The theory of cognitive structure and the theory of cognitive operations. Both theories seem essential to capture Piaget's major results and answer the formal and empirical criticisms directed at this theory. Cognitive algebra is in accord with Piaget, Werner, and Baldwin that cognitive development entails qualitative change in cognitive structures and successive structures tend toward greater integration and hierarchical subordination. Cognitive algebra asserts that cognitive structures obtain higher order integration through the realization of progressive group organization. Antecedent groups are subordinated to successive groups.
Subordination includes both operations and content.
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.