\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 X-MSMail-Priority: Normal X-Priority: 3 MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Precedence: bulk Status: ===================================================================== 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