We should drop arithmetic

Wednesday, January 23rd, 2019

Peter Gray makes the case for teaching less math in school:

In 1929, the superintendent of schools in Ithaca, New York, sent out a challenge to his colleagues in other cities. “What,” he asked, “can we drop from the elementary school curriculum?” He complained that over the years new subjects were continuously being added and nothing was being subtracted, with the result that the school day was packed with too many subjects and there was little time to reflect seriously on anything.

[...]

One of the recipients of this challenge was L. P. Benezet, superintendent of schools in Manchester, New Hampshire, who responded with this outrageous proposal: We should drop arithmetic! Benezet went on to argue that the time spent on arithmetic in the early grades was wasted effort, or worse. In fact, he wrote: “For some years I had noted that the effect of the early introduction of arithmetic had been to dull and almost chloroform the child’s reasoning facilities.” All that drill, he claimed, had divorced the whole realm of numbers and arithmetic, in the children’s minds, from common sense, with the result that they could do the calculations as taught to them, but didn’t understand what they were doing and couldn’t apply the calculations to real life problems. He believed that if arithmetic were not taught until later on — preferably not until seventh grade — the kids would learn it with far less effort and greater understanding.

[...]

In order to evaluate the experiment, Benezet arranged for a graduate student from Boston University to come up and test the Manchester children at various times in the sixth grade. The results were remarkable. At the beginning of their sixth grade year, the children in the experimental classes, who had not been taught any arithmetic, performed much better than those in the traditional classes on story problems that could be solved by common sense and a general understanding of numbers and measurement. Of course, at the beginning of sixth grade, those in the experimental classes performed worse on the standard school arithmetic tests, where the problems were set up in the usual school manner and could be solved simply by applying the rote-learned algorithms. But by the end of sixth grade those in the experimental classes had completely caught up on this and were still way ahead of the others on story problems.

Comments

  1. Felix says:

    Reasonably numerate readers, speak up: When was the last time you read something in the general media that wasn’t painfully innumerate? Yeah. I blame grade school math.

    Isegoria, this posting caused a watershed event in my life. As a first grader I hated how they wrote addition and subtraction. It was just wrong. Which, as the years went by, I found the same to be true of pretty much all math notation, excepting parenthesis. But, in all these decades, I never came up with something better.

    Until now.

    Let’s stick to ASCII and try this for five basic operations:

    [ 123 34 ] is 123 together with 34
    123 ][ 34 is how far 123 and 34 are apart
    123 34 is 123 scaled-by 34 or 123 duped 34 times
    123 == 34 is 123 split into 34 equal pieces
    123 >* 34 is 123 recursively replicated 34 times

    Maybe the square brackets should be pipes |. And maybe * and / work OK for scaling/times and division.

    Fun stuff.

    But, more importantly, teach for a world with calculators and computer data-processing and graphics. Teach addition from the high digits to the low, not the tedious, wrong, mistake-prone, useless way it’s been taught for centuries. Teach numbers so you see them everywhere.

    But, sigh, there have been other failures. Remember “new math”?

  2. Peter Whitaker says:

    Excessive drilling instills learned helplessness.

  3. CVLR says:

    >[ 123 34 ] is 123 together with 34

    Are you also doing away with standard words like “addition”?

    >123 ][ 34 is how far 123 and 34 are apart

    Now how are you going to parse for order of operations?

    >123 34 is 123 scaled-by 34 or 123 duped 34 times

    What is the rational for using an implicit operator for multiplication?

    >123 == 34 is 123 split into 34 equal pieces

    How do you propose to evaluate equivalence?

    >123 >* 34 is 123 recursively replicated 34 times

    You mean, like a factorial with a base?

  4. Bob Sykes says:

    Why don’t we race-norm mathematics. Blacks would be taught to count and do simple additions. Hispanics might get all the way to multiplication. Reserve arithmetic and other forms of mathematics to Whites, Asians and Jews.

    Or better yet, race-norm our schools. Have one set of schools, possibly going through third grade, but not beyond, for blacks. Another going to, say, sixth grade for Hispanics. And the complete El-Hi for Whites, Asians and Jews.

    We would save a lot of money, and blacks and Hispanics would not be harassed by having to go to school for years on end.

  5. Ezra says:

    Arithmetic has been done away a long time. Perhaps in a figurative sense much more than a literal but try to get some kid at a fast food register to make simple change without using the register or a calculator.

  6. Bomag says:

    Three of the most prominent mathematicians in history — Galois, Ramanujan, Grothendieck — had scant mathematical training in their early years.

    Thomas Hobbes had almost no exposure to math, but picked it up at a high level circa age 40.

  7. Aretae says:

    Read that. Did the experiment.

    Interested 14-year-olds require about 40 hours of instruction across one year to go from “What’s 6+7?” to starting algebra.

    Six years is a complete waste.

  8. Felix says:

    @CLVR “standard words” : Nope. Just avoided them to emphasize the meaning. Ambiguously, in the case of power, apparently. :)

    “parse the order” : Parens, my friend, parens. (Parenthetically, I often use parens in programming, even when not needed because different languages have different operator precedences. So why remember those language details?)

    “equivalence?” : Beats me. — (minus/minus, maybe?) BTW, speaking of equal signs, an ASR 33 rendered underscore as a back arrow. It was a sad day in the life of humanity when two such wonderful symbols had to fight to the death. And back-tick. watching from the sidelines, survived. Jeez. Life is not fair!

    “implicit mult” : Ooops. Comment system didn’t like open/close angle bracket together. Forgettable note to self: Never include Visual Basic code in a comment.

    “factorial” : Power. Some language’s ^ (hat character – capital 6). Or Python’s ** (star/star). Both of which are probably nicer than my oddity. My oddity emphasizes that order matters by being unsymmetrical.

  9. Felix says:

    The implication here is that you can take a bunch of (JR?) high school kids – right now – who are way, way behind in math and get ‘em up to speed pronto if only they do it right.

    Forget the IQ thing, too. Numbers and such are not rocket science.

    Anyway, this seems something cheaply verifiable.

  10. McChuck says:

    Experiments in India with a touch screen computer mounted on the side of a building show kids eagerly teaching themselves and each other, using a language none of them knew when they started.

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