Academic journal article Cognitie, Creier, Comportament

The Object File Model Perspective on the Development of Number Representation in Preschool Children

Academic journal article Cognitie, Creier, Comportament

The Object File Model Perspective on the Development of Number Representation in Preschool Children

Article excerpt

ABSTRACT

The object file model accounts for the development of exact number representation as a domain-general mechanism based on associating each element with temporary representations. Once a new object is detected, the new representation is updated by changes operated within the preceding scene. Two experiments assessed the implications of verbal counting for number representation in preschool children. First, a violation of expectation procedure was used to determine the extent to which the object file model can be applied to the language development of preschoolers. The pattern of success and failure in the object-first and screen-first procedure showed that an interpretation would favor the predictions of the object file model according to which the screen-first procedure requires more updates of a mental file than the object-first procedure. A second experiment tested another prediction of the object file model related to its resistance to continuous extent properties. As expected, the resistance to number/length interference increased with age and it was higher in the ordinal task than in the correspondence task, because the latter seems to require a systematic comparison behavior, which needs more refined numerical strategies. These results show that children were able to make numerical discriminations, if they possessed minimal numerical knowledge, but counting competence did not determine performance. Taken together these data suggest that preschool children represent small numbers in a similar way with that described by the object file model and the strategies implemented in order to solve these tasks make better use of symbolic representations, once numerical knowledge becomes salient in verbal strategies.

KEYWORDS: number representation, language development, numerical abilities, and object file model, counting skills.

In the past decades, there was an increasing interest to find answers regarding the origin and development of our cognitive system. One such line of research is aimed toward understanding the developmental process underlying number representation in children, as well as gaining insight into its phylogenetic and ontogenetic mechanisms (for reviews see Carey, 1998; Wynn, 1998; Gallistel & Gelman, 2000; Geary, 2000; Feigenson, Dehaene, & Spelke, 2004).

Recently, studies on humans and animals were integrated in two descriptive models of number representation: the object file model (Trick & Pylyshyn, 1994; Simon, 1997; Leslie, Xu, Tremoulet, & Scholl, 1998; Uller, Carey, Huntley-Fenner, & Klatt, 1999), and the accumulator model (Xu & Spelke, 2000; Chiang & Wynn, 2000; Xu, Spelke, & Goddard, 2005). Each model accounts for different mechanisms of number representation: 1) the object file model is related to exact number representation and it is partially dependent on acquiring mathematical symbols and verbal knowledge of numbers; while 2) the accumulator model is associated with approximate number representation, which is regarded as language-independent (Simon, 1997; Gallistel & Gelman, 2000).

As the object file model takes into account the mediating role of language in number representation development, we chose this perspective in order to determine: 1) the way in which number representation develops as a result of language development during preschool; and 2) evaluating the impact of language acquisition on performance in exact mathematical tasks.

THE ACCUMULATOR MODEL FOR APPROXIMATE NUMBER REPRESENTATION

First, we feel it is important to describe the assumptions of the two models presented above with an emphasis on the object file model and its relevance in the research of number representation in preschool children.

The accumulator model was proposed for approximate number representation, which allows computations using large sets of elements such as "8<16" (Gallistel & Gelman, 2000; Siegler & Opfer, 2003; Feigenson, Dehaene, & Spelke, 2004; Fias & Verguts, 2004). …

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