Describes a teaching experiment examining the possibility of the redefinition of a multiplication problem from a problem of remembering, to a problem of figuring out why arithmetic rules make sense. (YP)

How multiplication is usually taught in school and how it could be taught are discussed. Development of understanding is illustrated through children's words and work. (MNS)

This essay clarifies what it means to know mathematics by examining ways of knowing multiplication and explores what those ways of knowing imply for the teaching and learning of mathematics in schools. It reviews the perennial argument about whether computational skill or conceptual understanding should guide the school curriculum. A mathematical…