How Do Children Acquire Number Concepts ECI 314 Early Childhood Mathematics

Because level 1 childrens logic is still weak they

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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...
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This document was uploaded on 03/13/2014.

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