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Error Correction: The Specialization Theory 229

The Anatomy of a Single Learning Event

Evaluation of a complex scientific theory is necessarily a multifaceted affair
that covers a variety of dimensions. In particular, a learning mechanism must
prove its worth by passing two basic tests: It must be sufficient to aquire eco-
logically valid cognitive skills. Also, it must be robust in the sense that it works
in multiple task domains. A theory that fails either of those tests cannot be
the right theory, regardless of how it fares along other dimensions. Another
important test is that the theory is fruitful, both in the sense that it answers the
relevant theoretical questions and that it supports practical applications.
The constraint-based specialization theory describes the internal mechan-
ics of a single error-correcting event. But a rule is likely to suffer from multiple
faults and hence to need repeated revisions and a task strategy of even mod-
est complexity consists of multiple rules. A theory of what happens in a single
learning event is interesting only if it can be shown that the cumulative effects
of multiple such events suffice to construct the kinds of cognitive skills that
people learn. But it is almost impossible to predict with mere brainpower the
cumulative effects of a sequence of rule specialization events. A powerful tech-
nique for deriving those effects and to demonstrate sufficiency and generality
is to implement the theory as a computer simulation model and apply it to
multiple task domains.
Ernest Rees and I programmed a model that we called Heuristic Self-
Improvement or HS for short. The HS model consists of two parts. Its perfor-
mance mechanism is a cognitive architecture that implements the theory of
stable behavior put forth in Chapter 6. When faced with an unfamiliar task,
the performance mechanism proceeds through forward search. The learning
component consists of a constraint base and the rule specialization mecha-
nism described earlier in this chapter. To run a simulation, the user gives the
model a search space, defined in terms of an initial problem state, a goal and a
set of primitive actions. In addition, the user supplies a set of initial rules with
minimal conditions, and a set of constraints that encode correctness for the
task. The model learns by doing. It acts vis-à-vis the target task, makes errors,
detects them and corrects them by specializing the offending rule.
The following sections describe three applications of the HS model to
three different task domains, exemplifying learning from error in elemen-
tary science and mathematics. For all three task domains (chemistry, count-
ing, subtraction) the model had to work through multiple practice problems,
making many minor corrections to the rules in response to multiple errors.
The final learning outcomes – the correct procedures for these tasks – are