The Ratio Processing System and its Role in Fraction Understanding

• In Event: STEM: Cognition, Motivations, and Interventions

Abstract

Fractions play a critical role in the holistic development of numerical skills and have been shown to predict mathematics achievement later in life (Bailey, Hoard, Nugent, & Geary, 2012; Booth & Newton, 2012). Despite fraction instruction starting around grade 3 globally, children and adults struggle to understand fractions (Stigler, Givvin, & Thompson, 2010; Van Hoof, Lijnen, Verschaffel, & Van Dooren, 2013). The persistent difficulties in fraction understanding have led several researchers to postulate that the human neurocognitive architecture is not designed to deal with rational number quantities such as fractions (Bonato, Fabbri, Umiltà, & Zorzi, 2007; Feigenson et al., 2004). However, it has been recently hypothesized that the human neurocognitive architecture may include a perceptual system supporting non-symbolic ratio processing, the Ratio Processing System (RPS) (Lewis, Matthews, & Hubbard, 2015). In this study, we aim to provide further evidence for the universality of the RPS in individuals with a range of math skills (adults, children, and adults with dyscalculia) and also test to what extent the RPS may be involved in symbolic fraction processing.

We presented typical adults (n=42), elementary school children (grade 4th and 5th, n=38), and adults with dyscalculia (n=13) with two different versions of a match-to-sample task. In one version, participants were asked to match a non-symbolic ratio (a pair of lines) presented on the left side of a screen (i.e., target) to one of two non-symbolic ratios presented on the right side (i.e., the match and distractor). In another version, the pairs of lines were replaced by symbolic fractions. The ratio between the match and the distractor (ratio of ratios, or RoR) was systematically varied, such that it was small in some trials and large in others (to vary comparison difficulty). The ratio between numerators of the fraction was also categorized into small and large. Finally, we presented another group of adults (n=33) with a mixed-notation version of the task, in which non-symbolic ratios had to be matched to symbolic fractions. The task was timed and participants were asked to answer as quickly as possible without sacrificing accuracy. Proportion correct was analyzed using repeated measures ANOVA (frequentist and Bayesian) in Jamovi.

Children, adults, and adults with dyscalculia showed a RoR effect (i.e. more accurate performance for large than small RoR) in the non-symbolic version. This ratio sensitivity was also observed in another group of typical adults who performed the mixed notation task, indicating that the RPS may contribute to symbolic fraction understanding. However, no ratio dependence was observed when participants performed the task for symbolic fractions.

Our results add to growing evidence for an intuitive, perceptual sensitivity for non-symbolic relational magnitudes. However, the role of the RPS in symbolic fraction processing was found to be limited to tasks in which participants have to approximate the value of a fraction.

Authors

• Parnika Bhatia, CRNL, Bron, France
  Presenting Author

• Mael Delem
  Non-Presenting Author

• Jessica Leone
  Non-Presenting Author

• Esther Boisin
  Non-Presenting Author

• Anne Cheylus, Institut des Sciences Cognitives
  Non-Presenting Author

• Marie-Line Gardes, Université Claude Bernard Lyon 1
  Non-Presenting Author

• Jérôme Prado, Centre National de la Recherche Scientifique (CNRS)
  Non-Presenting Author