Conceptual constraints must change with age if they are to account for
children's acquisition of kinds of knowledge that do not fall within
the initial constraints. A bi-directional relation between competence
and performance is therefore hypothesized, such that cognitive compete
nces not only guide performance but also are shaped by it. This hypoth
esis offers a solution to the difficulties that current competence mod
els have in accounting for developmental change. Goals are proposed as
a potential source of changing constraints because they change with a
ge, they shape what children do, and they also influence what children
learn from what they do. These ideas are illustrated with examples dr
awn primarily from research on children's quantitative concepts.