| The relationship between children's judgements of magnitude and the Piagetian operations of seriation and class inclusion was assessed for 80 children, aged six to eight. Three groups, operational seriators, intuitive seriators and nonseriators, were given three tasks demanding judgements of magnitude. Nonseriators and intuitive seriators were randomly assigned to four experimental conditions comprising training with the continuous materials (COND 1), discrete materials (COND 2), discrete materials pointing to the salience of unit information (COND 3), and discrete materials plus explicit instructions to count (COND 4). Operational seriators were randomly assigned to two experimental conditions comprising training with continuous materials (COND 1) and discrete materials (COND 2).;Results indicated that children were able to discriminate magnitude equivalence, with both continous and discrete materials. Children either constructed arrays of equivalent magnitude by using a counting strategy, or by using a strategy based on perceptual information. Operational and intuitive seriators made significantly fewer errors when constructing arrays of equivalent magnitude, and consistently used a counting strategy upon which to base their constructions. Nonseriators made significantly more errors and used a perceptual strategy to construct arrays of equivalent magnitude. Furthermore, the condition variable significantly influenced children's performance. Nonseriators seemed to be only influenced by the most explicit instruction to count (COND 4), whereas intutitive seriators benefited significantly when unit information was available and when the counting instruction was made explicit. These results suggest that children demonstrated understanding of magnitude equivalence using perceptual information before understanding how to use unit information to describe magnitude. Subsequently, children understood how a notational symbol system can manipulate discrete units.;Children's judgements of magnitude were assessed in their construction of five arrays, which were replications of those arrays provided in training and introduced as caterpillar family members. In addition, children were required to indicate whether a different (non-member) array was a non-member of the family. Replication data were analyzed by considering children's errors, relative to the size of each array. Hypotheses were derived from Piaget's (1952) theory of number concepts, from Gelman & Gallistel's (1978) theory of number, and from Gamlin (1982) and Markman & Seibert's (1976) theory of number concepts emerging as a property of collections. |
