That is, schema of earlier thought are integrated into higher order thought. This process is rendered explicit in cognitive algebra. He argued that cognitive structures and action were isomorphic. Cognitive algebra disavows any such general claim. Cognitive structure and action may be isomorphic under some circumstances, but the theory does not rely on this claim.
Cognitive algebra is more akin to a theory of competence than a theory of performance.
In his formal theory, Piaget adopted standard logic to describe and evaluate the evolution of thought. He employed sentential or propositional calculus rather than a predicate or functional calculus. He worked at the level of the sentence, the truth value of the whole assertion, rather than the subject and predicate, the components of an assertion. Within these strictures, Piaget could only describe the young child as illogical, the concrete operational child as displaying islands of rationality, and the formal operational child as rational and logical. Cognitive algebra as a developmental theory rests upon a theory of cognitive operations which are more fundamental than the operations of standard logic.