ABSTRACT
Outside of school, children have fun with numbers. Preschool children count the stairs as they go up and down and recite numbers in nursery rhymes. School children play games using the numbers represented on cards and dice. Likewise, much of arithmetic instruction in school consists of learning such procedural routines as how to execute the long division algorithm or how to add or multiply fractions. There is widespread concern among educators today that schools are succeeding in teaching routines but not concepts. One indication is in the kinds of errors children make. An important question concerns the relationship between the learning of procedural routines and conceptual understanding. The “new math” movement of the 1960s sought to replace the traditional emphasis on computation with an emphasis on concepts such as sets. An influential idea in curriculum planning is that certain mathematical concepts are simply beyond children’s conceptual grasp until a certain point in development.
