for the learning of mathematics

an international journal of mathematics education

Brent Davis - Vol. 40 Num. 0 (2020)
 Number work: teachers as experts who can think like novices


This article is framed by the conviction that mathematics teachers should be adept at recognizing the instantiations – that is, metaphors, images, exemplars, and other sources of meaning – that are consolidated in their mathematical understandings. Phrased more provocatively, teachers should be able to think like novices. This notion oriented a year-long concept study, through which teachers identified distinct metaphors, metonyms, and metaforms of “number” at play in elementary school mathematics. In the process, a range of conceptual quandaries that arose while teaching were retroactively interpreted as occasions in which novices could not reconcile instantiations that experts could no longer distinguish.