Academic journal article Memory & Cognition

Encoding Numbers: Behavioral Evidence for Processing-Specific Representations

Academic journal article Memory & Cognition

Encoding Numbers: Behavioral Evidence for Processing-Specific Representations

Article excerpt

The aim of this study was to test the hypothesis of a complex encoding of numbers according to which each numerical processing requires a specific representational format for input. In three experiments, adult participants were given two numbers presented successively on screen through a self-presentation procedure after being asked to add, to subtract, or to compare them. We considered the self-presentation time of the first number as reflecting the complexity of the encoding for a given planned processing. In line with Dehaene's triple-code model, self-presentation times were longer for additions and subtractions than for comparisons with two-digit numbers but longer for subtractions than for additions and comparisons with one-digit numbers. The implications of these results for different theories of number processing are discussed.

A large part of our cognitive resources is allocated daily to number processing. Seldom does a day pass without one's having to read numbers, to perform calculations, or to retrieve numbers from memory. Counting, estimation, and comparison can also be added to this nonexhaustive list of activities that involve numbers. It has been suggested that the numbers we have to deal with differ not only in the format in which they are presented (e.g., number words, digits, patterns of dots on dice) or in the nature of the task in which they are involved, but also in the format of representation with which they are encoded and mentally manipulated. In the present study, to obtain behavioral evidence that humans use a variety of number representations, we tracked this variety in the very first steps of cognitive processing-the encoding stage.

Several theories have been advanced to account for this variety of number representations in humans. These theories differ mainly in how they conceive the cognitive architecture for number processing and the existence of notation-specific processes. McCloskey's (e.g., 1992) abstract-modular model assumes that numerical inputs of different forms (e.g., digits, number words) are converted by notation-specific comprehension modules into a common abstract format. This abstract quantity code provides the basis for any subsequent processing in production or calculation modules. Thus, the amodal representation would constitute an unavoidable bottleneck in number processing (McCloskey, 1992; McCloskey, Caramazza, & Basili, 1985). By contrast, Campbell and Clark (1988; Clark & Campbell, 1991) proposed an encoding complex hypothesis, in which it is assumed (1) that number processing may be mediated by modality-specific processes rather than abstract codes, (2) that different surface forms can influence strategies, and (3) that a single numerical function can involve several codes. According to this model, number skills would be based on multiple forms of internal representations and could be realized in many ways. It is even suggested that these different ways in which number processing can be realized could vary as a function of cultural or idiosyncratic experience. According to this general hypothesis of a variety of codes for number processing, Noël and Seron (1993) proposed their preferred entry code model, which states that certain representations may be more suitable to certain tasks and, moreover, that individuals may prefer certain representations for idiosyncratic reasons.

The most specified and precise theory relying on the encoding complex hypothesis is probably Dehaene's triple-code model of number processing (1992, 1997, 2001; Dehaene & Cohen, 1995,1997). According to this model, numerical information can be mentally manipulated in three different representation formats: an analogical quantity or magnitude code, a verbal code, and a visual Arabic code. Each activity involving numbers would rely on one of these specific codes (Dehaene & Cohen, 1997). Magnitude comparison would rely on an analogical representation of numbers or, in other words, a language-independent spatial representation of numbers on a mental line. …

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