Extending ideas of numerical order beyond the count-list from kindergarten to first grade.

Ordinal processing plays a fundamental role in both the representation and manipulation of symbolic numbers. As such, it is important to understand how children come to develop a sense of ordinality in the first place. The current study examines the role of the count-list in the development of ordinal knowledge through the investigation of two research questions: (1) Do K-1 children struggle to extend the notion of numerical order beyond the count-list, and if so (2) does this extension develop incrementally or manifest as a qualitative re-organization of how children recognize the ordinality of numerical sequences. Overall, we observed that although young children reliably identified adjacent ordered sequences (i.e., those that match the count-list; '2-3-4') as being in the correct ascending order, they performed significantly below chance on non-adjacent ordered trials (i.e., those that do not match the count-list but are in the correct order; '2-4-6') from the beginning of kindergarten to the end of first grade. Further, both qualitative and quantitative analyses supported the conclusion that the ability to extend notions of ordinality beyond the count-list emerged as a conceptual shift in ordinal understanding rather than through incremental improvements. These findings are the first to suggest that the ability to extend notions of ordinality beyond the count-list to include non-adjacent numbers is non-trivial and reflects a significant developmental hurdle that most children must overcome in order to develop a mature sense of ordinality.

The relation between subitizable symbolic and non-symbolic number processing over the kindergarten school year.

A long-standing debate in the field of numerical cognition concerns the degree to which symbolic and non-symbolic processing are related over the course of development. Of particular interest is the possibility that this link depends on the range of quantities in question. Behavioral and neuroimaging research with adults suggests that symbolic and non-symbolic quantities may be processed more similarly within, relative to outside of, the subitizing range. However, it remains unclear whether this unique link exists in young children at the outset of formal education. Further, no study has yet taken numerical size into account when investigating the longitudinal influence of these skills. To address these questions, we investigated the relation between symbolic and non-symbolic processing inside versus outside the subitizing range, both cross-sectionally and longitudinally, in 540 kindergarteners. Cross-sectionally, we found a consistently stronger relation between symbolic and non-symbolic number processing within versus outside the subitizing range at both the beginning and end of kindergarten. We also show evidence for a bidirectional relation over the course of kindergarten between formats within the subitizing range, and a unidirectional relation (symbolic â†’ non-symbolic) for quantities outside of the subitizing range. These findings extend current theories on symbolic and non-symbolic magnitude development by suggesting that non-symbolic processing may in fact play a role in the development of symbolic number abilities, but that this influence may be limited to quantities within the subitizing range.

Developmental specialization of the left intraparietal sulcus for symbolic ordinal processing.

Symbolic numbers have both cardinal (symbol-quantity) and ordinal (symbol-symbol) referents. Despite behavioural evidence suggesting distinct processing of cardinal and ordinal referents, little consensus has emerged from the neuroimaging literature on whether these processes have shared or distinct neural underpinnings. Moreover, it remains unclear how the neural correlates of cardinal and ordinal processing change with age. To address these unresolved questions, we investigated the neural correlates of cardinal (neural distance effect) and ordinal processing (neural reverse distance effect) in 50 children (ages 7-10) and 26 adults (ages 19-26). We found that adults recruited a largely left lateralized set of fronto-parietal regions for ordinal processing, whereas children showed activation in the right lateral orbital and inferior frontal gyri for both ordinal and cardinal processing. Additional analyses suggested that adults recruited the left intraparietal sulcus (IPS) more than children for ordinal processing, suggesting that the IPS may become increasingly tuned to ordinal symbolic properties over development. Together with previous literature documenting the importance of the left IPS for cardinal processing, our results suggest that cardinal and ordinal processing may share neural substrates in the left IPS and that this region may become specialized for both skills over development.

More Similar Than Different: Gender Differences in Children's Basic Numerical Skills Are the Exception Not the Rule.

This study investigates gender differences in basic numerical skills that are predictive of math achievement. Previous research in this area is inconsistent and has relied upon traditional hypothesis testing, which does not allow for assertive conclusions to be made regarding nonsignificant findings. This study is the first to compare male and female performance (N = 1,391; ages 6-13) on many basic numerical tasks using both Bayesian and frequentist analyses. The results provide strong evidence of gender similarities on the majority of basic numerical tasks measured, suggesting that a male advantage in foundational numerical skills is the exception rather than the rule.