We encounter various forms of quantity in our daily lives. These not only include symbolic labels like numbers of coins or sizes of clothes, but also include naturally occurring continuous quantities like sizes of fruit or sweetness of drinks. Indeed, a wealth of research in psychophysics has demonstrated that we humans perceptually extract many different forms of quantity information from the environment (e.g.,

In their 2016 Psych Science article, Matthews, Lewis and Hubbard (2016, https://doi.org/10.1177/0956797615617799) leveled a challenge against the prevailing theory that fractions—as opposed to whole numbers—are incompatible with humans’ primitive nonsymbolic number sense. Their ratio processing system (RPS) account holds that humans possess a primitive system that confers the ability to process nonysmbolic ratio magnitudes. Perhaps the most striking finding from Matthews et al. was that ratio processing ability predicted symbolic fractions knowledge and algebraic competence. The purpose of the current study was to replicate Matthews et al.’s novel results and to extend the study by including a control measure of fluid intelligence and an additional nonsymbolic magnitude format as predictors of multiple symbolic math outcomes. Ninety-nine college students completed three comparison tasks deciding which of two nonsymbolic ratios was numerically larger along with three simple magnitude comparison tasks in corresponding formats that served as controls. The formats included were lines, circles, and dots. We found that RPS acuity predicted fractions knowledge for three university math placement exam subtests when controlling for simple magnitude acuities and inhibitory control. However, this predictive power of the RPS measure appeared to stem primarily from acuity of the line-ratio format, and that predictive power was attenuated with the inclusion of fluid intelligence. These findings may help refine theories positing the RPS as a domain-specific foundation for building fractional knowledge and related higher mathematics.

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A substantial body of research has found that human and nonhuman animals are capable of processing the magnitudes of nonsymbolic ratios. Lewis, Mathews and Hubbard (2015) hypothesized that this ability may depend on a neurocognitive architecture called the ratio processing system (RPS). They further hypothesized 1) that the RPS might serve as a neurocognitive startup tool—an evolutionarily conserved cognitive architecture—and 2) that it can be recycled to support the acquisition of symbolic fractions knowledge. We tested these two predictions of the RPS account by comparing neural signatures of the RPS in 2nd-graders, who have not yet received formal symbolic fraction instruction, and 5th-graders, who have. During fMRI scanning, children performed ratio comparison tasks in which they determined which of two ratios or symbolic fractions was larger. Both cohorts showed behavioral and neural evidence of processing symbolic and nonsymbolic fractions magnitudes, with performance modulated by the numerical distance between stimuli. Consistent with our predictions, 2nd-grade children reliably recruited a right parietal-frontal network for nonsymbolic ratio comparisons but not symbolic fractions, and 5th-grade children recruited a bilateral parietal-frontal network for both nonsymbolic and symbolic fractions that overlapped with, but extended beyond, that found for 2nd-graders. These results present the first neuroimaging evidence that neural substrates for nonsymbolic ratios exist prior to formal learning and that this nonsymbolic foundation may be recycled to process symbolic fractions. These findings open the door for pedagogical strategies that focus on supporting this recycling process to improve students’ understanding of symbolic fractions.