Abstract
Whether two-digit numbers are represented holistically (each digit pair processed as one number) or compositionally (each digit pair processed separately as a decade digit and a unit digit) remains unresolved. Two experiments were conducted to examine the distance, magnitude, and SNARC effects in a number-matching task involving two-digit numbers. Forty undergraduates were asked to judge whether two two-digit numbers (presented serially in Experiment 1 and simultaneously in Experiment 2) were the same or not. Results showed that, when numbers were presented serially, unit digits did not make unique contributions to the magnitude and distance effects, supporting the holistic model. When numbers were presented simultaneously, unit digits made unique contributions, supporting the compositional model. The SNARC (Spatial-Numerical Association of Response Codes) effect was evident for the whole numbers and the decade digits, but not for the unit digits in both experiments, which indicates that two-digit numbers are represented on one mental number line. Taken together, these results suggested that the representation of two-digit numbers is on a single mental number line, but it depends on the stage of processing whether they are processed holistically or compositionally.
Highlights
One of the most important issues in the area of numerical processing is how numbers are represented in the memory
The SNARC effect was not significant for unit digits, but it was significant for the whole numbers and the decade digits
By using a number-matching paradigm, this study found that the mental representation of two-digit numbers depended on the stage of processing
Summary
One of the most important issues in the area of numerical processing is how numbers are represented in the memory. The distance effect (e.g., Moyer & Landauer, 1967) is revealed when subjects take longer and/or make more errors to process (e.g., to compare) two numbers close to each other in magnitude (e.g., 5 vs 6) than to process two numbers farther away from each other (e.g., 3 vs 8). The problem-size or magnitude effect means that subjects have more difficulty processing larger numbers than smaller ones (e.g., Brysbaert, 1995). Because these two effects rely on the magnitude or semantic representation of numbers, they have been used as an index of semantic processing of numbers. Their existence in a particular task would be considered as evidence of semantic processing, whereas their absence has been interpreted as a lack of semantic processing (Zhou et al, in press)
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