What Should We Teach?

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In arithmetic we use and manipulate numbers to create concrete answers to specific numeric questions. Algebra is the theory of arithmetic.  The two main tools used to create this theory are abstraction and generalization.  First, we try to describe abstractly, without reference to specific numbers, the manipulations and processes that are used in arithmetic.  The

Sad State of Mathematics Education Part VI

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The section, in one of the best algebra books, for Linear Equations in One Variable consists of ten pages.  Important definitions (concepts) are presented on about a page, there are 9 examples of solving equations, and 111 exercises.  The examples and exercises are all numerical and are really the same except for different numbers. The