28 July 2014

How to Properly Set The Table

A continuing sub-theme of these endeavors is the growing innumeracy of both the general population, and more significantly, the developer community. Two recent essays pick up the theme.

First, we have a PG developer, who was once a pure coder by his own admission, advocating against loops. Froot loops? Too much sugar. Now, whether one needs to use a host language (python, here) rather than the engine's data loading command (syntax peculiar to each engine, since it's not SQL) is another issue. But looping? Nah.

Second, of much greater importance, is a NYT Magazine piece on "new math". I read the dead trees version yesterday, which was titled, " (New Math) - (New Teaching) = Failure ", while the web version is titled, "Why Do Americans Stink at Math?". The dead trees title is more descriptive of the text.

As mentioned a few times in the course of these endeavors, I was a guinea pig for at least two previous "new math" initiatives, back in the dark ages of the 1960s: SMSG (which we alliterated, Some Math Some Garbage, but was officially School Mathematics Study Group) which was an implementation of New Math, per se and later (for me) the TutorText approach.

If you follow the link to the New Math essay, you'll see complaints from that era which are nearly verbatim to current complaints voiced by opponents to Common Core today. If I didn't know better (and I might not), I'd conclude that the opposition derives from religious refusal. "The Bible doesn't teach math, so why should my kids have to know it?" The opposition is strongest in Red Religious States where the earth is 6,000 years old, after all.
One 1965 Peanuts cartoon depicts the young blond-haired Sally struggling to understand her new-math assignment: "Sets . . . one to one matching . . . equivalent sets . . . sets of one . . . sets of two . . . renaming two. . . ." After persisting for three valiant frames, she throws back her head and bursts into tears: "All I want to know is, how much is two and two?"

The issue, as it was in the 1960s, is two fold. First, teaching arithmetic to ten year and younger juveniles is fraught with danger. Adults, whether curriculum developers, mathmeticians, text book authors, or teachers, simply don't remember why learning math-y stuff was tough at that age. We're still only guessing. Sally is right. But, Sally is also wrong. The issue is how soon to move from rote memorization (2 + 2 = 4, and don't forget it) to understanding how addition works.
And yet, once again, the reforms have arrived without any good system for helping teachers learn to teach them. Responding to a recent survey by Education Week, teachers said they had typically spent fewer than four days in Common Core training, and that included training for the language-arts standards as well as the math.

"Why Johnny Can't Add: The Failure of the New Math". That is from 1974, toward the tail end of the first New Math excursion. Especially, read the comments. There aren't many, and some are awfully cynical.
But our innumeracy isn't inevitable. In the 1970s and the 1980s, cognitive scientists studied a population known as the unschooled, people with little or no formal education. Observing workers at a Baltimore dairy factory in the '80s, the psychologist Sylvia Scribner noted that even basic tasks required an extensive amount of math. For instance, many of the workers charged with loading quarts and gallons of milk into crates had no more than a sixth-grade education. But they were able to do math, in order to assemble their loads efficiently, that was "equivalent to shifting between different base systems of numbers." Throughout these mental calculations, errors were "virtually nonexistent." And yet when these workers were out sick and the dairy's better-educated office workers filled in for them, productivity declined.
(Emphasis mine.)

Remind any of you, if only distantly, of sub-prime mortgages and London Whales? It should.

I'll close with the punch line:
One of the most vivid arithmetic failings displayed by Americans occurred in the early 1980s, when the A&W restaurant chain released a new hamburger to rival the McDonald's Quarter Pounder. With a third-pound of beef, the A&W burger had more meat than the Quarter Pounder; in taste tests, customers preferred A&W's burger. And it was less expensive. A lavish A&W television and radio marketing campaign cited these benefits. Yet instead of leaping at the great value, customers snubbed it.

Only when the company held customer focus groups did it become clear why. The Third Pounder presented the American public with a test in fractions. And we failed. Misunderstanding the value of one-third, customers believed they were being overcharged. Why, they asked the researchers, should they pay the same amount for a third of a pound of meat as they did for a quarter-pound of meat at McDonald's. The "4" in "¼" larger than the "3" in "⅓" led them astray.
(Again, emphasis mine.)

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