Neural and behavioral correlates of arithmetic development and learning in children

Arithmetic learning improves mathematical competence, which is necessary for successful daily life. However, little is known about the neural underpinnings of arithmetic learning during childhood, the age when individuals learn most of the mathematical skills and the vast majority of our knowledge comes from adult studies. In this dissertation project, four studies were conducted to investigate the neural and behavioral correlates of arithmetic development and learning in children. In Study 1 arithmetic development was evaluated longitudinally to see whether it is monotonous or there are intermediate phases in which certain domain-general processes become important but disappear later. In Study 2 arithmetic complexity was evaluated to see whether it relies on both magnitude and cognitive processes, such as in adults. In Study 3 it was asked whether the findings in adults are valid for children or are there intermediate stages. Furthermore, it was evaluated whether few training sessions are reflective of more long-term learning processes. In Study 4 the brain activation changes during the course of learning were measured to see whether they reveal similar changes as in after arithmetic learning. The findings revealed that different domain-general cognitive processes are involved in different steps of arithmetic development and learning. Furthermore, arithmetic achievement occurs in two steps in children, first from slow effortful procedural processes to fast compacted procedural processes, and then to retrieval processes. These changes are distinguishable after one and several training sessions, and also during the course of learning. The findings are integrated in a theoretical model of arithmetic achievement in children, which contains two phases: (i) the efficiency increase (from slow effortful procedural processes to fast compacted procedural processes) and (ii) the strategy change (from fast compacted procedural processes to retrieval processes) phases. The model was developed based on two principles of brain function, optimum performance and energy consumption, and supported by several empirical studies. Taken together, this dissertation project provides a comprehensive framework for arithmetic development and learning in children. The findings might be helpful to develop educational and therapeutic interventions and also a new measure of intervention outcomes, particularly in individuals with mathematical learning disabilities

The neural circuits of number and letter copying: an fNIRS study

In our daily lives, we are constantly exposed to numbers and letters. However, it is still under debate how letters and numbers are processed in the brain, while information on this topic would allow for a more comprehensive understanding of, for example, known influences of language on numerical cognition or neural circuits shared by numerical cognition and language processing. Some findings provide evidence for a double dissociation between numbers and letters, with numbers being represented in the right and letters in the left hemisphere, while the opposing view suggests a shared neural network. Since processing may depend on the task, we address the reported inconsistencies in a very basic symbol copying task using functional near-infrared spectroscopy (fNIRS). fNIRS data revealed that both number and letter copying rely on the bilateral middle and left inferior frontal gyri. Only numbers elicited additional activation in the bilateral parietal cortex and in the left superior temporal gyrus. However, no cortical activation difference was observed between copying numbers and letters, and there was Bayesian evidence for common activation in the middle frontal gyri and superior parietal lobules. Therefore, we conclude that basic number and letter processing are based on a largely shared cortical network, at least in a simple task such as copying symbols. This suggests that copying can be used as a control condition for more complex tasks in neuroimaging studies without subtracting stimuli-specific activation

Math Anxiety in Combination With Low Visuospatial Memory Impairs Math Learning in Children

Math anxiety impairs academic achievements in mathematics. According to the processing efficiency theory (PET), the adverse effect is the result of reduced processing capacity in working memory (WM). However, this relationship has been examined mostly with correlational designs. Therefore, using an intervention paradigm, we examined the effects of math anxiety on math learning. Twenty-five 5th graders underwent seven training sessions of multiplication over the course of 2 weeks. Children were faster and made fewer errors in solving trained problems than untrained problems after learning. By testing the relationship between math anxiety, WM, and math learning, we found that if children have little or no math anxiety, enough WM resources are left for math learning, so learning is not impeded. If they have high math anxiety and high visuospatial WM, some WM resources are needed to deal with math anxiety but learning is still supported. However, if they have high math anxiety and low visuospatial WM capacity, math learning is significantly impaired. These children have less capacity to learn new math content as cognitive resources are diverted to deal with their math anxiety. We conclude that math anxiety not only hinders children’s performance in the present but potentially has long-lasting consequences, because it impairs not only math performance but also math learning. This intervention study partially supports the PET because only the combination of high math anxiety and low WM capacity seems critical for hindering math learning. Moreover, an adverse effect of math anxiety was observed on performance effectiveness (response accuracy) but not processing efficiency (response time)

Semantic cognition versus numerical cognition : a topographical perspective

Semantic cognition and numerical cognition are dissociable faculties with separable neural mechanisms. However, recent advances in the cortical topography of the temporal and parietal lobes have revealed a common organisational principle for the neural representations of semantics and numbers. We discuss their convergence and divergence through the prism of topography

Pick the smaller number : No influence of linguistic markedness on three-digit number processing

The symbolic number comparison task has been widely used to investigate the cognitive representation and underlying processes of multi-digit number processing. The standard procedure to establish numerical distance and compatibility effects in such number comparison paradigms usually entails asking participants to indicate the larger of two presented multi-digit Arabic numbers rather than to indicate the smaller number. In terms of linguistic markedness, this procedure includes the unmarked/base form in the task instruction (i.e., large). Here we evaluate distance and compatibility effects in a three-digit number comparison task observed in Bahnmueller et al. (2015) using a marked task instruction (i.e., ‘pick the smaller number’). Moreover, we aimed at clarifying whether the markedness of task instruction influences common numerical effects and especially componential processing as indexed by compatibility effects. We instructed German- and English-speaking adults (N=52) to indicate the smaller number in a three-digit number comparison task as opposed to indicating the larger number in Bahnmueller et al. (2015). We replicated standard effects of distance and compatibility in the new pick the smaller number experiment. Moreover, when comparing our findings to Bahnmueller et al. (2015), numerical effects did not differ significantly between the two studies as indicated by both frequentist and Bayesian analysis. Taken together our data suggest that distance and compatibility effects alongside componential processing of multi-digit numbers are rather robust against variations of linguistic markedness of task instructions

Automatic place-value activation in magnitude-irrelevant parity judgement

Research on multi-digit number processing suggests that, in Arabic numerals, their place-value magnitude is automatically activated, whenever a magnitude-relevant task was employed. However, so far, it is unknown, whether place-value is also activated when the target task is magnitude-irrelevant. The current study examines this question using the parity congruency effect in two-digit numbers: It describes that responding to decade-digit parity congruent numbers (e.g., 35, 46; same parity of decades and units) is faster than to decade-digit parity incongruent numbers (e.g., 25; 36; different parities of decades and units). Here we investigate the (a-) symmetry of the parity congruency effect; i.e. whether it makes a difference whether participants are assessing the parity of the unit digit or the decade digit. We elaborate, how and why such an asymmetry is related to place-value processing, because the parity of the unit digit only interferes with the parity of the decade digit, while the parity of the decade digit interferes with both the parity of the unit digit and the integrated parity of the whole two-digit number. We observed a significantly larger parity congruency effect in the decade parity decision than in the unit parity decision. This suggests that automatic place-value processing also takes place in a typical parity judgment task, in which magnitude is irrelevant. Finally, because of the cross-lingual design of the study, we can show that these results and their implications were language-independent

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