A Geometric Path to the Concept of Function: Transformations using dynamic software can provide a unique perspective on a common topic.

The concept of function spans elementary school through high school. When introducing the topic to elementary school and middle school students, we ask them to work with a variety of examples and representations of functions, since a formal definition of a function is rather abstract. These representations involve experiences in which students—

  • use function machines to generate output from input,
  • record input and output values in a table,
  • substitute an input value in a formula to generate an output value, and
  • graph input and output values using rectangular coordinates.

Our objective is to prepare students to deal with functions in an increasingly formal way by the time they begin studying algebra in late middle school or in high school. The most commonly used representations of functions are numeric in nature. Unfortunately, this emphasis on numeric experiences fails to acquaint students with the variety of mathematical relationships that can be represented as functions. As a result, it may contribute to common student misconceptions.