Revisiting and refining relations between nonsymbolic ratio processing and symbolic math achievement

Abstract

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.

Investigating the relationships between temporal and spatial ratio estimation and magnitude discrimination using structural equation modeling: Evidence for a common ratio processing system.

“…This result is surprising because the secondary analysis on data from Park et al (2021), which included similar discrimination tasks, yielded factor loadings between .74 and .81, which is far greater than the loadings found in the current study. Though the tasks were closely modeled after the ones used in Park et al (2021) as well as other studies by that research group (Matthews et al, 2016;Park & Matthews, 2020), the difference in factor loadings could be partially explained by differences in task parameters, either the comparison ratios chosen or the low number of trials, and sample characteristics (i.e., children vs. adults). However, despite the reliability of the tasks, the spatial magnitude factor still showed strong relationships with the other more reliable latent variables and replicated findings from a secondary analysis on similar tasks (Park et al, 2021).…”

Testing the whole number interference hypothesis: contributions of inhibitory control and whole number knowledge to fraction understanding

“…Prior work has found associations between various Stroop tasks and rational number outcomes (Avgerinou & Tolmie, 2019;Coulanges et al, 2021;Gómez et al, 2015), and also the Hearts and Flowers task (Abreu-Mendoza et al, 2020;Ren & Gunderson, 2021). In fact, the Flanker task is the only measure of inhibitory control studied so far that has not been found to be associated with rational number performance (Matthews et al, 2016;Park & Matthews, 2021).…”

“…The majority of studies examining inhibitory control have found positive associations with rational number outcomes (Abreu-Mendoza et al, 2020;Avgerinou & Tolmie, 2019;Coulanges et al, 2021;Gómez et al, 2015;Ren & Gunderson, 2021), but not all (Matthews, Lewis, & Hubbard, 2016;Park & Matthews, 2021). Notably, Matthews et al (2016) found that inhibitory control was not related to performance on a non-symbolic fraction comparison task or to conceptual understanding of rational numbers, nor was it related to symbolic fraction comparison (Park & Matthews, 2021). These conflicting results could potentially stem from the type of inhibition task employed.…”

“…These conflicting results could potentially stem from the type of inhibition task employed. While these studies (Matthews et al, 2016;Park & Matthews, 2021)…”

Are Rational Numbers Spontaneous? Natural Numbers Suffice all Processing by the Number Sense

“…Interestingly, the typical ANS ratio signature characterizes performance in proportional reasoning (McCrink & Wynn, 2007;Roberts, MacDonald, & Lo, 2018;Rugani et al, 2016). Although it has been suggested that the ratio processing system can independently hold this operation (Park & Matthews, 2021), it seems that, by its very nature, the ANS can support the computation of sequential comparisons of integer components and provide an online strategy to assess the meaning of fractions.…”