Date: Nov 14, 2013 7:48 PM
Author: Joe Niederberger
Subject: Re: Simplifying Algebraic Expressions with Subtracted Expressions

Lou Talman says:
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In Ma's solution, there's no *formal* manipulation of a symbol that used consciously to represent an unknown number. It's the conscious formal, symbolic representation of an unknown, together with its subsequent
manipulation, that turns the solution into an algebraic one.

Manipulating one or more unknowns, in and of itself, isn't algebra. Representing the unknowns symbolically, and then manipulating those symbols without having to think about what they represent is algebra.
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Well, your distinction is crisp enough, and useful. However it sheds no light on the origin of Ma's expression. Is she claiming most students would write down her one liner and proceed to simplify just by thinking about the word problem? If they (generally) would do so, some summary and explanation of their thoughts would be nice, though I realize that wasn't really the point of the paper.

Joe N