Center for Applied Research and Educational Improvement
Scholarly Text or Essay
The Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989) recommend that high
school students should be able to do the following: "represent and analyze relationships using tables,
verbal rules, equations, and graphs; translate among tabular, symbolic, and graphical representations of
functions; recognize that a variety of problem situations can be modeled by the same type of function;
and analyze the effects of parameter changes on the graphs of functions" (p. 154). The teaching of
functions by emphasizing the tabular, symbolic and graphical representations and the connections
between them became known as "The Rule of Three." Functions can also be represented by real-world
situations themselves so "The Rule of Three" later was called by some as "The Rule of Four". These
representations should not be learned in isolation and that true learning of the concept of function occurs
when a person can easily make connections between the various representations and see how changes in
one representation effects the other three.
Technology in the Mathematics Classroom: Helping Students Make Connections.
Center for Applied Research and Educational Improvement.
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