THE DEVELOPMENT OF EXECUTIVE FUNCTION IN EARLY ...

Thus, increases in reflection on lower order rules are logically required for increases in embedding to occur.
However, it is the increases in embedding that provide the metric for measuring the degree of complexity of the
entire rule system that needs to be kept in mind (i.e., in working memory) in order to perform particular tasks.
That is, complexity is measured as the number of degrees of embedding in the rule systems that children
formulate when solving a particular problem. More complex rule systems permit the more flexible selection of
certain rules for acting when multiple conflicting rules are possible. This allows for flexible responding, as
opposed to perseveration; it allows for cognitive control, as opposed to stimulus control.
According to CCC theory, several age-related changes in executive function occur during childhood, and for
each developmental transition, a general process is recapitulated. Specifically, a rule system at a particular level
of complexity is acquired, and this rule system permits children to exercise a new degree of control over their
reasoning and their behavior. However, the use of this rule system is subject to limitations that cannot be
overcome until yet another level of complexity is achieved. In particular, the rule system cannot be selected
when there is a salient, conflicting rule system. Consequently, according to the CCC theory, abulic dissociations
dissociations between having knowledge and actually using that knowledge—occur until incompatible pieces of
knowledge are integrated into a single, more complex rule system via their subordination to a new higher order
rule. On this account, reflection and higher order rule use are the primary psychological functions accomplished
by systems involving prefrontal cortex (although different regions of prefrontal cortex are associated with
reflection on different kinds of rules; e.g., abstract vs. motivationally significant; see Zelazo & Muller, 2002b).
In terms of the DCCS, rule A might be, "If it's red, put it here," and rule B might be, "If it's blue, put it there"
(see Figure 3). To sort flexibly by color, children would need to reflect on rule A and contrast it with rule B.
According to the CCC theory, 2-year-olds typically only represent a single rule at a time (e.g., "If red ... here"),
and hence have difficulty even on the preswitch phase of the DCCS (they perseverate on one of the rules). By 3
years, children can easily consider a pair of rules simultaneously (e.g., "If red ... here" vs. "if blue ... there").
Indeed, on this account, 3- to 4-yearolds know both the first pair of rules (e.g., "If red ... here" vs. "if blue ...
there") and the second pair of rules (e.g., "If rabbit ... here" vs. "if boat ... there"), and they can use either pair of
rules if presented alone or in separate contexts, but because they typically fail to reflect on these rule pairs in
relation to one another, the two pairs of rules remain unintegrated (see Figure 4). As a result, the particular pair
of rules that underlies responding in a single context is determined by relatively local considerations, such as the
way in which the question is asked or the way in which they have approached the situation in the past. In other
words, they can exhibit knowledge of one pair of rules in one context, and knowledge of the other pair of rules
in a different context, but they fail to recognize the incompatibility between rule pairs; therefore, the particular
rule pair they end up selecting and using to sort test cards may be determined associatively rather than
deliberately. In contrast, by 4 years of age, children typically represent a higher order rule (such as E) that
allows them to integrate incompatible rules into a single rule system and appreciate that different rule pairs
apply under different setting conditions. They can then use this higher order rule deliberately to select between
two different pairs of rules ("If we're playing by color, then if red ... here, if blue ... there, but if we're playing by
shape, then if rabbit ... here, if flower ... there"), and hence, to switch flexibly in response to situational
demands.
On this account, then, 3- to 4-year-olds' difficulty with the DCCS might be described as a kind of
representational inflexibility: During the postswitch phase, 3- to 4-year-olds persistently select the preswitch
pair of rules. In terms of the problem-solving framework, performance breaks down during problem
representation; in the absence of a change in context, children actually try to sort according to the preswitch
dimension (Frye & Zelazo, 2003).