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.