The Curriculum and Evaluation of Standards for School Mathematics (NCTM 1989) targeted the concept of function as one that should receive increased attention. A function can be defined as a rule that assigns to every input value exactly one output value. To make it easier for novices to recognize a function, we should select the rule, the input, and the output to be straightforward.

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In this month's column, we hear from two teachers and a student who discover different approaches to ordinary problems.

Consider a typical mathematics-classroom scenario: The teacher asks if anyone can state the Pythagorean theorem. Several students respond, “a2 + b2 = c2.” In another class, the teacher asks how to find the vertex of a parabola and a student quickly responds “−b/2a.” In yet another class, the question is how to find the slope of a line to which the students shout “m.”

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