Recent research on numerical cognition has begun to systematically detail the ability to perceive the magnitudes of sym-bolic fractions and non-symbolic ratios. The current study extended this line of research by investigating spatial represen-tations of symbolic fractions and nonsymbolic ratios with two behavioral measures: the Spatial-Numerical Associationof Response Codes (SNARC) effect and number line estimation. The two research questions were: 1) what are the simi-larities and differences of spatial representations between symbolic fractions and nonsymbolic ratios? 2) do mechanismsdriving the SNARC effect and performance on number line estimation rely on a shared cognitive mechanism? Participantscompleted four tasks: magnitude comparison with symbolic fractions, magnitude comparison with nonsymbolic ratios,number line estimation with symbolic fractions, and number line estimation with nonsymbolic ratios. Results suggestedthe existence of both shared and specific spatial representations of symbolic fractions and nonsymbolic ratios. Moreover,individual participants SNARC effects and number line estimation performances were not correlated with each other.Findings further elucidate the relations between different spatial representations for symbolic fractions and nonsymbolicratios and cast doubt on the prospect of their sharing common cognitive mechanisms.

Whereas much is known about how humans categorize andreason based on absolute quantities, research investigating theprocessing of relative quantities, such as proportions, iscomparatively limited. The current study used a Stroop-likeparadigm to examine adults’ automatic processing ofnonsymbolic proportions and how presentation formatsmodulate this processing. Participants were asked to compareindividual components across proportions in six differentpresentation formats. Congruity between component size andoverall proportion affected accuracy of comparison, such thatparticipants were less accurate when proportion (the irrelevantdimension) was incongruent with absolute quantity (therelevant) dimension. Moreover, the congruity effect wasmodulated by the presentation format. These findings serve asevidence that humans automatically access relative quantitywhen presented in nonsymbolic formats and provide evidencethat the strength of this processing is modulated by the formatof presentation.

Non-symbolic ratio processing and symbolic fraction processing both involve thinking about relations between two partsand relational thinking. Despite the close connections between non-symbolic ratio and symbolic fractions, previous re-search on non-symbolic ratio processing and symbolic fraction learning have proceeded separately. The current researchinvestigated whether children’s non-symbolic ratio sense support their symbolic fraction success. Using sample of 151children, we found that non-symbolic ratio sense significantly predicted fraction knowledge assessment scores and sym-bolic fraction comparison performance, but not for fraction number line estimation performance. The implications of thesefindings for theories of numerical development and for improving mathematics learning are discussed.

An issue in higher-order reasoning is the influence of irrelevant surface (perceptual) features in tasks involving a deep(relational) structure. Many machine learning models use feature vector representations of objects. However, the extent towhich these representations predict or explain human behavior and learning is unclear. A feature vector model facilitatesabstraction and transfer when weights on irrelevant features are minimized and weights on the diagnostic (relational)features are increased. The current study tested whether a feature vector model applies to human behavior in the contextof magnitude relations (line ratio comparison). We systematically varied the degree of surface feature variation whilemaintaining relational structure. We found that, consistent with a feature vector model, participants were more accurateat recognizing common relational structure when surface features differed (t = 4.22, p ¡.001). This approach may bepreferable to a progressive alignment approach to relational magnitude learning.