Beyond magnitude: Judging ordinality of symbolic number is unrelated to magnitude comparison and independently relates to individual differences in arithmetic

In the field of numerical cognition, ordinality, the sequence of numerals, has received less attention than cardinality, the number of items in a set. Therefore it is unclear whether numerical effects generated from ordinality and cardinality tasks are associated, and whether they relate to math achievement and more domain-general variables in similar ways. To address these questions, sixty adults completed ordinality, cardinality, visual-spatial working memory, inhibitory control and math achievement tasks. The numerical distance effect from the cardinality task and reverse distance effect from the ordinality task were reliable but not associated with one another. Additionally, both distance effects predicted independent unique variance in math scores, even when visual-spatial working memory and inhibitory control were included in the regression model. These findings provide support for dissociation in the mechanisms underlying cardinal and ordinal processing of number symbols and thereby highlight the critical role played by ordinality in symbolic numerical cognition

How does the brain represent digits? Investigating the neural correlates of symbolic number representation using fMRI-Adaptation

How does the brain represent numerical symbols (e.g., Arabic digits)? Activity in left parietal regions correlates with symbolic number processing. Research with functional resonance imaging adaptation (fMRI-A) indicates that the intraparietal sulcus (IPS) exhibits a rebound (increase in activation) effect when a repeatedly presented number is followed by a new number. Importantly, this rebound effect is modulated by numerical ratio as well as the difference between presented numbers (distance). This ratio-dependent rebound effect could reflect a link between symbolic numerical representation and an approximate number system (ANS). In this doctoral dissertation, fMRI-A is used to investigate mechanisms underlying symbolic number representation. The first study investigates an alternative to the ANS hypothesis of symbolic number representation: could the positional relations between ordered symbols (e.g., letters, numbers) explain activity observed in the parietal cortex for number symbols? The predicted distance-dependent rebound effect is exhibited in bilateral IPS for number symbols. This effect is not found for letters (which, like numbers, can be represented using an ordered sequence – the alphabet). The contrast between numbers and letters reveals greater activity for numbers in the left inferior parietal lobule. The hypothesis that general ordinal mechanisms underpin neural parametric recovery in the IPS is not supported. What does the development of symbolic number representation look like in the brain? In the second study, I replicate Vogel et al. (2015; n=19) with a larger sample (n=45) of 6-14-year-olds. While Vogel et al. found a correlation between age and the ratio-dependent rebound effect in the left IPS, my data suggest an age-invariant, ratio-dependent rebound effect in bilateral IPS. Therefore, findings from Vogel et al. were not replicated. The final study asks: does handedness of participants play a role in the neural lateralization of symbolic number representation? Right-handers demonstrate the predicted left-lateralized rebound effect within the IPS. When left- and right-handed groups are compared, results do not suggest group differences in laterality. These findings do not support the hypothesis that handedness plays a role in neural lateralization of symbolic number processing. Results from these studies are discussed in terms of theoretical implications for symbolic numerical representations in the brain

Developmental specialization of the left parietal cortex for the semantic representation of Arabic numerals: an fMR-adaptation study

The way the human brain constructs representations of numerical symbols is poorly understood. While increasing evidence from neuroimaging studies has indicated that the intraparietal sulcus (IPS) becomes increasingly specialized for symbolic numerical magnitude representation over developmental time, the extent to which these changes are associated with age-related differences in symbolic numerical magnitude representation or with developmental changes in non-numerical processes, such as response selection, remains to be uncovered. To address these outstanding questions we investigated developmental changes in the cortical representation of symbolic numerical magnitude in 6- to 14-year-old children using a passive functional magnetic resonance imaging adaptation design, thereby mitigating the influence of response selection. A single-digit Arabic numeral was repeatedly presented on a computer screen and interspersed with the presentation of novel digits deviating as a function of numerical ratio (smaller/larger number). Results demonstrated a correlation between age and numerical ratio in the left IPS, suggesting an age-related increase in the extent to which numerical symbols are represented in the left IPS. Brain activation of the right IPS was modulated by numerical ratio but did not correlate with age, indicating hemispheric differences in IPS engagement during the development of symbolic numerical representation

Registered replication report on Fischer, Castel, Dodd, and Pratt (2003)

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

Numeracy and COVID-19: Examining interrelationships between numeracy, health numeracy and behaviour

During the COVID-19 pandemic, people across the globe have been exposed to large amounts of statistical data. Previous studies have shown that individuals mathematical understanding of health-related information affects their attitudes and behaviours. Here, we investigate the relation between (i) basic numeracy, (ii) COVID-19 health numeracy, and (iii) COVID-19 health-related attitudes and behaviours. An online survey measuring these three variables was distributed in Canada, the United States (US) and the United Kingdom (UK) (n = 2032). In line with predictions, basic numeracy was positively related to COVID-19 health numeracy. However, predictions, neither basic numeracy nor COVID-19 health numeracy was related to COVID-19 healthrelated attitudes and behaviours (e.g. follow experts recommendations on social distancing, wearing masks etc.). Multi-group analysis was used to investigate mean differences and differences in the strength of the correlation across countries. Results indicate there were no between-country differences in the correlations between the main constructs but there were between-country differences in latent means. Overall, results suggest that while basic numeracy is related to one s understanding of data about COVID-19, better numeracy alone is not enough to influence a population s health-related attitudes about disease severity and to increase the likelihood of following public health advice

Registered Replication Report on Fischer, Castel, Dodd, and Pratt (2003)

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

Registered Replication Report on Fischer, Castel, Dodd, and Pratt (2003)

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

Registered replication report on Fischer, Castel, Dodd, and Pratt (2003)

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

Beyond magnitude: Judging ordinality of symbolic number is unrelated to magnitude comparison and independently relates to individual differences in arithmetic

In the field of numerical cognition, ordinality, or the sequence of numerals, has received much less attention than cardinality, or the number of items in a set. Therefore it is unclear whether the numerical effects generated from ordinality and cardinality tasks are associated, and whether they relate to math achievement and more domain-general variables in similar ways. To address these questions, sixty adults completed ordinality, cardinality, visual-spatial working memory, inhibitory control and math achievement tasks. The numerical distance effect from the cardinality task and the reverse distance effect from the ordinality task were both relatively reliable but not statistically significantly associated with one another. Additionally, both distance effects predicted independent unique variance in math scores, even when visual-spatial working memory and inhibitory control were included in the regression model. These findings provide support for dissociation in the mechanisms underlying cardinal and ordinal processing of number symbols and thereby highlight the critical role played by ordinality in symbolic numerical cognition