Number Work: Recovering the Original Complexity of Learning Arithmetic

Abstract

Illustrating the discussion with moments drawn from mathematics lessons in which teachers found themselves stymied by ``simple'' concepts, I analyze the metaphors of number that are encountered by learners in grade-school mathematics. I begin with a list of four, based on Lakoff and Nùñez's ``grounding metaphors of arithmetic,'' which they argue are sufficient to derive highly abstract mathematics. I then point to three more that are not necessary to formal mathematics, but that may be necessary to learning mathematics. These metaphors are phenomenologically distinct and educationally ubiquitous. Implications for curriculum design, resource development, and teaching are considered.