Piaget – The Child’s Conception of Number
1941

First some KEY TERMS:
o Seriation: ability to arrange items along a quantitative dimension, such as length
or weight
o Conservation tasks require one to “maintain magnitudes and relations despite
displacements and perceptual transformations of all sorts” (e.g. realize that the
amount of water has not changed just because we poured it into a shallow dish)
 “Necessary for all rational activity”
 Centration: a focus on superficial perceptual appearances, which is seen
during preoperational stage (2 – 7) and leads to errors on conservation
tasks; might focus on height of C (below) and think it has more
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Similarly, you might focus on the superficial appearance of your toast and not realize it is bread:
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
Conservation of numbers
o Example of a task: child sees line of eight pennies lined up very close together
and another line of eight pennies lined up with more space between them (and,
thus, looks longer) – “which line has more pennies in it?”
 Can use “continuous quantities,” such as liquid or clay, as well as
“discontinuous quantities,” such as pennies or beads (which also allow us
to examine the relationship between conservation and one-to-one
correspondence)
o Requires synthesis of seriation (order) and classification (understanding of
subclasses within classes; one penny within the subclass of two, two pennies
within the subclass of three, etc.)
o I THINK he says (but am not 100% clear) that conservation develops BEFORE
the notion of quantity develops – child does not first develop notion of quantity
and then apply constancy to it; she only discovers quantity once she can conceive
of constant wholes – top of page 303
o Develops gradually
 First stage: frequent centration errors
 Continuous quantities
o Quantity of liquid increases or decreases, in the child’s
eyes, according to size or number of containers
o Will often contradict himself and focus on one dimension
in one instance (i.e. level of liquid) and then another on a
subsequent task (i.e. number of containers)
 Can only reason with one dimension at a time!
 Discontinuous quantities
o Makes similar errors despite being shown one-to-one
correspondence! (Count beads together one-by-one into a
taller and shorter jar – the taller one still has “more”)
 Second stage: conservation gradually emerges but not consistently
 Intermediary step: continues to make errors, but not when one-toone correspondence is shown
 Cognitive dissonance, baby: child feels conflict between one-toone correspondence and his perception of the dimensions at times
 Third stage: consistent conservation appears
 Can finally “know” that it’s the same a priori – perceptual factors
are overcome! – the previously perceptual relationships have
become “operational” – the child can manipulate them mentally
 This occurs from the coordination of the relations of various
dimensions
 New task: child given two sets of different shapes and cannot
check to see whether they are equivalent or not – then asked
whether she thinks they are
o Able to “logically multiply” relations of height and width:
“taller jar holds the same amount since it’s also more
narrow; shorter jar is indeed shorter, but it’s also has more
width”