Abstract:

In the area of mathematics, different studies have shown that preschoolers have more abilities than previously assumed by the traditional Piagetian account (Piaget & Szeminska, 1941). Gelman and Gallistel (1978) have revealed that the counting experience has a central role in the child’s understanding of number. Besides, they have found empirical evidence of hierarchical acquisition order of the counting principles (one-to-one correspondence, stable order, cardinality, abstraction and order irrelevance). However, at present, the debates around the processes underlying the development of the counting skills remain alive.
Although there are several techniques to let us deepen child’s understanding of counting, many authors have assessed it using the “error detection paradigm” (Briars and Siegler, 1984; Gelman and Meck, 1983, 1986; Lago, 1992; LeFevre, Smith-Chant, Fast, Skwarchuk, Sargla, Arnup, Penner-Wilger, Bisanz and Kamawar, 2006). This paradigm has proved to be more useful for young children than the traditional “production paradigm” (Gelman and Meck, 1983, 1986).
In the detection paradigm, the child observes a puppet counting an array of objects and has to judge whether or not the puppet’s count is right. Several types of tasks have been employed: Correct counting according to the conventional rules; erroneous counting where a puppet violates essential aspects of counting principles (for expample, skipping or doubled-counting and item), and unusual counting or “pseudo-errors”. In the pseudo-errors, the counting is logically correct but conventionally atypical, such as counting in a non-standard direction (from the right row to the left row). This last type of task has been used less frequently and less consistently than the other two ones. Probably due to the fact that different studies have used different pseudo-errors (some of them focusing only on the one-to-one correspondence principle, Gelman and Meck, 1983, 1986; others mixing this principle with the order-irrelevance principle, Briars and Siegler, 1984; LeFevre et al., 2006), their findings differ in great extent.
We can conclude that a detailed analysis of children’s responses to counting pseudo-errors for each principle has been barely carried out. However, this analysis could contribute to clarify the acquisition and development of counting. The purpose of the present study was to analyse the understanding that children between 3 and 6 years old have about the five counting principles, by using both specific errors and specific pseudo-errors for each one of them.
Seventy five Spanish preschool children from three age groups (i.e., 3-4; 4-5; 5-6 years old) judged a total of twenty-five trials. More precisely, they judged five different trials for every counting principle: Two errors, two pseudo-errors and a standard correct counting trial. We designed a computer-game software ad hoc for this research in order to present the tasks on screen.
Our findings showed that children’s performance, regardless age group and counting principle, was better in errors than in pseudo-errors trials. In the same way, the probability that children accepted the pseudo-errors as correct increased as they grew older. Nevertheless, our results indicated that even older children comprehension of the counting principles was still incomplete, and highlighted the strong influence that the conventional rules learned at school have on children´s judgments about the logic of counting.

Keywords:

Counting skills, erroneous counting, pseudo-error, conventional rules.