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Topic: Another Precalculus Doorstop, Another Migrane
Replies: 29   Last Post: Sep 8, 2010 8:38 PM

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 Haim Posts: 7,807 Registered: 12/6/04
Re: Another Precalculus Doorstop, Another Migrane
Posted: Sep 1, 2010 11:02 AM

Clyde Greeno Posted: Sep 1, 2010 3:24 AM

>Every professional exposition in mathematics tacitly
>knowledge--- which is prerequisite for comprehending
>that exposition.

Clyde,

You have discovered Haim's Law of Conservation of Mathematics:

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http://mathforum.org/kb/message.jspa?messageID=6126238&tstart=0

You may recall that the old fashioned (pre-relativity) Conservation of Mass law states that in a closed system you can re-arrange mass all you like but you cannot create or destroy it. I.e., the mass of a closed system is constant.

Now, think of the math curriculum from arithmetic to the calculus as a closed system. For the last 30 yrs, math has been falling out of the pre-calculus (mainly K-12) part of this closed system. Well, I claim that if you are not going to play a charade when teaching the calculus, that is if you are not pretending to teach while your students pretend to learn, then all the math that fell out of the pre-calculus part must find its way back into the curriculum somewhere and, usually, that somewhere is going to be the calculus text.

Of course, these days so much math has fallen out of the K-12 curriculum that even the monstrous modern calculus texts cannot contain all of it. That is why so many college students have to take remedial math courses.

The result is the same. If you are going to teach math effectively, then you may be forced to re-arrange the math, but you cannot have lost any, otherwise you cannot teach math effectively.
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In other words---and I have tried making this point to Dom, in the past---Dom is not wrong to criticize these modern "doorstops" but, like a fever, they are not the problem, they are merely a symptom of the problem.

Haim