On Mon, Jun 17, 2013 at 7:28 AM, Joe Niederberger <email@example.com>wrote:
> Everyone here should read it - > > > http://opinionator.blogs.nytimes.com/2013/06/16/the-faulty-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).
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.
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.
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.