Date: Sep 27, 2013 8:41 AM
Author: GS Chandy
Subject: Re: Math Wars Philosophizing in the NY Times

Kirby Urner posted Jun 18, 2013 8:31 AM (http://mathforum.org/kb/message.jspa?messageID=9138447):
> On Mon, Jun 17, 2013 at 7:28 AM, Joe Niederberger
> <niederberger@comcast.net>wrote:
>

> > Everyone here should read it -
> >

> http://opinionator.blogs.nytimes.com/2013/06/16/the-fa
> ulty-logic-of-the-math-wars/?hp

> >
> > Cheers,
> > Joe N
> >

> I think the article over-simplifies quite a bit, in
> purporting to be about
> K-12, but actually being more about K-4 or K-8. You
> can't stretch the
> four arithemetic operations out for twelve years
> unless you've been
> drinking lead (Pb) and maybe too much fluoride (there
> is an upper limit in
> Fl good for you, plus in Portland we also care about
> fish and safe levels
> in waters salmon will tolerate, nothing to do with
> humans eating them, just
> where they'll willingly go with the flow).
>

Thanks for that reference to the NYT article. I've just glanced at it, and I broadly agree with you that it tends to over-simplify stuff.

Shall look at the various links you've provided in due course.
>
> http://www.chem4kids.com/files/elements/009_shells.htm
> l
> http://chemistry.about.com/od/chemistryfaqs/f/what-is-
> fluoride.htm
>
> The key question is how to best spiral along various
> STEM threads to make a
> smooth segue at each turn, and to make K-16 an
> enjoyable / enriching
> experience in a highly fertile environment.
> Even those who choose to not
> study much should reap more than they sew, thanks to
> synergy.
>

Indeed. I believe this is really the whole heart of what is needed in our educational systems.

If we ever learn how to accomplish this, then we have the entire 'problem of education' resolved!

GSC
>
> http://4dsolutions.net/presentations/p4t_notes.pdf
> (PDF mentioning
> 'spiraling')
> (from a workshop for STEM teachers Hyatt/Regency
> O'Hare, Urner / Holden,
> Pycon 2009)
>
> If you really understand the addition algorithm,
> which the article
> describes, learning to align by place value and carry
> to the left, then you
> really understand what it means to add in base 5 or
> base 11.
>
> That was the approach of SMSG / New Math: to teach
> the addition and
> subtraction algorithms generally enough that a shift
> in bases, away from
> base 10, would not throw students off. They would
> follow.
>
> Tom Lehrer made fun of the parent reaction by singing
> through a subtraction
> problem in nightclubs. The laughers on the
> soundtrack didn't really get
> that the joke was on them, as junior really was
> getting it, and could
> follow the base eight version just fine, or I know I
> could, and my
> classmates were right there with me, and this was
> early grade school.
>
> http://youtu.be/DfCJgC2zezw (has the base 8 part,
> which some weak of heart
> tend to skip)
>
> 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 non-STEM-informed
> imaginations extend
> to the set object, nor the multidimensional array
> object when thinking of
> algorithms (nor where algorithms come from: Algebra
> City).
>
> That we in the STEM world embed sets in lists of
> lists and consider "data
> structures" important came later than New Math, in
> terms of pedagogy. The
> parents with their pitch forks had already buried
> that Sputnik-inspired
> alien stuff. It felt too imposed and Americans
> fought back, claiming their
> right to remain ignorant, to keep the clock from
> accelerating. Future shock
> was for "developing" nations.
>
> By the 1970s, a pretty interesting curriculum had
> been done away with, in the
> rush to stay dumb. "New new math", as far as I can
> tell, is not worth my
> time or interest. I went for "Gnu Math" instead,
> wherein we phase in the
> open source languages especially (the most
> transparent). 'Mathematics for
> the Digital Age and Programming in Python' is an
> offering there, where we
> use it in 10th grade, or something like it.
>
> I think the grandparents who "got" New Math when
> still available are more
> likely to be investing in what I call "Gnu Math"
> today versus "New New
> Math", a miasma of mediocrity promoted by an
> idiocracy (dumber than the
> real Mafia).
>
> In Gnu Math we want to *program* addition with
> fractions. We learn the
> algorithm in such detail that we can tell *a
> programmable computer* how to
> do it, which is also to tell ourselves in another way
> (another logic).
>
> Having rational numbers on computer means facing that
> problem of finding
> the greatest common denominator (GCD). You need to
> divide numerator and
> denominator by that GCD to get lowest terms in an
> equivalence relation (1/2
> == 2/4 == 4/8 ==... == p/q * 2/2). When does a
> computer know terms are
> lowest? What's a good algorithm?
>
> GCD(a, b) is of critical importance and the algorithm
> we so often use in
> STEM world is named for Euclid, it's called Euclid's
> Method, and LCM = (a
> * b) / GCD(a, b). In the dumb and dumber texts used
> by slobs in the
> laziest of hoods, zip codes you'd like to not live
> in, they don't tell you
> Euclid's Method even exists or what it is.
>
> If you have this hole in your own knowledge, consider
> yourself shot through
> the head by your own alma mater and seek medical /
> remedial attention
> immediately. Not knowing Euclid's Algorithm means
> you should think twice
> about voting or registering an opinion on any matter.
> Don't get up in the
> morning. Get out your smartphone and learn it
> instead.
>
> That's what the Math Wars are all about. Those
> without any knowledge of
> Euclid's Method by the end of high school are the
> losers, and that goes for
> any professors in the same boat. Lets help these
> poor vanquished back on
> their feet again shall we? I urge empathy towards
> the world's least
> privileged. Lets start a new charity if need be.
>
> Kirby Urner
>
> Proposer of:
>
> NCLB Polynomial
> NCLB Polyhedron