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Re: When math makes sense  w/ cooking, consruction
Posted:
May 29, 2013 1:15 PM


> > On May 28, 2013, at 4:43 PM, "Louis Talman" > <talmanl@gmail.com> wrote: > > > I don't know what is. And Robert acquiesces, > suggesting that "a student of algebra" would never > avoid algebraleaving us to guess that he agrees > that Wayne's strategy is Real Algebra. > > When I use the phase "student of algebra" I mean a > bonafide student of algebra. A student that is > getting it. There has to be a way in these > discussions to distinguish between students getting > it and students not. How can you even discuss > pedagogy if the student is just some random variable? > A student of algebra is having the epiphanies we had, > the least of which and the most fundamental is the > personal recognition of algebraic reasoning and that > these problems can be "solved". And I said that once > you cross this point you no longer guess (I didn't > say avoid). That blissful ignorance is gone forever. > From this point forward, as far as you (the student) > are concerned, problems are either solvable or not, > and when they are not solvable, to you that means you > just don't know "how". Only later, as an advanced > student of algebra, will you realize that some of > these problems are actually NOT solvable. > > I actually didn't understand Wayne's response, at > least in the context of "teaching algebra", that the > students should plug in the values into the formulas > and compare results. That isn't algebra. However, if > I am given a problem with discrete values, that is > generally what I do first. Run the numbers. > > I ran numbers prior to knowing algebra and after > knowing algebra. I can say without a doubt that > running numbers never taught me algebra. I ran a lot > of numbers prior to knowing algebra. I was/am a huge > fan of "number" and when I first saw adding machines > and then calculators I tested the machines, not the > other way around. But it was all arithmetic. The > closest it ever came to "algebra" was with situations > involving simultaneous linear relationships, but the > thinking was still not algebraic. Pre algebraic at > best. And this goes for tables and graphs as well. > Without algebra and the reasoned certainty it brings, > you might as well be (and you will be) guessing. > > Wayne does bring up an interesting point though. If > students "know" the formula for the volume of a > cylinder and are given two explicit examples of > cylinders, then why wouldn't they immediately be able > to answer which has the greatest volume? These > students misunderstand more than just the formula for > volume. I can't even say that their misunderstanding > stops at math. > > The only door to algebra is algebra. That is all I am > saying. At least we all agree that what Richard > continues to post here is not algebra. I have long > moved past the question of "What the heck is it that > Dan is teaching?" to "Why did Dan stop teaching > algebra?" My conclusion, and this goes also to why > Richard stopped teaching algebra, is that they are no > longer teaching students of algebra. Without students > of algebra how can you possibly be a teacher of > algebra? Either you teach something that none of your > students get OR as Dan and Richard have chosen to do, > you teach something else. My only concerns are... > > 1. Don't call it algebra (that is a lie to both the > students and their parents). > 2. Are all of your students properly placed in this > nonalgebra class (could any of them have gotten > algebra if given the chance)? > > Bob Hansen
Bob, I'm teaching geometry.
Richard



