberger and Robert Hansen (which, I believe, > largely developed from misunderstanding of the issues by Robert Hansen). > [See thread "New tutor here", headed by > http://mathforum.org/kb/message.jspa?messageID=9134056 ). > > By "Algebra City" I meant Baghdad, ancient (not that ancient) site of the Wisdom School and Al Khwarizmi, a math whiz (wiz) from whose name we get Al Gorithm (yes sounds like Al Gore  didn't AG transact with Al Jazeera after all?).[0]
And what did we get from Baghdad then? From Algebra City? Al Jabber of course.
And if you think "jibber jabber" or "abacadabra" that's right. You should also think of cryptography and keeping secrets, an ancient purpose for which the terms "function" and "inverse function" (encrypt / decrypt) have relevance. You'd be smart to build lots about crypto into algebra class and some curricula do that, others don't. Steer towards the ones that do is what I'm suggesting.[1]
If you're a student living in the United States of [North] America and you notice your high school's curriculum has no mention of Euclid's Method for finding the GCD, feel free to write to the Governor of your state, which office will know to route it to the Core Standards people who have been using the governorships as a network to create new standards for your nation. You want your nation to be at least mildly competent right? Canadian? Well then, you probably already know Euclid's Method as Canadians tend to be twice as smart as their brethren to the south  I read in a study somewhere (Moore?).
Anyway, learn Euclid's Method yourself first. Can you find a good cartoon? It doesn't involve "factor trees" or "prime factors" but does involve division and taking note of the remainder. It's a doorway into "recursion" but needn't be given that treatment.
There's also an "extended" Euclid's Method (EEM) that's been used to solve Diophantine Equations and to help with RSA, another algorithm, named for three crypto whizzes: Rivest, Shamir, Adleman.[2]
Kirby
ENDNOTES
[0] http://cnsnews.com/news/article/algorealjazeerahonestgoodnessnews
[1][2] Like mine! http://www.4dsolutions.net/ocn/crypto3.html
For further reading:
Fiction: Cryptonomicon by Neal Stephenson (cryptonomicon.com)
History:
Crypto: Secrecy and Privacy in the New Code War by Steven Levy http://www.amazon.com/CryptoSecrecyPrivacyNewCode/dp/0713993464 http://www.worldcat.org/search?q=isbn%3A0140244328
RSA: http://searchsecurity.techtarget.com/definition/RSA
To Read (on my list): http://www.amazon.com/CypherpunksFreedomInternetJulianAssange/dp/1939293006 ...
STEM / STEM / STEM
Search: "NCLB Polynomial" "NCLB Polyhedron"

