The analogies in the writing of secondary mathematics teachers about the concept of function: an application of the structure-mapping theory

This study examines the analogies made by 42 secondary mathematics teachers when they write about the concept of function: how students would (anticipating) and should (desired) define and exemplify the function; and what questions the teachers would ask to assess students' understanding of the function (assessing). The argument of the study is that the descriptions present in the writing of this sort provide information about how the teachers view and construct functions.Using examples from an extensive set of responses from the teachers, the article presents the major analogies found in the writing of the teachers and examines ways in which these are structurally mapped in the concept of the function by applying the structure-mapping theory (Gentner, 1983). Among the analogies discussed are a 'child-mother' (the biological link between a child and mother - every child has exactly one mother) and 'machine/factory' analogies. Of interest is the similarity between the analogies formed by the teachers. At the close, the article makes the case for using the tool 'analogy' in research on teachers' knowledge for teaching.