No calculation necessary: Accessing magnitude through decimals and fractions

Abstract

Research on how humans understand the relative magnitude of symbolic fractions presents a unique case of the symbol-grounding problem with numbers. Specifically, how do people access a holistic sense of rational number magnitude from decimal fractions (e.g. 0.125) and common fractions (e.g. 1/8)? Researchers have previously suggested that people cannot directly access magnitude information from common fraction notation, but instead must use a form of calculation to access this meaning. Questions remain regarding the nature of calculation and whether a division-like conversion to decimals is a necessary process that permits access to fraction magnitudes. To test whether calculation is necessary to access fractions magnitudes, we carried out a series of six parallel experiments in which we examined how adults access the magnitude of rational numbers (decimals and common fractions) under varying task demands. We asked adult participants to indicate which of two fractions was larger in three different conditions: decimal-decimal, fraction-fraction, and mixed decimal-fraction pairs. Across experiments, we manipulated two aspects of the task demands. 1) Response windows were limited to 1, 2 or 5 s, and 2) participants either did or did not have to identify when the two stimuli were the same magnitude (catch trials). Participants were able to successfully complete the task even at a response window of 1 s and showed evidence of holistic magnitude processing. These results indicate that calculation strategies with fractions are not necessary for accessing a sense of a fractions meaning but are strategic routes to magnitude that participants may use when granted sufficient time. We suggest that rapid magnitude processing with fractions and decimals may occur by mapping symbolic components onto common amodal mental representations of rational numbers.