## ABSTRACT

An implication of the theory that children’s acquisition of knowledge about whole-number arithmetic is guided by innate counting structures is that formal instruction is not necessary for the development of that knowledge. Indeed, it might well be thought that because an understanding of the conceptual principles underlying whole-number arithmetic is assured, the primary objective of instruction in whole-number arithmetic in children’s first years of schooling is just to familiarize children with conventional symbol systems and computational procedures. From the same perspective, instruction is crucial for acquiring knowledge about rational numbers, which do not fit well with the ideas about numbers that children are likely to derive from innate counting structures and so are bound to be difficult. An implication of the view that there is a conceptual discontinuity between counting numbers and fractions is that early instruction in whole-number arithmetic can do little to facilitate later fraction learning. Instead, instructional recommendations have focused on the need for extensive practice (Geary, 1995) and on the use of general information-processing principles to develop effective instructional approaches (e.g., English & Halford, 1995; Geary & Hamson, 2005).