THE DEVELOPMENT OF EXECUTIVE FUNCTION IN EARLY ...

cards by the first dimension. Moreover, they do this despite being told the new rules on every trial, despite
having sorted cards by the new dimension on other occasions, and despite correctly answering questions about
the postswitch rules (e.g., "Where do the flowers go in the shape game?"). In other words, 3- to 4-year-olds
typically exhibit inflexibility on this task. In contrast, by 5 years of age, children typically perform well.
Children's performance on the DCCS is correlated with their performance on a variety of measures of executive
function—even after controlling for age and verbal ability (Carlson & Moses, 2001; Lang & Perner, 2002), and
age-related changes in performance on the DCCS indicate that executive function develops rapidly during the
preschool years. However, the cognitive processes underlying executive function in children (and by
implication, what develops) remain unclear. This Monograph describes a series of studies in which different
features of the DCCS are manipulated experimentally in order to elucidate these processes. By determining the
circumstances in which children are susceptible to inflexibility on the DCCS, it should be possible to describe
the development of executive function more precisely and reveal the way in which basic cognitive processes are
orchestrated in order to fulfill the higher order function of problem solving. Four studies (including 9
experiments) are described. These studies are interpreted in the context of four leading approaches to the study
of executive function and its development, including complexity theories, memory accounts, accounts
emphasizing inhibitory control, and accounts emphasizing the redescription of representations. These theories
will now be reviewed in turn and described with reference to the assessment of executive function in young
children.
COMPLEXITY THEORIES
Several theories of executive function and its development emphasize the importance of complexity. The
importance of complexity has long been recognized in the developmental literature (e.g., Inhelder & Piaget,
1964; Vygotsky, 1962) , and it is also starting to be appreciated in the neuroscience literature (Dias, Robbins,
& Roberts, 1996; Stuss et al., 1999; Wise, Murray, & Gerfen, 1996). One influential complexity theory,
proposed by Halford and colleagues (1998), suggests that as children develop they are able to understand
increasingly complex relations among objects. Halford et al. defined complexity in terms of the number of
relations that can be processed in parallel. According to these authors, each argument of a relation, such as "X"
in the relation "X is greater than Y," represents a source of variation, or a dimension. Processing a single
relation (i.e., a "unary" relation) is less complex than processing a binary relation, which is less complex than
processing a ternary relation, and so forth. Although increases in relational complexity are related to experience
rather than age on this account, Halford and colleagues have found that unary relations are processed at a
median age of 1 year, binary relations at 2 years, ternary relations at 5 years, and quaternary relations at 11
years.