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Error Correction: The Specialization Theory 241

These details of how learning progressed in this particular simulation
run are not interesting in themselves, but they illustrate the complexity of
the interaction between the knowledge embedded in the constraints, the
initial rule set, the particular errors encountered during practice and the
resulting sequence of learning events. All constraints apply at each moment
during practice, and a learning event is massively contingent on the state of
the current practice problem, the current version of the relevant rules and
exactly which constraints the learner knows. The learning of the HS model
is lifelike.
The counting application provides a natural test of the HS transfer mech-
anism because Gelman and co-workers not only investigated how young chil-
dren acquire the competence to perform the standard counting task (count
how many teddy bears there are), but also the kinds of modified counting tasks
they are able to perform. In a series of studies, they confronted children with
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several such tasks. In one of these, ordered counting, the child is asked to count
a set of objects in a particular order. For example, the child might be asked to
count from left to right, or to count yellow objects before blue ones. Ordered
counting thus imposes a constraint that is not a normal part of counting. In
a second modified counting task, the child is asked to count a set of objects
in such a way that a designated object is assigned a designated number (count
these but make sure that the yellow bear is number five). Gelman called this task
constrained counting, but as the term “constraint” is used in this book, both
modified tasks are constrained, but in different ways. I will call this second
modified task targeted counting, because the counting process has to land on
a particular target, the designated object, at a particular point in the counting
sequence. The results of the studies by Gelman and co-workers show, contrary
to the results of many other transfer studies, that young children are capable of
adapting their knowledge of the standard counting procedure to both of these
modified counting tasks.
What about HS? Rees and I put the model through the complete set of
transfers for the three counting procedures (standard, ordered and targeted).
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That is, it first learned one of the three counting methods from scratch and
then transferred the acquired strategy to each of the other two counting tasks;
then it learned another of the three from scratch, and transferred to the other
two; and so on. There were thus six different simulation runs in all. The two
modified counting tasks were defined by giving the model the obvious con-
straints to define ordering and targeting (if X is counted after Y, it should be
after Y in the ordering; if X is assigned the designated number, it should be