The role of numerosity in processing nonsymbolic proportions

Abstract

The difficulty in processing fractions seems to be related to the interference between the whole-number value of the numerator and the denominator and the real value of the fraction. Here we assess whether the reported problems with symbolic fractions extend to the nonsymbolic domain, by presenting fractions as arrays of black and white dots representing the two operands. Participants were asked to compare a target array with a reference array in two separate tasks using the same stimuli: a numerosity task comparing just the number of white dots in the two arrays; and a proportion task comparing the proportion of black and white dots. The proportion task yielded lower accuracy and slower response, confirming that even with nonsymbolic stimuli accessing proportional information is relatively difficult. However, using a congruity manipulation in which the greater numerosity of white dots could co-occur with a lower proportion of them, and vice versa, it was found that both task-irrelevant dimensions would interfere with the task-relevant dimension suggesting that both numerosity and proportion information was automatically accessed. The results indicate that the magnitude of fractions can be automatically and holistically processed in the nonsymbolic domain.

The numerator bias exists in millions of real-world comparisons

“…As expected, we found that the bias changes with the probability of observing a large numerator in the larger fraction. Perhaps more interesting, we replicated previous findings that the bias persists in the balanced 50/50 condition (Alonso-Diaz et al, 2018;Fabbri, Caviola, Tang, Zorzi, & Butterworth, 2012). It is a common but strange result for the adaptation theory: with balanced probabilities, the bias should disappear, i.e., picking based on the numerator will lead to chance-behavior.…”

The Relational SNARC: Spatial Representation of Nonsymbolic Ratios

“…Participants performed quickly and accurately on a perceptually based task comparing nonsymbolic ratio magnitudes, adding to recent work demonstrating human perceptual sensitivity to nonsymbolic ratio magnitudes in various formats (e.g., Bonn & Cantlon, 2017;Duffy, Huttenlocher, & Levine, 2005;Jacob et al, 2012;Lewis, Matthews, & Hubbard, 2015;Mock et al, 2018; see also Spence, 1990;Stevens & Galanter, 1957;Hollands & Dyre, 2000). This stands alongside recent work showing that this ratio perception is in some respects automatic (Fabbri, Caviola, Tang, Zorzi, & Butterworth, 2012;Yang, Hu, Wu, & Yang, 2015) and that humans seem to represent nonsymbolic ratio magnitudes as specific values instead of as nondescript generalized magnitudes less than one (Matthews & Chesney, 2015;; but see Kallai & Tzelgov, 2009). Moreover, the work also stands alongside research showing that nonsymbolic ratio perception extends to nonhuman primates (e.g., Drucker et al, 2016;Vallentin & Nieder, 2008) and other animals (e.g., McComb, Packer, & Pusey, 1994;Rugani, McCrink, de Hevia, Vallortigara, & Regolin, 2016).…”

Talking about proportion: Fraction labels impact numerical interference in non‐symbolic proportional reasoning

“…The interference between absolute number and relative proportion has been at the center of a substantial amount of work with symbolic (e.g., Alibali & Sidney, 2015;Durkin & Rittle-Johnson, 2015;Ni & Zhou, 2005) and non-symbolic representations (e.g., Boyer et al, 2008;Boyer & Levine, 2015;Fabbri, Caviola, Tang, Zorzi, & Butterworth, 2012;Hurst & Cordes, 2018a;Jeong, et al, 2007). The interference between absolute number and relative proportion has been at the center of a substantial amount of work with symbolic (e.g., Alibali & Sidney, 2015;Durkin & Rittle-Johnson, 2015;Ni & Zhou, 2005) and non-symbolic representations (e.g., Boyer et al, 2008;Boyer & Levine, 2015;Fabbri, Caviola, Tang, Zorzi, & Butterworth, 2012;Hurst & Cordes, 2018a;Jeong, et al, 2007).…”

“…When proportion is presented discretely (i.e., with distinct, divided units that can be explicitly counted, like a bag of candy or a rectangle divided into quarters), this countable numerical information may be particularly salient and can interfere with our ability to focus on the relation between the two components. The interference between absolute number and relative proportion has been at the center of a substantial amount of work with symbolic (e.g., Alibali & Sidney, 2015;Durkin & Rittle-Johnson, 2015;Ni & Zhou, 2005) and non-symbolic representations (e.g., Boyer et al, 2008;Boyer & Levine, 2015;Fabbri, Caviola, Tang, Zorzi, & Butterworth, 2012;Hurst & Cordes, 2018a;Jeong, et al, 2007). In particular, the availability of countable, discrete quantities leads to systematic and predictable errors in the way children respond in proportion tasks.…”