The Extended Mind: The Power of Thinking Outside the Brain

by Annie Murphy Paul

“Being it”—embodying a conceptual object—is a very different experience from “watching it,” or viewing a conceptual object as “remote and separate from oneself,” notes Carmen Petrick Smith of the University of Vermont, who has studied the effects of physically embodying mathematical concepts. Groups of students might form a triangle with their outstretched arms, for example, and then experiment with moving closer to and farther away from one another; in this way they come to understand that the size of a triangle can vary without changing the degree of the angles at its corners. Smith notes that such “body-based activities” have been shown to deepen students’ understanding and strengthen their memory of mathematical concepts. Mathematics teachers have long incorporated manipulatives into their instruction—counting rods and cubes, for example. The research of Smith and others suggests that students learn even more when the “manipulatives” they employ are their own bodies.

Mathematics