The Function Machine as a Cognitive Root for the Function Concept.

The concept of function is considered as foundational in mathematics. Yet, it proves to be elusive and subtle for students. A generic image that can act as a cognitive root for the concept is the function box. This is not a simple pattern-spotting device, but a concept that embodies the salient features of the idea of function, including process (input-output) and object, with the various representations seen as methods of controlling input-output. (Contains 16 references.) (Author/MM)