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This exploratory study provides evidence that middle-grade students' symbolic fraction knowledge relates to grounded and embodied cognitive learning processes such as spatial ability and anxiety. These findings (N = 89) are consistent with several previous findings on fraction knowledge and mathematics learning more generally while highlighting several novel associations. Three key findings include: 1) mental rotation and spatial visualization are specifically predictive of fraction knowledge scores; 2) spatial anxiety may moderate the relationship between spatial ability and fraction knowledge scores; and 3) fraction knowledge is not only grounded in processes operating at biological and cognitive timescales individually, but components of these processes are interconnected. Though exploratory, these findings may provide the foundations for future work exploring the mechanisms behind these associations.

Fractions are a critical building block for the development ofhuman mathematical cognition, but the origins of this conceptare not well-understood. Recent work has found that a wholenumber sense is present in deep convolutional neural networks(DCNNs) pre-trained for object recognition and uses them asa model for investigating human numerical cognition. Do DC-NNs also have a fraction sense? If so, is it dependent or in-dependent of whole number processing? We investigated theneural sensitivity of a pretrained DCNN to both whole num-bers and fractions. We replicated and extended previous re-search that the sense of whole number emerges in a differentDCNN architecture. Further, we showed that DCNN is alsosensitive to fraction value, i.e., the ratio of numerosities. Test-ing this model, our results suggest that the fraction sense relieson the whole number sense.

Recent research has highlighted the operation of a ratioprocessing system that represents the analog magnitudes ofnonsymbolic ratios. This study investigated whether suchrepresentations would demonstrate spatial associationsparallel to the SNARC (spatial numeric association ofresponse codes) effect previously demonstrated with wholenumber magnitudes. Participants judged whethernonsymbolic ratio test stimuli were larger or smaller thanreference stimuli using response keys located alternatelyeither on the left or on the right side of space. Larger ratiomagnitudes were associated with the right side of space andsmaller magnitudes with the left. These results demonstratethat nonsymbolic ratio magnitudes – defined relationally bypairs of components – are characterized by a left-to-rightspatial mapping. The current focus on ratio magnitudesexpands our understanding of the basic human perceptualapparatus and how it might provide tools that grant intuitiveaccess to more advanced numerical concepts beyond wholenumbers.

The three target articles presented in this special issue converged on an emerging theme: the importance of spatial proportional reasoning. They suggest that the ability to map between symbolic fractions (like 1/5) and nonsymbolic, spatial representations of their sizes or "magnitudes" may be especially important for building robust fractions knowledge. In this commentary, we first reflect upon where these findings stand in a larger theoretical context, largely borrowed from mathematics education research. Next, we emphasize parallels between this work and emerging work suggesting that nonsymbolic proportional reasoning may provide an intuitive foundation for understanding fraction magnitudes. Finally, we end by exploring some open questions that suggest specific future directions in this burgeoning area. [For the target articles in this special issue, see "Fractions Learning in Children with Mathematics Difficulties" (EJ1157276); "Delaware Longitudinal Study of Fraction Learning: Implications for Helping Children with Mathematics Difficulties" (EJ1157256); and "Fraction Intervention for Students with Mathematics Difficulties: Lessons Learned from Five Randomized Controlled Trials" (EJ1157268).]

Although important for the acquisition of later math skills, fractions are notoriously difficult. Previous studies have shown that higher math anxiety (MA) is associated with lower performance in symbolic fraction tasks in adults and have suggested that MA may negatively impact the acquisition of fractions in children. However, the effects of MA on fraction skills in school‐aged children remain underexplored. We, therefore, investigated the impact of MA on the performance of younger (second and third graders) and older (fifth and sixth graders) children in math fluency (MF), written calculation, fraction knowledge (FK), and symbolic fraction and nonsymbolic ratio processing. On the basis of our prior work suggesting a perceptual foundation for fraction processing, we predicted that symbolic, but not nonsymbolic, math skills (especially fractions) would be impaired by MA. As predicted, higher MA was associated with lower performance in general mathematics achievement and symbolic fraction tasks, but nonsymbolic ratio processing was not affected by MA in either age group. Furthermore, working memory capacity partially mediated the effects of MA on general mathematics achievement, FK, and symbolic fraction processing. These results suggest that understanding the bidirectional interactions between MA and fractions may be important for helping children acquire these critical skills. [ABSTRACT FROM AUTHOR]