How do the developmental epistemologist does indeed observe the mental operations?

A summary answer is that the developmental epistemologist uses models of functions, schemes, and systems such as groups, groupings, lattice, to follow the operatory aspect of thought, its reasoning among figural states. In the example of classification, the researcher attempts to uncover the relationships the subject uses among the various nouns and within a noun. These transformations the child performs in her thought allow the researcher to see to what extent the transformations employed are coordinated and to what extent they form a rational and therefore stable system of operations.

Thus, we cannot know whether a noun represents a concept until we determine what operations or pre-operations constitute its meaning and to what extent those operations are grouped into a system. The fact that the child names an object as a cow tells us only about a single state of thought of the child, its figural aspect; it is the transformational aspect of thought that is fundamental and that defines the different states leading up to the noun as finally representational of a concept composed of logical operations.

We can look at the transformations operating in the child’s notion of cows by asking her questions about the relationships between cows and animals. Are cows animals? Are pigs animals? What makes an animal a cow and not a pig? Are all cows animals? Are all animals cows? When observing a single transformation such as when the child includes pigs in the class of cows, we cannot tell if this single action is an operation unless we know what other operations are coordinated with the inclusion operation. We have to ask multiple questions that reveal the whole comprised of transformations she is making in order to determine which operations are actually working together in her system of thinking.

The differences between behaviorism and developmental epistemology thus appear to at least partially consist in differences in the scientific assimilatory tools each uses—whether it is the individual behaviors taken as units and hence, quantifiable, or whether it is the wholes taken as the proper ‘units’. But clearly there are also profound differences among researchers in the degree of penetration of their observables into the subject’s activity—whether the observables are restricted to outward behaviors and performances or whether they penetrate into the inner mechanisms of production of behavior—the systems of mental operations. 

The conclusion is that to observe a mental operation as a special form of mental activity is necessarily to see how it is coordinated with other transformations so as to be a part of a system of coordinated operations. Hence, the definition of operations is dependent on the concept of system (and note these definition themselves are examples of classification system at work):

“DF. We shall call operations [the] interiorized actions or interiorizable actions, reversible and coordinated in total structures…” (vol. 2 of the Introduction to Genetic Epistemology, p 45).

“…psychologically te operation is an interiorized action and becomes reversible by coordination with other interiorized actions in the same structure of a group containing certain laws of the whole” (vol. 1, p. 35).

“The criterion for the existence of operations will be heir grouping…” (The Child’s Conception of Movement and Speed, p. 29).