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Re: To K-12 teachers here: Another enjoyable post from Dan Meyer > myopia
Posted:
Jul 19, 2012 7:55 AM
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Transforming? There is a step before applying the technique of "completing the square" that is required and that is to come up with the technique of completing the square in the first place. You're not suggesting that the purpose of a course in elementary algebra is to just teach a finite set of techniques to be memorized, understood and used when appropriate, are you? Although I agree that is a subset of the purpose of an algebra class, that still leaves a lot of gaps in between those (finite number of) techniques taught in an algebra class and the only way to fill those gaps is that the student also develop the skill to invent new solutions without prior art. And some techniques, even though they are labeled "techniques" are not algorithmic or formulaic at all, such as substitution of variables or induction. Most students are poor with these because they are just a very high level form and the student must fill in the form with a solution. Call it study, call it practice, call it whatever, but there is a lot of brain work left to do even after you see that a technique works.
Bob Hansen
On Jul 18, 2012, at 3:03 PM, Louis Talman wrote:
> And, in particular, I never thought of learning to complete a square as "studying the solution of quadratic equations". I thought of it, instead, as a way of transforming an expression into an equivalent expression that was more useful in a given context.
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