Piaget�s studies of how knowledge develops in human beings led him to certain constructivist conclusions regarding knowledge as being a �set of structures constructed progressively through continual interaction between the subject and its environment�. His work in Simon�s laboratory on age-standardised IQ tests is perhaps reflected in developmental terms by the idea of four universal and sequential stages: sensorimotor; pre-operational; concrete operational; and formal operational. It is on the concrete operational phase, the early school years, that this essay will focus upon.
In the Piagetian school, logical development depends on the acquisition of reversible thought processes, such as cancelling perceptual transformations in our mind, and in the wider sense of his term, manipulating perceptions and perspectives in our imagination. Piaget used this concept to unite the ostensibly heterogenous abilities tested in experiments on invariance, class inclusion, seriation, transitivity and the three-mountain problem, claiming that children remain egocentric and illogical as long as they are unable to manipulate their immediate perceptual input.
His testing of transitive inferences, inspired by Burt�s earlier work, seems somewhat removed from this idea of reversibility, providing the infant with premises like A>B and B>C, demonstrating that children under 10 could not make the inferential jump to conclude that A must therefore be greater than C. Piaget�s keenness to explain this among other results as another symptom of what he termed �irreversibility� is suspect. His analysis of the problem as being the need to simultaneously conceive that B is smaller than A and larger than C certainly requires holding two concepts in working memory at once and performing a deductive operation on them. However, he appears to be drawing a correspondence between manipulation in conception as opposed to perceptual imagination, with little rational or empirical justification.
He tested children�s ability to recognise relevant and irrelevant changes to quantity with his conservation tasks, such as moving a row of beads further apart, pouring liquid into differently-shaped receptacles and re-shaping a solid lump of matter. Younger children, the non-conservers, displayed their lack of understanding of the principle of invariance as they demonstrated a preference for a row of sweets which had been moved further apart over another row containing an equal number, for instance, while older children maintain that the two rows are still equal. Gratifyingly explicable further experiments have even demonstrated that children born to sea-faring and boating cultures understand the principle of invariance in liquid volumes earlier, just as children in poor countries can distinguish the relevant adding and subtracting from merely perceptual transformations at� young age. However, Piaget�s conservation experiment suffers from a flaw of execution since children may sometimes change their answer in response to the repeated question or the intonation of� the experimenter (the social context). A more profound criticism concerns the baseless assumption that being able to imagine the reverse of a perceptual transformation does not tell you that it is irrelevant, since a child could �reverse� an addition or subtraction with the same faculty. McGarrigle & Donaldson�s teddy bear experiment further diminished the impact of the results, as they used a marauding teddy bear as the agent of �accidental� conditions to compare against �intentional� transformations wrought by the experimenter. The results demonstrated that children were fooled less frequently by perceptual transformations when �accidental�, although even 6-year olds were still making mistakes 20% of the time, although even this experiment may have suffered from misdirected attention and false positives through not noticing the transformation at all.
Piaget used a multitude of other experimental tests, all of which he explained in terms of reversibility. The three-mountain problem involves matching a 2-dimensional elevation to another perspective of a 3-dimensional landscape. However, reversibility implies reversing from another perspective to the child�s own, rather than what they are actually required to do, which is to use their understanding of person permanence to see that other people have separate perspectives, and manipulate their own three-dimensional visual representation to match another�s correspondingly. The class inclusion test involving a string of red and yellow beads could be attacked as being misleading, even to adults, and his seriation experiment could only really be said to demonstrate a misunderstanding of seriation.
Associating these disparate measures of the level of a child�s understanding of the mechanics of its environment with the child�s ability to make logical inferences seems baseless. Just as object permanence, perception of depths or shapes or VOT in speech sounds all require a new schema to be devised and assimilated to accommodate apparent phenomena, tests such as conservation and the three-mountain problem assume that a successful response can be logically inferred by a child or adult, without any constructed understanding of how the world works. Moreover, uniting these problems with tasks like seriation and class inclusion under the banner of �reversibility� is simplifying the varied specificity of requirements made by the different tasks on the child, just because they can all be categorised as being non-sequential parts of the �concrete operational� stage.
It is dangerous to attempt any post-rationalisation of empirical research since the conclusions themselves are not subject to any empirical validation. One such particulalry suspect theorem is Piaget�s constructivist claim that inductive learning and the schematic development of an imagination capable of performing powerful transformations on internal perceptual representations is the same faculty used for the supposedly logical, i.e. deductive, inferential demands of some of his other tests, such as transitive inferences. To say that a child�s ability to serialise stems from a schema for visually imagining alternative arrangements ignores the need for the child to understand what is required and the conceptual relationship between the objects of different sizes.