Do Young Children Understand Conservation of Number?

Reflections on 25 Years of Piagetian Cognitive Developmental Psychology, 1963–1988

“…The result was that 3-and 4-yearolds showed no evidence of conservation, whereas 5-year-olds did. When an 'acciden tal' transformation, which had been found by McGarrigle and Donaldson [ 1975] to pro duce superior conservation performance in young children, was employed, Halford and Boyle [1985] again found that children un der 5 years did not succeed. Siegal et al [1988] found better performance on a onequestion version of the Halford and Boyle [1985] technique, as compared with their own multiquestion technique, but the per formance of 4-year-olds still did not exceed chance, and one-question performance did not clearly exceed the performance observed by Halford and Boyle [1985].…”

“…Halford and Boyle [1985] ar gued that because Bryant's posttransforma tion display provided no cues, whereas the pretransformation display did, it might have produced a false positive by causing children to repeat the pretransformation judgment by default. Accordingly, Halford and Boyle adopted neutral pre-and posttransformation displays.…”

Commentary

“…However, 1 have had to abandon this hypothesis because our original observations -that children transfer judgment over a transformation from a one-to-one correspondence display, or a display in which rows are of different lengths, to a neutral display -have turned out to be unreliable in other laboratories [Katz and Beilin, 1976;Halford and Boyle, 1985] and in our own. I do not know the reasons for this, but 1 cannot maintain any longer that young children do expect invar iance over a perceptual transformation.…”

“…Halford's argu ment against this suggestion mystifies me. In an experiment on number, Halford and Boyle [1985] found that if children are shown one neutral display (two rows side by side of the same length but not arranged in one-to-one correspondence) that is changed into another neutral display, young children often change their judgments about the rela tive number of beads in the two rows after the transformation. This seems precisely what should happen if the children are un sure (as they must be) about the merits of a perceptual judgment based on either display.…”

Reply

“…Bryant questions whether con sistency of quantity judgments as used by Halford and Boyle [1985] assesses conserva tion and refers to an analogy quoted by Gelman in which a hunter judges that the num ber of ducks is different when they are in flight than when they settle. Bryant claims that the hunter's change of mind retlects his beliefs about the reliability of the estimate, rather than failure to recognize that number is conserved.…”