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Error Correction: The Specialization Theory 215

for state dinners, fit the constraint format. Less obviously, at least some math-
ematical principles can also be expressed as constraints. Consider the concept
of a one-to-one mapping: If object X is mapped onto object Y, and Z is some
third object, different from Y, then X had better not be mapped onto Z as well
(or else the mapping is not one-to-one). All these examples pertain to artifi-
cial, invented task environments.
Surprisingly, the constraint concept also applies to material reality. Many
natural laws and scientific principles can be reinterpreted as constraints.
Consider the laws of conservation of mass and energy. The function of these
laws is to constrain theoretical calculations and laboratory work. The fact that
neither mass nor energy can be either created or destroyed constrains the pos-
sible reactions between chemical compounds: Chemist Walter J. Gensler wrote,
“There is so much trust in the mass conservation law that an experimental result
… that does not conform is automatically treated as false and rejected.” 20
It is not surprising that this is true centuries after the discovery of the
law, and after the collection of large amounts of data in support of the law, but
surely this natural law was regarded as a description rather than a prescrip-
tion for the chemists who first discovered it? Some historians of chemistry
disagree: “These [data] did not provide an independent confirmation of …
the principle of the conservation of mass. Rather Lavoisier relied on what
was for him the axiomatic truth of the principle to adjust one result through
21
another …” So even for Lavoisier, who was the first to formulate the mass
conservation law and use it in his laboratory practice, conservation of mass
22
functioned as a constraint on the interpretation of his experimental results.
The law is as much a constraint on the analysis of chemical data as it is a
description of the material world.
Although the interpretation of declarative knowledge as prescriptive
rather than descriptive reaches further than one might expect, there is no need
to assume that all declarative knowledge is of one kind or that all pieces of
declarative knowledge have the same form and function. For the constraint
concept to play a role in a theory of learning, it is enough if a significant subset
of the learner’s declarative knowledge consists of constraints.

ERROR CORRECTION
Error detection is not yet learning. A detected error is a learning opportunity,
but learning has not occurred until the error has been corrected. What this
means is not self-evident because an erroneous action, once carried out, is his-
tory and so cannot be changed. The effect of an incorrect action on the person’s