Plenary
Speaker
Rafael Núñez
University of California, San Diego
Mathematics education deals with the teaching and learning of mathematical concepts. These concepts--which are human concepts--are highly imaginary (e.g. Euclidean point, complex numbers, transfinite cardinals) yet they are extremely precise and inferentially rich (e.g., theorems). Research in cognitive science--the multidisciplinary scientific study of the mind-- has in the last two decades shown that human imagination is largely realized through everyday mechanisms, such as conceptual metaphor, analogy, and metonymy. In ordinary contexts (e.g., advertising, art, politics), however, these terms are often seen as mere figures of speech, and as such, as a simple matter of words-- a purely *linguistic* phenomenon that helps illustrating what is being said. This is usually also what mathematics education take metaphor and analogy to be. In contemporary cognitive science such terms designate phenomena about thought and cognition, not just language, and they have specific technical meanings (e.g., distinction between "metaphorical expressions" and "conceptual metaphors"). Moreover conceptual metaphor, analogy, and conceptual metonymy are seen as specific cases of "conceptual mappings", which also involve conceptual blends, fictive motion, and other mechanisms. Together, and often working in complicated networks, they are hypothesized to form the vast family of cognitive mechanisms that make human abstraction and imagination possible.