Date: Aug 26, 2013 11:11 AM
Author: Joe Niederberger
Subject: Re: Log Sense

R Hansen says (long quote):
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With regards to your suggestion for teaching more advanced topics earlier, sure. That would work fine for the math-smart kids and it should be done anyways. Compared to what we had I think many smart kids today are being defrauded. But in the context of the vast majority that don't get it, that wouldn't work at all. I have watched them try to teach algebra a dozen different ways. With pictures. With computers. With writing. With modeling. With social studies. With peer instruction. With discovery. Etc. Etc. Etc. And they fail. My conclusion...

Algebra is too hard for these students because these students are not thinking. My solution. Make sure that they can think first, before you teach them algebra. Stop taking for granted what we know is not true! And that doesn't mean teach them formal logic. They will suck at that just as well. Math-smart kids can take these courses and thrive because they think. The others wilt and die because they don't. Courses like algebra work great for kids already thinking. That is historically what that track was about. Putting everyone in algebra might have been a noble thought a long time ago, but at this point with what we now know, it is nothing but irresponsibility and negligence.
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Well, that I would say is a fairly concise summary of your theory of math education.

You seem, to me, to be saying their are kids who *can* and *do* think and they are good in math, and the others don't or can't. (Do you suppose their are some who can but don't think?)

I think their are lots of kids who could, but don't, and at least part of that is because of milieu they find themselves in. As far as talent goes, I believe in that too, but for things like the basic ideas of exp and log, nearly everyone has the potential to understand the basic concepts, and a least partially grasp the math.

Joe N