Investigating Secondary Mathematics Teachers' Analogies to Function

This study investigates the analogies used by a sample of secondary mathematics teachers when they described the concept of function. The study is concerned with understanding what analogies were used by the participant teachers and conceptions of functions positioned in those analogies. Using examples from a set of responses to five open-ended questionnaire items, the article presents the main analogies found in the descriptions of the participant teachers and examines ways in which these are structurally mapped to function by applying Gentner's "structure-mapping" theory of analogy. Among those discussed are the "child-mother linkage" and "machine/factory" analogies. Of interest is the predominance of illustrations that show a correspondence approach to functions (mappings and input-output machines), while a covariation approach is entirely absent. The article makes the case for using the concept of analogy as a tool in research on teachers' Mathematical Knowledge for Teaching (MKT).