Publications

Recent research in numerical cognition has begun to systematically detail the ability of humans and nonhuman animals to perceive the magnitudes of nonsymbolic ratios. These relationally defined analogs to rational numbers offer new potential insights into the nature of human numerical processing. However, research into their similarities with and connections to symbolic numbers remains in its infancy. The current research aims to further explore these similarities by investigating whether the magnitudes of nonsymbolic ratios are associated with space just as symbolic numbers are. In two experiments, we found that responses were faster on the left for smaller nonsymbolic ratio magnitudes and faster on the right for larger nonsymbolic ratio magnitudes. These results further elucidate the nature of nonsymbolic ratio processing, extending the literature of spatial–numerical associations to nonsymbolic relative magnitudes. We discuss potential implications of these findings for theories of human magnitude processing in general and how this general processing relates to numerical processing.

Recent studies have explored the foundations of mathematical skills by linking basic numerical processes to formal tests of mathematics achievement. Of particular interest is the relationship between spatial-numerical associations—specifically, the Spatial Numerical Association of Response Codes (SNARC) effect—and various measures of math ability. Thus far, studies investigating this relationship have yielded inconsistent results. Here, we investigate how individual implicit and explicit spatial representations of fractions relate to fraction knowledge and other formal measures of math achievement. Adult participants (n = 105) compared the magnitude of single digit, irreducible fractions to ½, a task that has previously produced a reliable SNARC effect. We observed a significant group-level SNARC effect based on overall fraction magnitude, with notable individual variability. While individual SNARC effects were correlated with performance on a fraction number-line estimation (NLE) task, only NLE significantly predicted scores on a fractions test and basic standardized math test, even after controlling for IQ, mean accuracy, and mean reaction time. This suggests that–for fractions–working with an explicit number line is a stronger predictor of math ability than implicit number line processing. Neither individual SNARC effects nor NLE performance were significant predictors of algebra scores; thus, the mental number line may not be as readily recruited during higher-order mathematical concepts, but rather may be a foundation for thinking about simpler problems involving rational magnitudes. These results not only characterize the variability in adults’ mental representations of fractions, but also detail the relative contributions of implicit (SNARC) and explicit (NLE) spatial representations of fractions to formal math skills.

Whereas much is known about how humans categorize and reason based on absolute quantities, research investigating the processing of relative quantities, such as proportions, is comparatively limited. The current study used a Stroop-like paradigm to examine adults’ automatic processing of nonsymbolic proportions and how presentation formats modulate this processing. Participants were asked to compare individual components across proportions in six different presentation formats. Congruity between component size and overall proportion affected accuracy of comparison, such that participants were less accurate when proportion (the irrelevant dimension) was incongruent with absolute quantity (the relevant) dimension. Moreover, the congruity effect was modulated by the presentation format. These findings serve as evidence that humans automatically access relative quantity when presented in nonsymbolic formats and provide evidence that the strength of this processing is modulated by the format of presentation.

Recent research has highlighted the operation of a ratio processing system that represents the analog magnitudes of nonsymbolic ratios. This study investigated whether such representations would demonstrate spatial associations parallel to the SNARC (spatial numeric association of response codes) effect previously demonstrated with whole number magnitudes. Participants judged whether nonsymbolic ratio test stimuli were larger or smaller than reference stimuli using response keys located alternately either on the left or on the right side of space. Larger ratio magnitudes were associated with the right side of space and smaller magnitudes with the left. These results demonstrate that nonsymbolic ratio magnitudes – defined relationally by pairs of components – are characterized by a left-to-right spatial mapping. The current focus on ratio magnitudes expands our understanding of the basic human perceptual apparatus and how it might provide tools that grant intuitive access to more advanced numerical concepts beyond whole numbers.