PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
How Limit can be Embodied and Arithmetized: A Critique of Lakoff and Núñez
Page: 1051
In Where Mathematics Comes From, Lakoff and Núñez (2001) describe how the notions of infinity, continuity, and limit can be constructed through metaphorical extensions of embodied experiences. This paper will critique their historical and psychological analysis, revealing an unresolved tension between a simplified, geometric “approaching” conception and the arithmetization of calculus by Weierstrass. A proposal of how to rectify this conflict through acknowledging how novices can metaphorically tie these concepts together is discussed.