for the learning of mathematics

an international journal of mathematics education

Susan Gerofsky - Vol. 43 Num. 0 (2023)
 “The having of multiple metaphors”: opening imaginative spaces for mathematical noticing


This paper explores the idea that educators’ encouragement of students ‘having of multiple metaphors’ for mathematical objects (here, the graphs of functions) may be important to learners in several ways: in finding apt imagery for new mathematical ideas, helping notice and recall mathematically salient features of the graphs, and feeling welcomed to explore new mathematical ideas with imagination, creativity and joy. Examples of secondary students’ verbal and gestural metaphors are drawn from video recordings from the Graphs and Gestures research project. The paper frames its story from Pimm and other mathematics education researchers’ work on metaphor in mathematics, and the title intentionally recalls Duckworth’s ‘The having of wonderful ideas’.