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1. Shared Numerosity Representations Across Formats and Tasks Revealed with 7 Tesla fMRI: Decoding, Generalization, and Individual Differences in Behavior

   https://doi.org/10.1093/texcom/tgaa038  

   Wilkey, Eric D; Conrad, Benjamin N; Yeo, Darren J; Price, Gavin R (January 2020, Cerebral Cortex Communications)

   null (Ed.)

   Abstract Debate continues on whether encoding of symbolic number is grounded in nonsymbolic numerical magnitudes. Nevertheless, fluency of perceiving both number formats, and translating between them, predicts math skills across the life span. Therefore, this study asked if numbers share cortical activation patterns across formats and tasks, and whether neural response to number predicts math-related behaviors. We analyzed patterns of neural activation using 7 Tesla functional magnetic resonance imaging in a sample of 39 healthy adults. Discrimination was successful between numerosities 2, 4, 6, and 8 dots and generalized to activation patterns of the same numerosities represented as Arabic digits in the bilateral parietal lobes and left inferior frontal gyrus (IFG) (and vice versa). This indicates that numerosity-specific neural resources are shared between formats. Generalization was also successful across tasks where participants either identified or compared numerosities in bilateral parietal lobes and IFG. Individual differences in decoding did not relate to performance on a number comparison task completed outside of the scanner, but generalization between formats and across tasks negatively related to math achievement in the parietal lobes. Together, these findings suggest that individual differences in representational specificity within format and task contexts relate to mathematical expertise. 

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2. First and Second Graders Successfully Reason About Ratios With Both Dot Arrays and Arabic Numerals

   https://doi.org/10.1111/cdev.13470  

   Szkudlarek, Emily; Brannon, Elizabeth M. (May 2021, Child Development)

   Children struggle with exact, symbolic ratio reasoning, but prior research demonstrates children show surprising intuition when making approximate, nonsymbolic ratio judgments. In the current experiment, eighty‐five 6‐ to 8‐year‐old children made approximate ratio judgments with dot arrays and numerals. Children were adept at approximate ratio reasoning in both formats and improved with age. Children who engaged in the nonsymbolic task first performed better on the symbolic task compared to children tested in the reverse order, suggesting that nonsymbolic ratio reasoning may function as a scaffold for symbolic ratio reasoning. Nonsymbolic ratio reasoning mediated the relation between children’s numerosity comparison performance and symbolic mathematics performance in the domain of probabilities, but numerosity comparison performance explained significant unique variance in general numeration skills. 

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3. Sharpening, focusing, and developing: A study of change in nonsymbolic number comparison skills and math achievement in 1st grade

   https://doi.org/10.1111/desc.13194  

   Wilkey, Eric D.; Shanley, Lina; Sabb, Fred; Ansari, Daniel; Cohen, Jason C.; Men, Virany; Heller, Nicole A.; Clarke, Ben (May 2022, Developmental Science)

   Bortfeld, Heather; de Haan, Michelle; Nelson, Charles A.; Quinn, Paul C. (Ed.)

   Abstract Children's ability to discriminate nonsymbolic number (e.g., the number of items in a set) is a commonly studied predictor of later math skills. Number discrimination improves throughout development, but what drives this improvement is unclear. Competing theories suggest that it may be due to a sharpening numerical representation or an improved ability to pay attention to number and filter out non‐numerical information. We investigate this issue by studying change in children's performance (N = 65) on a nonsymbolic number comparison task, where children decide which of two dot arrays has more dots, from the middle to the end of 1st grade (mean age at time 1 = 6.85 years old). In this task, visual properties of the dot arrays such as surface area are either congruent (the more numerous array has more surface area) or incongruent. Children rely more on executive functions during incongruent trials, so improvements in each congruency condition provide information about the underlying cognitive mechanisms. We found that accuracy rates increased similarly for both conditions, indicating a sharpening sense of numerical magnitude, not simply improved attention to the numerical task dimension. Symbolic number skills predicted change in congruent trials, but executive function did not predict change in either condition. No factor predicted change in math achievement. Together, these findings suggest that nonsymbolic number processing undergoes development related to existing symbolic number skills, development that appears not to be driving math gains during this period.Children's ability to discriminate nonsymbolic number improves throughout development. Competing theories suggest improvement due to sharpening magnitude representations or changes in attention and inhibition.The current study investigates change in nonsymbolic number comparison performance during first grade and whether symbolic number skills, math skills, or executive function predict change.Children's performance increased across visual control conditions (i.e., congruent or incongruent with number) suggesting an overall sharpening of number processing.Symbolic number skills predicted change in nonsymbolic number comparison performance. 

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4. Approximate multiplication in young children prior to multiplication instruction

   Chuyan Qu, Emily Szkudlarek (January 2021, Journal of experimental child psychology)

   Prior work indicates that children have an untrained ability to approximately calculate using their approximate number system (ANS). For example, children can mentally double or halve a large array of discrete objects. Here, we asked whether children can per-form a true multiplication operation, flexibly attending to both the multiplier and multiplicand, prior to formal multiplication instruc-tion. We presented 5- to 8-year-olds with nonsymbolic multipli-cands (dot arrays) or symbolic multiplicands (Arabic numerals) ranging from 2 to 12 and with nonsymbolic multipliers ranging from 2 to 8. Children compared each imagined product with a vis-ible comparison quantity. Children performed with above-chance accuracy on both nonsymbolic and symbolic approximate multipli-cation, and their performance was dependent on the ratio between the imagined product and the comparison target. Children who could not solve any single-digit symbolic multiplication equations (e.g., 2
   3) on a basic math test were nevertheless successful on both our approximate multiplication tasks, indicating that children have an intuitive sense of multiplication that emerges independent of formal instruction about symbolic multiplication. Nonsymbolic multiplication performance mediated the relation between chil-dren’s Weber fraction and symbolic math abilities, suggesting a pathway by which the ANS contributes to children’s emerging symbolic math competence. These findings may inform future educational interventions that allow children to use their basic arithmetic intuition as a scaffold to facilitate symbolic math learning. 

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5. Predicting children’s math skills from task-based and resting-state functional brain connectivity

   https://doi.org/10.1093/cercor/bhab476  

   Lynn, Andrew; Wilkey, Eric D; Price, Gavin R (December 2021, Cerebral Cortex)

   Abstract A critical goal of cognitive neuroscience is to predict behavior from neural structure and function, thereby providing crucial insights into who might benefit from clinical and/or educational interventions. Across development, the strength of functional connectivity among a distributed set of brain regions is associated with children’s math skills. Therefore, in the present study we use connectome-based predictive modeling to investigate whether functional connectivity during numerical processing and at rest “predicts” children’s math skills (N = 31, Mage = 9.21 years, 14 Female). Overall, we found that functional connectivity during symbolic number comparison and rest, but not during nonsymbolic number comparison, predicts children’s math skills. Each task revealed a largely distinct set of predictive connections distributed across canonical brain networks and major brain lobes. Most of these predictive connections were negatively correlated with children’s math skills so that weaker connectivity predicted better math skills. Notably, these predictive connections were largely nonoverlapping across task states, suggesting children’s math abilities may depend on state-dependent patterns of network segregation and/or regional specialization. Furthermore, the current predictive modeling approach moves beyond brain–behavior correlations and toward building models of brain connectivity that may eventually aid in predicting future math skills. 

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