\doc\web\99\03\fruit.txt
Reply-To: "Ken Gough"
From: "Ken Gough"
To: "ClearingHouse"
Subject: [education-consumers] Do your own thing, or, how to solve a problem the hard way
Date: Thu, 11 Feb 1999 07:47:00 -0500
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Some time ago, Arthur Hu (I think) gave a problem from the Washington State
4th grade math test. It was:
There are 14 pieces of fruit in a bowl. There are twice as many apples as
oranges, and half as many pears as oranges. How many of each type of fruit
are in the bowl?
As anyone who took high school algebra knows, this is a simple
problem. It takes maybe 30 seconds to set up and solve the equation, a
minute if you're a bit rusty. As I remember it, Arthur's point was that
it's ridiculous to expect a 4th grader, who hasn't had any exposure to
algebra (and isn't ready for it), to solve such a problem. Yes, it can be
done by various trial and error schemes, but who in his right mind would
advocate guessing as an efficient or effective problem-solving method when
clearly superior methods are available? Therefore, the problem is nothing
more than a "setup" that the vast majority of kids are expected to miss, to
prove whatever political point the testmaker is advocating.
Well, I'm not sure Arthur is totally right in his assessment - I'm inclined
to think that simple test-writing incompetence plays as large a part as
political gamesmanship - but he surely isn't completely wrong, either.
There is no better way to increase your influence, power and funding than
to "prove" there is a "crisis" that you are uniquely situated to solve.
It's a loser in the long term, but the short term can be loads of fun - and
lucrative. But conspiracy theories rarely hold up, and that's why I keep
coming back to simple incompetence, an attribute not to be discounted among
true believers of any and all ideologies (for example, Nazism, fascism,
communism, mercantilism, name-your-ism).
But I digress. Just out of curiosity, I posed the above-mentioned problem
to my 5th-grade son, a lad of whom I am inordinately proud (as any father
should be), and who has proven through more objective means than a father's
biased assessment that he's a bright kid and serious about his studies.
And, lo and behold, he solved it! It took him about 5 minutes of
concentrated thought, but he did it. I complimented him on getting the
right answer, and then asked him a very loaded question: How did you do it?
The answer was a look of pure befuddlement, and then he said (and I quote)
"I estimated." In other words, he didn't have a clue. He didn't solve the
problem in a structured "mathematical" fashion, he had simply guessed at
answers until he found the right one. A constructivist would be proud of
him. After all, he did get the right answer, and much more importantly, he
did it his own way. Give my son an "A" for cleverness. Give the
constructivists an "A" for dumbness.
Anyone of average abilities who had studied algebra for a few months can
solve this problem in seconds with little more effort than a second grader
needs to say "2 plus 2 equals 4". Yet it took my son, who tests borderline
gifted, 5 minutes of concentrated effort to find the answer. This is
better? In what universe? Furthermore, he knows no more than he did
before. Algebra, the right way to solve this problem, is still a mystery
to him. The next time he sees such a problem, it will take him another 5
minutes to play his guessing games. It takes no genius
to understand that instruction in mathematics, and I don't mean
facilitation, I mean stand-up-in-front-of -the-class, put-it-on-the-board,
do-it-this-way-because-it-works-best, practice-until-you've-got-it-right
instruction, is what my son needs. Likewise all our sons and daughters.
Life is too short to let our children waste time groping their way through
school when we know how to impart the knowledge they need in clear,
straightforward fashion. It's not a mystery, it's just common sense.
Am I preaching to the choir? Probably so. But my little experiment has
reinforced my conviction that we advocates of "non-progressive" educational
methods are on the right track and need to press forward. No doubt about
it.
Oh, and then my son really made me proud. I quickly showed him how the
problem was solved using algebra. Not surprisingly, he didn't understand
it. But he looked at me with a smile and said, "I guess that's why I need
to stay in school, huh?" Can't teach that kind of comon sense.
Ken Gough
Elizabethton, Tennessee
ampcokdg@planetc.com