Abstract
A theory of partial knowledge is proposed as an explanation of cognitive development, and methods are described for testing the theory. The theory consists of three structure-process pairs, each of which postulates a type of cognitive structure and a developmental process specific to that type. In restricted knowledge, a unitary algorithm is the cognitive structure, and amendment is the developmental process. In variable sampling, a structure of unitary substitutes is paired with a process of selection. In variable integration, modular components are paired with self-monitoring. Methods for testing the theory form a sequence of mathematical models. The first model in the sequence, called a model of double assessment, is described both verbally and mathematically. Other models in the sequence are described verbally with reference to other articles for the formal mathematics. Also described are some nonmathematical methods to be used as sequels to the double assessment model.
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