Mapping numbers onto space is a common cognitive representation that has been explored in both behavioral and neuroimaging contexts. Empirical work probing the diverse nature of these spatial-numerical associations (SNAs) has led researchers to question 1) how the human brain links numbers with space, and 2) whether this link is biologically vs. culturally determined. We review the existing literature on the development of SNAs and situate that empirical work within cognitive and neuroscientific theoretical frameworks. We propose that an evolutionarily-ancient frontal-parietal circuit broadly tuned to multiple magnitude dimensions provides the phylogenetic substrate for SNAs, while enculturation and sensorimotor experience shape their specific profiles. We then use this perspective to discuss educational implications and highlight promising avenues for future research.

A central question in cognitive and educational neuroscience is whether brain operations supporting non-linguistic intuitive number sense (numerosity) predict individual acquisition and academic achievement for symbolic or “formal” math knowledge. Here, we conducted a developmental functional MRI study of nonsymbolic numerosity task performance in 44 participants including 14 school age children (6–12 years-old), 14 adolescents (13–17 years-old), and 16 adults and compared a brain activity measure of numerosity precision to scores from the Woodcock-Johnson III Broad Math index of math academic achievement. Accuracy and reaction time from the numerosity task did not reliably predict formal math achievement. We found a significant positive developmental trend for improved numerosity precision in the parietal cortex and intraparietal sulcus (IPS) specifically. Controlling for age and overall cognitive ability, we found a reliable positive relationship between individual math achievement scores and parietal lobe activity only in children. In addition, children showed robust positive relationships between math achievement and numerosity precision within ventral stream processing areas bilaterally. The pattern of results suggests a dynamic developmental trajectory for visual discrimination strategies that predict the acquisition of formal math knowledge. In adults, the efficiency of visual discrimination marked by numerosity acuity in ventral occipital-temporal cortex and hippocampus differentiated individuals with better or worse formal math achievement, respectively. Overall, these results suggest that two different brain systems for nonsymbolic numerosity acuity may contribute to individual differences in math achievement and that the contribution of these systems differs across development.

Mathematical competence is crucial for a wide range of outcomes. Numerous studies demonstrate its importance for the advancement of science, technology engineering and math (STEM) fields (Cross, Woods, & Schweingruber, 2009). Several studies have further demonstrated that numeracy skills impact individual outcomes, including occupational prospects, legal troubles and even mental health (Bynner & Parsons, 2006). Recent evidence has highlighted the importance of understanding fraction magnitudes as a key skill in establishing a solid foundation in mathematics (Booth & Newton, 2012). For example, performance on fraction tests at age 10 has been shown to uniquely predict successful understanding of high-order concepts such as algebra in high school (Siegler et al., 2012). Despite the central role of fractions in mathematical understanding, children and adults struggle to comprehend them (National Mathematics Advisory Panel, 2008). To take one classic example, when eighth graders were asked to choose whether the sum of 12/13 and 7/8 was closest to 1, 2, 19 or 21, more than 50% chose 19 or 21, rather than the correct answer, 2 (Carpenter, Corbitt, Kepner, Lindquist, & Rey, 1981). Furthermore, this error is not restricted to children; when university undergraduates were presented with this same item, 15% of them chose 19 or 21 (Lewis, Matthews, & Hubbard, 2015). These incorrect responses indicate that learners focused on the components (the numerator and denominator) rather than the holistic meaning of the fraction and simply added the numerators (to arrive at 19

The attentional spatial-numerical association of response codes (Att-SNARC) effect (Fischer, Castel, Dodd, & Pratt, 2003)—the finding that participants are quicker to detect left-side targets when the targets are preceded by small numbers and quicker to detect right-side targets when they are preceded by large numbers—has been used as evidence for embodied number representations and to support strong claims about the link between number and space (e.g., a mental number line). We attempted to replicate Experiment 2 of Fischer et al. by collecting data from 1,105 participants at 17 labs. Across all 1,105 participants and four interstimulus-interval conditions, the proportion of times the effect we observed was positive (i.e., directionally consistent with the original effect) was .50. Further, the effects we observed both within and across labs were minuscule and incompatible with those observed by Fischer et al. Given this, we conclude that we failed to replicate the effect reported by Fischer et al. In addition, our analysis of several participant-level moderators (finger-counting habits, reading and writing direction, handedness, and mathematics fluency and mathematics anxiety) revealed no substantial moderating effects. Our results indicate that the Att-SNARC effect cannot be used as evidence to support strong claims about the link between number and space.

There are multiple levels of processing relevant to reading that vary in their visual, sublexical, and lexical orthographic processing demands. Segregating distinct cortical sources for each of these levels has been challenging in EEG studies of early readers. To address this challenge, we applied recent advances in analyzing high-density EEG using Steady-State Visual Evoked Potentials (SSVEPs) via data-driven Reliable Components Analysis (RCA) in a group of early readers spanning from kindergarten to second grade.