Metaphors in mathematics classrooms: analyzing the dynamic process of teaching and learning of graph functions

摘要

This article presents an analysis of a phenomenon that was observed within the dynamic processes of teaching and learning to read and elaborate Cartesian graphs for functions at high-school level. Two questions were considered during this investigation: What types of metaphors does the teacher use to explain the graphic representation of functions at high-school level? Is the teacher aware of the use he/she has made of metaphors in his/her speech, and to what extent does he/she monitor them? The theoretical framework was based on embodied cognition theory. Our findings include teachers’ expressions that suggest, among other ideas: (1) orientation metaphors, such as “the abscissa axis is horizontal”; (2) fictive motion, such as “the graph of a function can be considered as the trace of a point that moves over the graph”; (3) ontological metaphors; and (4) interaction of metaphors. We also show that teachers were not aware of using metaphors.