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2005-07-05 9:05 AM Why Do We Teach Algebra Anyway? Previous Entry :: Next Entry Read/Post Comments (4) Kevin Drum is talking about algebra.
He's framing the current struggle over gradeschool curricula this way:
And a lot of the debate is swirling around a book by Addison-Wesley informally dubbed "Rainforest Algebra" because it has a great deal of multicultural readings and sociological and environmental tie-ins along with the algebra problems. It was up for approval in Arizona and apparently is up for review in Texas now. Now I taught high school algebra for 2 years in Texas. I don't remember the names or publishers of the textbooks we used, but they were pretty standard fare. Early chapters dealt with the concepts of variables and coefficients. Then they learned how to perform arithmetic functions they already knew (addition, multiplication) to terms with variables. This scaled up in a logical way to more complicated problems involving similar concepts. Each chapter generally had a 1-3 page explanation of the concepts with sample problems stepped through. Then there would generally be 30-40 homework problems, with 5-7 word problems at the end. Answers to the odd-numbered problems were in the back of the book. The idea was for the student to learn the basic concepts and practice them before applying them in a more complicated situational problem. This seems pretty sound to me. I haven't seen the book they're talking about, and I have no problem with an interdisciplinary approach to any subject, but there does need to be an initial approach of learning the basic concepts before they can be applied to a situational problem. There's just no way around it.
Drum presents the following problem:
Which he says can be rephrased as:
Okay, but how is a high school freshman supposed to know how to rephrase the problem? Drum's rephrasing doesn't use the concept of a variable. But that's kind of the key to understanding and reframing the problem, isn't it? If a student understands that a variable can represent an unknown, they're one step closer to reframing this problem in a meaningful way. What is the unknown in the problem above? The price of an item, right? So let that be x. Then the total amount Peter paid would be 70x and the total amount Sue paid would be 90x. Then the problem would be framed as: 70x + 90x = 800 Which would then be easy to solve for x, and then since Sue bought 90 x's, all that's left is to multiply the price times the number she bought. If you don't teach the students how to use the abstraction of a variable to represent an unknown quantity or rate, then how the hell are they supposed to get from the original problem to Drum's rephrasing? How do they know how to even start? And in the early part of the course they need to simply work problems like: 10x + 5x = 60 so they know what to do once they've framed the problem in the right way. There simply is no shortcut around learning some of the basic concepts and skills. There are different ways of presenting them, and I don't know if the text in question does a good job or not, but there's no way around teaching the basics of any discipline. Drum then quotes Richard Neill, a member of the Texas State Board of Education:
To which Drum says:
Ah, very cute. Drum conveniently avoids Neill's reference to critical thinking. Could we all at least agree that one of the reasons we teach algebra in the first place is for critical thinking skills? Most of us don't use the quadratic formula on a daily basis, but the point of teaching higher levels of math is not for direct practical application, but for critical thinking and general problem solving skills. Drum almost seems to be saying that the focus should be on the end result, that however the kids reach the answer doesn't really matter...maybe I'm putting words in his mouth, but that's what he seems to be saying. But in the example he gave, the process of reframing a word problem is predicated on understanding fundamental concepts. And he just doesn't seem to acknowledge that. Read/Post Comments (4) Previous Entry :: Next Entry Back to Top |
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