From symbols to analog magnitudes: A process model of fraction comparison, with fits to experimental data

Abstract

Recent evidence suggests that fractions are represented as visuo-spatial analog magnitudes on a “mental number line” (Schneider and Siegler, 2010). In order to test this theory, we evaluated subjects in two tasks: fraction comparison and number-line marking. Both magnitude difference and response time to mark a fraction on the number line predicted response time to compare the fraction’s magnitude to a standard held in memory. This supports the notion that even symbolic numerical cognition is grounded in visuo-spatial processing. We also found a symbolic cost to processing: fractions with more digits were processed more slowly. We propose a model of fraction comparison wherein fractions are processed from symbols into analog magnitudes, then compared to a standard by sequential sampling decision-making. This model provides a superior fit when compared to the log distance model, despite having fewer parameters. Furthermore, it has a direct interpretation in terms of psychological processes.


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