This preview shows page 1. Sign up to view the full content.
Unformatted text preview: them into an ordered relationship. What is im
portant is that he or she order them mentally.
Why Nonconservers Do Not Conserve and Conservers Do. The various levels found
in the conservation task can now be explained by the mental structure of number
that children gradually construct. This structure, as discussed above, results from
the synthesis of hierarchical inclusion and order by constructive abstraction.
The Level-1 arrangement shown in Figure 1.2b indicates that the child’s
logic has become strong enough to make an arrangement superior to the one in
Figure 1.2a. Children who use the spatial frontiers of the rows do so because
they are now thinking about quantities. Because Level-1 children’s logic is still
weak, they use their eyes and make a quantity that looks the same. They thus
think of the space occupied by the counters and use the frontiers of the two rows
as the criterion of “same quantity.”
My (CK) studies of children from middle-income families indicate that the
logic of most has advanced to the point of thinking about one-to-one correspon
dence by about 4 years of age. However, this logic is not yet strong enough to
overcome the perceptual “trap” set by destroying the visible one-to-one corre
spondence. Like the advanced Level-1 children who use space to judge the
equality of the two rows, Level-2 children use space to make the one-to-one Figure 1.4. (a) The arrangement of eight objects and (b) the mental
relationship of order made by a child. How Do Children Acquire Number Concepts? 13 correspondence. When this observable correspondence is destroyed, the logic
of the Level-2 child is not strong enough to overcome the perceptual trap.
Most children from middle-income families begin to conserve number
between the ages of 5 and 6, thereby attaining Level 3. (Those in lower socio
economic groups attain Level 3 later.) Level-3 children say that there are as many
counters in the longer row as in the shorter one and justify this answer with one
of the three logical arguments given earlier. Level-3 children conserve because
they have constructed the logic synthesizing hierarchical inclusion and order
(Figures 1.3b and 1.4b).
Note that to “conserve” is a verb. Children conserve or do not conserve by
doing their own reasoning. However, most authors of books about Piaget’s theory
misinterpret conservation because they do not know the difference between
physical and logico-mathematical knowledge. For example, Ginsburg and Opper
(1988) say, “If quantity is seen to change whenever mere physical arrangement
is altered, then the child fails to appreciate certain basic constancies or invari
ants in the environment” (p. 141). Conservation is not an appreciation of an
empirical fact. The constancy of quantity is a logical deduction and not an ap
preciation of something that exists in the environment.
Many other authors tell us that, at Level 3, children come to “understand”
or “recognize” that the quantity does not change when counters are moved. Many
authors also tell us that children “discover” conservation. These terms all reflect
an empiricist assumption that conservation is “out there” to be “discovered,”
“understood,” or “recognized.” America was already “out there” when it was
discovered. But conservation is not out there in the external world waiting to be
discovered by children. The ability to conserve results from children’s logic,
which they construct from within.
The synthesis of hierarchical inclusion and order can be seen in another
task in which one-to-one correspondence is made empirically. The difference
between empirical knowledge and logico-mathematical knowledge can again be
seen in this task that teachers can use. A Task Involving the Dropping of Beads
This task, originally devised by Inhelder and Piaget (1963), uses two iden
tical glasses and 30 to...
View Full Document
This document was uploaded on 03/13/2014.
- Spring '14
- The Land