Brian Butterworth

The transition to digital, Bring-Your-Own-Device (BYOD) environments has vastly expanded the scale and accessibility of psychological and educational testing. However, unstandardizedhardware introduces systematic mechanical latencies that contaminate timed cognitive performance, leading to measurement error and possible diagnostic misclassification. Furthermore, naive device-specific normalization strategies are inadequate, as they inadvertently suppress meaningful sociodemographic variance that inherently correlates with device ownership. To address this methodological gap, we introduce a chronometric normalization framework designed to isolate and remove hardware-driven latency without altering underlying cognitive capacity. The model leverages a brief motor task to estimate individual mechanical delay and calibrates this correction against a device-minimal, untimed cognitive task that is substantially less sensitive to hardware speed. This anchors the calibration so that real between-group differences in ability are retained. We demonstrate the framework’s practical utility using data from COSMOS, a large-scale dyscalculia screening battery administered to 54,538 students across 910 schools using the hardware available at each school. Results indicate that while trackpad users initially exhibited severe, artifactual underperformance on timed fluency tasks, the chronometric correction successfully neutralized this hardware penalty. By realigning score distributions while preserving structuraldemographic differences, this open-source method ensures that subsequent norming and diagnostic decisions reflect true cognitive architecture rather than the mechanical limitations of the user’s interface.

Is there an innate sense of number? Lorenzi et al. (2025) argue that the ability to extract numerical information from the environment is vital for a wide range of species, suggesting “a likely common origin”. Studies in different species show that the neural mechanism for doing this—numerosity-selective neurons—can be found in animals with no opportunity to learn. This leaves open important questions: How do numerosity-selective neurons code for numerosities? Is the code the same in different species? How do the neurons participate in arithmetical operations?

A sense of non-symbolic numerical magnitudes is widespread in the animal kingdom and has been documented in adult zebrafish. Here, we investigated the ontogeny of this ability using a group size preference (GSP) task in juvenile zebrafish. Fish showed GSP from 21 days post-fertilization and reliably chose the larger group when presented with discriminations of between 1 versus 3, 2 versus 5 and 2 versus 3 conspecifics but not 2 versus 4 conspecifics. When the ratio between the number of conspecifics in each group was maintained at 1 : 2, fish could discriminate between 1 versus 2 individuals and 3 versus 6, but again, not when given a choice between 2 versus 4 individuals. These findings are in agreement with studies in other species, suggesting the systems involved in quantity representation do not operate separately from other cognitive mechanisms. Rather they suggest quantity processing in fishes may be the result of an interplay between attentional, cognitive and memory-related mechanisms as in humans and other animals. Our results emphasize the potential of the use of zebrafish to explore the genetic and neural processes underlying the ontogeny and function of number cognition.

A sense of non-symbolic numerical magnitudes is widespread in the animal kingdom and has been documented in adult zebrafish. Here we investigated the ontogeny of this ability using a group size preference task in juvenile zebrafish. Fish showed group size preference from 21 days post fertilization (dpf) and reliably chose the larger group when presented with discriminations of between 1 vs. 3, 2 vs. 5 and 2 vs. 3 conspecifics but not 2 vs. 4 conspecifics. When the ratio between the number of conspecifics in each group was maintained at 1:2, fish could discriminate between 1 vs. 2 individuals and 3 vs. 6, but again, not when given a choice between 2 vs. 4 individuals. These findings are in agreement with studies in other species suggesting the systems involved in quantity representation do not operate separately from other cognitive mechanisms. Rather they suggest quantity processing in fish may be the result of an interplay between attentional, cognitive and memory-related mechanisms as in humans and other animals. Our results emphasise the potential of the use of zebrafish to explore the genetic and neural processes underlying the ontogeny and function of number cognition.

It is widely agreed that humans inherit a numerical competence, though the exact nature of this competence is disputed. I argue that it is the inherited competence with whole numbers (the ‘number module’) that is foundational for arithmetical development. This is clear from a longitudinal study of learners from kindergarten to year 5. Recent research has identified a brain network that underlies our capacity for numbers and arithmetic, with whole number processing a core region of this network. A twin study shows a strong heritable component in whole number competence, its link to arithmetical development and to the brain region. These findings have implications for improving numeracy skills especially among low-attaining learners.