You can count on your fingers: Finger-based intervention improves first-graders' arithmetic learning.

The question of whether finger use should be encouraged or discouraged in early mathematics instruction remains a topic of debate. Scientific evidence on this matter is scarce due to the limited number of systematic intervention studies. Accordingly, we conducted an intervention study in which first-graders (Mage = 6.48 years, SD = 0.35) completed a finger-based training (18 sessions of âˆ¼ 30 min each) over the course of the first school year. The training was integrated into standard mathematics instruction in schools and compared with business-as-usual curriculum teaching. At the end of first grade and in a follow-up test 9 months later in second grade, children who received the finger training (n = 119) outperformed the control group (n = 123) in written addition and subtraction. No group differences were observed for number line estimation tasks. These results suggest that finger-based numerical strategies can enhance arithmetic learning, supporting the idea of an embodied representation of numbers, and challenge the prevailing skepticism about finger use in primary mathematics education.

Don't SNARC me now! Intraindividual variability of cognitive phenomena - Insights from the Ironman paradigm.

Two implicit generalizations are often made from group-level studies in cognitive experimental psychology and their common statistical analysis in the general linear model: (1) Group-level phenomena are assumed to be present in every participant with variations between participants being often treated as random error in data analyses; (2) phenomena are assumed to be stable over time. In this preregistered study, we investigated the validity of these generalizations in the commonly used parity judgment task. In the proposed Ironman paradigm, the intraindividual presence and stability of three popular numerical cognition effects were tested in 10 participants on 30 days: the SNARC (Spatial-Numerical Association of Response Codes, i.e., faster left-/right-sided responses to small/large magnitude numbers, respectively; Dehaene, Bossini, & Giraux, 1993), MARC (Linguistic Markedness of Response Codes; i.e., faster left-/right-sided responses to odd/even numbers, respectively; Nuerk, Iversen, & Willmes, 2004), and Odd (i.e., faster responses to even numbers; Hines, 1990) effects. We replicated the group-level effects; however, they were reliably present in only four to five (SNARC), six (MARC) or five (Odd) of 10 participants. Fluctuations seemed unsystematic, although the SNARC effect decreased over time along with reaction times. No correlation between the SNARC and MARC effects and sleep duration, tiredness, daytime, and consumption of stimulants were detected in most participants. These results challenge the frequent generalizations from group-level phenomena to individual participants and from single sessions to typical behavior. The innovative Ironman paradigm combined with bootstrap analyses permits unique insights into the intraindividual presence and stability of cognitive phenomena.

High-definition turns timing-dependent: Different behavioural consequences during and following cathodal high-definition transcranial direct current stimulation (HD tDCS) in a magnitude classification task.

Neuromodulation with transcranial direct current stimulation (tDCS) can transiently alter neural activity, but its spatial precision is low. High-definition (HD) tDCS was introduced to increase spatial precision by placing additional electrodes over the scalp. Initial evaluations of HD tDCS indicated polarity-specific neurophysiological effects-similar to conventional tDCS albeit with greater spatial precision. Here, we compared the effects of cathodal tDCS or HD tDCS in a 4 × 1 configuration over prefrontal cortex (PFC) regions on behavioural outcomes in a magnitude classification task. We report results on overall performance, on the numerical distance effect as a measure of numerical processing, and on the spatial-numerical associations of response codes (SNARC) effect, which was previously affected by prefrontal tDCS. Healthy volunteers (n = 68) received sham or cathodal HD tDCS at 1 mA over the left dorsolateral prefrontal cortex (DLPFC) or the left inferior frontal gyrus (IFG). Results were compared to an identical protocol with conventional cathodal tDCS to the left PFC versus sham (n = 64). Mixed effects models showed performance gains relative to sham tDCS in all conditions after tDCS (i.e. 'offline'), whereas montages over PFC and DLPFC already showed performance gains during tDCS (i.e. 'online'). In contrast to conventional tDCS, HD tDCS did not reduce the SNARC effect. Neither condition affected numerical processing, as expected. The results suggest that HD tDCS with cathodal polarity might require further adjustments (i.e. regarding tDCS intensity) for effective modulations of cognitive-behavioural performance, which could be achieved by individualised current density in electric field modelling.

Trait-dependent effects of theta burst stimulation after psychosocial stress: a sham-controlled study in healthy individuals.

OBJECTIVE: Previous studies suggest that theta burst stimulation (TBS), a form of repetitive transcranial magnetic stimulation (rTMS), applied to the left dorsolateral prefrontal cortex (DLPFC) might be a promising approach to modulate stress-reactive rumination and the associated psychophysiological stress response. Crucially, individuals showing higher levels of trait rumination might benefit more from prefrontal stimulation. METHODS: In this sham-controlled study, 127 healthy individuals, with varying ruminative tendencies, received a single-session of intermittent TBS (iTBS), continuous TBS (cTBS) or sham TBS (sTBS) over the left DLPFC before being confronted with a Trier Social Stress Test. RESULTS: Results showed significant TBS effects on salivary cortisol as a function of trait rumination. cTBS, as compared to sTBS and iTBS, resulted in an attenuated stress-induced cortisol response in high compared to low trait ruminators. Although independent of trait rumination levels, cTBS showed positive effects on stress-related changes in mood and, both cTBS and iTBS (versus sham) presented an enhanced heart rate recovery following the stressor. We found no evidence for (trait rumination-dependent) TBS effects on stress-reactive rumination, negative affect, subjective stress or heart rate variability. CONCLUSIONS: cTBS shows beneficial effects on certain measures of stress, especially in high trait ruminators. SIGNIFICANCE: These findings highlight the importance of accounting for individual differences when examining TBS effects.

tDCS effects in basic symbolic number magnitude processing are not significantly lateralized.

Functional lateralization was previously established for various cognitive domains-but not for number processing. Although numbers are considered to be bilaterally represented in the intraparietal sulcus (IPS), there are some indications of different functional roles of the left vs. right IPS in processing number pairs with small vs. large distance, respectively. This raises the question whether number size plays a distinct role in the lateralization within the IPS. In our preregistered study, we applied anodal transcranial direct current stimulation (tDCS) over the left vs. right IPS to investigate the effect of stimulation as compared to sham on small vs. large distance, in both single-digit and two-digit number comparison. We expected that anodal tDCS over the left IPS facilitates number comparison with small distance, while anodal tDCS over the right IPS facilitates number comparison with large distance. Results indicated no effect of stimulation; however, exploratory analyses revealed that tDCS over the right IPS slowed down single-digit number processing after controlling for the training effect. In conclusion, number magnitude processing might be bilaterally represented in the IPS, however, our exploratory analyses emphasise the need for further investigation on functional lateralization of number processing.

Oral language comprehension of young adults with low-level reading comprehension.

Significant difficulties in reading comprehension, despite attendance of compulsory schooling, are a worldwide phenomenon. While previous research on adults with low literacy skills focused primarily on their reading ability, less is known about their oral language skills. In this Brief Research Report, we present an investigation of the listening comprehension skills of a selected group of German-speaking young adults, whose reading comprehension is at a primary school level (n = 32, ages 16 to 19 years). In addition, the relationship between listening comprehension and reading comprehension, beyond word reading skills, was tested. Standardized tests of reading and listening comprehension in the German language were administered. The average performance of the group in the listening comprehension tasks was below the level expected by age and educational level. In addition, when entered into a stepwise regression equation, listening comprehension, but not word reading, explained a significant amount of variance in reading comprehension. This pattern of relationship differs from previous findings in studies of adults struggling to read the opaque English orthography. Whether orthographic transparency explains this discrepancy should be further tested in cross-orthography studies with larger samples of adults with low literacy skills.

Cultural similarities and specificities of finger counting and montring: Evidence from Amazon Tsimane' people.

Numerical cognition might be embodied, that is, grounded in bodily actions. This claim is supported by the observation that, potentially due to our shared biology, finger counting is prevalent among a variety of cultures. Differences in finger counting are apparent even within Western cultures. Relatively few indigenous cultures have been systematically analyzed in terms of traditional finger counting and montring (i.e., communicating numbers with fingers) routines. Even fewer studies used the same protocols across cultures, allowing for a systematic comparison of indigenous and Western finger counting routines. We analyze the finger counting and montring routines of Tsimane' (N = 121), an indigenous people living in the Bolivian Amazon rainforest, depending on handedness, education level, and exposure to mainstream, industrialized Bolivian culture. Tsimane' routines are compared with those of German and British participants. Tsimane' reveal a greater variation in finger counting and montring routines, which seems to be modified by their education level. We outline a framework on how different factors such as handedness and reading direction might affect cross-cultural and within-cultural variation in finger counting.

Blue-light stimulation of the blind-spot constricts the pupil and enhances contrast sensitivity.

Short- and long-wavelength light can alter pupillary responses differently, allowing inferences to be made about the contribution of different photoreceptors on pupillary constriction. In addition to classical retinal photoreceptors, the pupillary light response is formed by the activity of melanopsin-expressing intrinsically photosensitive retinal ganglion cells (ipRGC). It has been shown in rodents that melanopsin is expressed in the axons of ipRGCs that bundle at the optic nerve head, which forms the perceptual blind-spot. Hence, the first aim of this study was to investigate if blind-spot stimulation induces a pupillary response. The second aim was to investigate the effect of blind-spot stimulation by using the contrast sensitivity tests. Fifteen individuals participated in the pupil response experiment and thirty-two individuals in the contrast sensitivity experiment. The pupillary change was quantified using the post-illumination pupil response (PIPR) amplitudes after blue-light (experimental condition) and red-light (control condition) pulses in the time window between 2 s and 6 s post-illumination. The contrast sensitivity was assessed using two different tests: the Freiburg Visual Acuity Test and Contrast Test and the Tuebingen Contrast Sensitivity Test, respectively. Contrast sensitivity was measured before and 20 minutes after binocular blue-light stimulation of the blind-spot at spatial frequencies higher than or equal to 3 cycles per degree (cpd) and at spatial frequencies lower than 3 cpd (control condition). Blue-light blind-spot stimulation induced a significantly larger PIPR compared to red-light, confirming a melanopsin-mediated pupil-response in the blind-spot. Furthermore, contrast sensitivity was increased after blind-spot stimulation, confirmed by both contrast sensitivity tests. Only spatial frequencies of at least 3 cpd were enhanced. This study demonstrates that stimulating the blind-spot with blue-light constricts the pupil and increases the contrast sensitivity at higher spatial frequencies.

The plural counts: Inconsistent grammatical number hinders numerical development in preschoolers - A cross-linguistic study.

The role of grammar in numerical development, and particularly the role of grammatical number inflection, has already been well-documented in toddlerhood. It is unclear, however, whether the influence of grammatical language structure further extends to more complex later stages of numerical development. Here, we addressed this question by exploiting differences between Polish, which has a complex grammatical number paradigm, leading to a partially inconsistent mapping between numerical quantities and grammatical number, and German, which has a comparatively easy verbal paradigm: 151 Polish-speaking and 123 German-speaking kindergarten children were tested using a symbolic numerical comparison task. Additionally, counting skills (Give-a-Number and count-list), and mapping between non-symbolic (dot sets) and symbolic representations of numbers, as well as working memory (Corsi blocks and Digit span) were assessed. Based on the Give-a-Number and mapping tasks, the children were divided into subset-knowers, CP-knowers-non-mappers, and CP-knowers-mappers. Linguistic background was related to performance in several ways: Polish-speaking children expectedly progressed to the CP-knowers stage later than German children, despite comparable non-numerical capabilities, and even after this stage was achieved, they fared worse in the numerical comparison task. There were also meaningful differences in spatial-numerical mapping between the Polish and German groups. Our findings are in line with the theory that grammatical number paradigms influence. the development of representations and processing of numbers, not only at the stage of acquiring the meaning of the first number-words but at later stages as well, when dealing with symbolic numbers.

Cognitive-Driven Activities of Daily Living Impairment as a Predictor for Dementia in Parkinson Disease: A Longitudinal Cohort Study.

OBJECTIVES: One-third of Parkinson's disease (PD) patients with mild cognitive impairment (PD-MCI) convert to dementia within a few years. Markers with a high prognostic value for dementia conversion are needed. Loss of everyday function primarily caused by cognitive dysfunction is the core criterion for the diagnosis of PD dementia, with an onset of more complex instrumental activities of daily living (IADL) dysfunction in the prodromal stage. This study evaluated the phenotype associated with cognitive IADL impairment and its predictive value for defining a high-risk group for PD dementia. METHODS: An observational longitudinal study using cognitive and clinical scores in addition to genetic and CSF biomarkers was conducted. The Functional Activities Questionnaire (FAQ) quotient (cut-off ≥1), indicating more cognitive than motor-driven IADL impairment, defined cognitive IADL impairment status at baseline. Hazard ratios (HR) were used to compare the impact of baseline classifications on dementia conversion. RESULTS: Of 268 patients with PD assessed at baseline, 108 (40.3%) had PD-MCI. After a period of 3.78±0.84 years, 164 (61.2%) patients were re-assessed. At follow-up, 93 (56.7%) patients had no cognitive impairment, 54 (32.9%) fulfilled PD-MCI criteria, and 17 (10.4%) had developed dementia. The HR of baseline cognitive IADL impairment (n=37) for dementia conversion was descriptively higher than for PD-MCI, but highest in patients with both markers (HR=12.01, 95%-CI 4.47-32.22, p<0.001). In the follow-up sample, nearly half of patients (n=10, 47.6%) with baseline classification of cognitive IADL impairment and PD-MCI converted to dementia. Baseline status of cognitive IADL impairment was associated with higher non-motor burden, worse cognitive performance, and more severe IADL progression over the study period. CONCLUSION: The importance of differentiating between cognitive and motor aspects on ADL function in PD and monitoring cognitive ADL impairment in the prodromal stage of dementia is paramount. Patients with PD-MCI and cognitive IADL impairment may be a valuable target group for clinical trials aiming to slow down development of dementia. TRIAL REGISTRATION INFORMATION: ClinicalTrials.gov NCT03687203. CLASSIFICATION OF EVIDENCE: This study provides Class II evidence that impairment of cognitive activities of daily living is associated with progression from mild cognitive impairment to dementia among patients with Parkinson's disease.

Finger-Based Numerical Training Increases Sensorimotor Activation for Arithmetic in Children-An fNIRS Study.

Most children use their fingers when learning to count and calculate. These sensorimotor experiences were argued to underlie reported behavioral associations of finger gnosis and counting with mathematical skills. On the neural level, associations were assumed to originate from overlapping neural representations of fingers and numbers. This study explored whether finger-based training in children would lead to specific neural activation in the sensorimotor cortex, associated with finger movements, as well as the parietal cortex, associated with number processing, during mental arithmetic. Following finger-based training during the first year of school, trained children showed finger-related arithmetic effects accompanied by activation in the sensorimotor cortex potentially associated with implicit finger movements. This indicates embodied finger-based numerical representations after training. Results for differences in neural activation between trained children and a control group in the IPS were less conclusive. This study provides the first evidence for training-induced sensorimotor plasticity in brain development potentially driven by the explicit use of fingers for initial arithmetic, supporting an embodied perspective on the representation of numbers.

Mathematics-gender stereotype endorsement influences mathematics anxiety, self-concept, and performance differently in men and women.

Mathematics anxiety (MA) is negatively associated with mathematics performance. Although some aspects, such as mathematics self-concept (M self-concept), seem to modulate this association, the underlying mechanism is still unclear. In addition, the false gender stereotype that women are worse than men in mathematics can have a detrimental effect on women. The role that the endorsement of this stereotype (mathematics-gender stereotype (MGS) endorsement) can play may differ between men and women. In this study, we investigated how MA and mathematics self-concept relate to arithmetic performance when considering one's MGS endorsement and gender in a large sample (n = 923) of university students. Using a structural equation modeling approach, we found that MA and mathematics self-concept mediated the effect of MGS endorsement in both men and women. For women, MGS endorsement increased their MA level, while in men, it had the opposite effect (albeit weak). Specifically, in men, MGS endorsement influenced the level of the numerical components of MA, but, unlike women, it also positively influenced their mathematics self-concept. Moreover, men and women perceived the questions included in the considered instruments differently, implying that the scores obtained in these questionnaires may not be directly comparable between genders, which has even broader theoretical and methodological implications for MA research.

The complexity of simple counting: ERP findings reveal early perceptual and late numerical processes in different arrangements.

The counting process can only be fully understood when taking into account the visual characteristics of the sets counted. Comparing behavioral data as well as event-related brain potentials (ERPs) evoked by different task-irrelevant arrangements of dots during an exact enumeration task, we aimed to investigate the effect of illusory contour detection on the counting process while other grouping cues like proximity were controlled and dot sparsity did not provide a cue to the numerosity of sets. Adult participants (N = 37) enumerated dots (8-12) in irregular and two different types of regular arrangements which differed in the shape of their illusory dot lattices. Enumeration speed was affected by both arrangement and magnitude. The type of arrangement influenced an early ERP negativity peaking at about 270 ms after stimulus onset, whereas numerosity only affected later ERP components (> 300 ms). We also observed that without perceptual cues, magnitude was constructed at a later stage of cognitive processing. We suggest that chunking is a prerequisite for more fluent counting which influences automatic processing (< 300 ms) during enumeration. We conclude that the procedure of exact enumeration depends on the interaction of several perceptual and numerical processes that are influenced by magnitude and arrangement.

Training causes activation increase in temporo-parietal and parietal regions in children with mathematical disabilities.

While arithmetic training reduces fronto-temporo-parietal activation related to domain-general processes in typically developing (TD) children, we know very little about the training-related neurocognitive changes in children with mathematical disabilities (MD), who seek evidenced-based educational interventions. In a within-participant design, a group of 20 children (age range = 10-15 years old) with MD underwent 2 weeks of arithmetic training. Brain activation was measured using functional near-infrared spectroscopy (fNIRS) before and after training to assess training-related changes. Two weeks of training led to both behavioral and brain changes. Training-specific change for trained versus untrained (control) simple multiplication solving was observed as activation increase in the bilateral temporo-parietal region including angular gyrus and middle temporal gyrus. Training-specific change for trained versus untrained (control) complex multiplication solving was observed as activation increase in the bilateral parietal region including intraparietal sulcus, superior parietal lobule, and supramarginal gyrus. Unlike the findings of a similar study in TD children, 2 weeks of multiplication training led to brain activation increase in the fronto-parietal network in children with MD. Interestingly, these brain activation differences between the current findings and a recent similar study in TD children underlie a rather similar behavioral improvement as regards response time and accuracy after 2 weeks of training. This finding provides valuable insights into underlying mechanisms of mathematics learning in special samples and suggests that the findings in TD children may not be readily generalized to children with MD.

Deficits in or preservation of basic number processing in Parkinson's disease? A registered report.

Neurodegenerative diseases such as Parkinson's disease (PD) have a huge impact on patients, caregivers, and the health-care system. To date, the diagnosis of mild cognitive impairments in PD has been established based on domain-general functions such as executive functions, attention, or working memory. However, specific numerical deficits observed in clinical practice have not yet been systematically investigated. PD-immanent deterioration of domain-general functions and domain-specific numerical areas suggests the mechanisms of both primary and secondary dyscalculia. The current study will systematically investigate basic number processing performance in PD patients for the first time, targeting domain-specific cognitive representations of numerosity and the influence of domain-general factors. The overall sample consists of patients with a diagnosis of PD, according to consensus guidelines, and healthy controls. PD patients will be stratified into patients with normal cognition or mild cognitive impairment (level I-PD-MCI based on cognitive screening). Basic number processing will be assessed using transcoding, number line estimation, and (non)symbolic number magnitude comparison tasks. Discriminant analysis will be employed to assess whether basic number processing tasks can differentiate between a healthy control group and both PD groups. All participants will be subjected to a comprehensive numerical and a neuropsychological test battery, as well as sociodemographic and clinical measures. Study results will give the first broad insight into the extent of basic numerical deficits in different PD patient groups and will help us to understand the underlying mechanisms of the numerical deficits faced by PD patients in daily life.

Arithmetic Errors in Financial Contexts in Parkinson's Disease.

Research on dyscalculia in neurodegenerative diseases is still scarce, despite high impact on patients' independence and activities of daily living function. Most studies address Alzheimer's Disease; however, patients with Parkinson's Disease (PD) also have a higher risk for cognitive impairment while the relation to arithmetic deficits in financial contexts has rarely been studied. Therefore, the current exploratory study investigates deficits in two simple arithmetic tasks in financial contexts administered within the Clinical Dementia Rating in a sample of 100 PD patients. Patients were classified as cognitively normal (PD-NC) or mildly impaired (PD-MCI) according to Level I consensus criteria, and assessed using a comprehensive neuropsychological test battery, neurological motor examination, and sociodemographic and clinical questionnaires. In total, 18% showed arithmetic deficits: they were predominately female, had longer disease duration, more impaired global cognition, but minor signs of depression compared to PD patients without arithmetic deficits. When correcting for clinical and sociodemographic confounders, greater impairments in attention and visuo-spatial/constructional domains predicted occurrence of arithmetic deficits. The type of deficit did not seem to be arbitrary but seemed to involve impaired place × value processing frequently. Our results argue for the importance of further systematic investigations of arithmetic deficits in PD with sensitive tests to confirm the results of our exploratory study that a specific subgroup of PD patients present themselves with dyscalculia.

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.

A gifted SNARC? Directional spatial-numerical associations in gifted children with high-level math skills do not differ from controls.

The SNARC (Spatial-Numerical Association of Response Codes) effect (i.e., a tendency to associate small/large magnitude numbers with the left/right hand side) is prevalent across the whole lifespan. Because the ability to relate numbers to space has been viewed as a cornerstone in the development of mathematical skills, the relationship between the SNARC effect and math skills has been frequently examined. The results remain largely inconsistent. Studies testing groups of people with very low or very high skill levels in math sometimes found relationships between SNARC and math skills. So far, however, studies testing such extreme math skills level groups were mostly investigating the SNARC effect in individuals revealing math difficulties. Groups with above average math skills remain understudied, especially in regard to children. Here, we investigate the SNARC effect in gifted children, as compared to normally developing children (overall n = 165). Frequentist and Bayesian analysis suggested that the groups did not differ from each other in the SNARC effect. These results are the first to provide evidence for the SNARC effect in a relatively large sample of gifted (and mathematically highly skilled) children. In sum, our study provides another piece of evidence for no direct link between the SNARC effect and mathematical ability in childhood.

Self-Regulation and Mathematics Performance in German and Iranian Students of More and Less Math-Related Fields of Study.

Self-regulation is a multidimensional construct that is positively related to academic achievement, such as successful mathematics performance. However, this relation of self-regulation and mathematics performance has mainly been investigated in Western countries with similar cultural contexts, although self-regulation is assumed to be context-sensitive. Therefore, the present study investigated the relation of self-regulation and mathematics performance across two different countries (Germany vs. Iran) in college students. The relation of self-regulation and mathematics performance was expected to be weaker in students of math-related fields, such as Engineering/Informatics, as they are assumed to need less self-regulation to solve the mathematics problems than students of less math-related fields, such as Human Sciences. In total, 122 undergraduate students (German = 60; Iranian = 62) of Human Sciences or Engineering/Informatics participated in this study. We measured self-regulation with the Brief Self-Control Scale (Tangney et al., 2004) and mathematics performance with a complex multiplication test. Results showed that self-regulation did not predict multiplication performance in German or Iranian students, in general. However, when the field of study was considered, self-regulation predicted multiplication performance in the subgroup of German and Iranian students studying Human Sciences within each country. We conclude that cultural context does not seem to play a dominant role in moderating the relation between self-regulation and math performance, however, field of study and more generally familiarity with math may be an important factor to consider in single or cross-cultural studies.

Professional mathematicians do not differ from others in the symbolic numerical distance and size effects.

The numerical distance effect (it is easier to compare numbers that are further apart) and size effect (for a constant distance, it is easier to compare smaller numbers) characterize symbolic number processing. However, evidence for a relationship between these two basic phenomena and more complex mathematical skills is mixed. Previously this relationship has only been studied in participants with normal or poor mathematical skills, not in mathematicians. Furthermore, the prevalence of these effects at the individual level is not known. Here we compared professional mathematicians, engineers, social scientists, and a reference group using the symbolic magnitude classification task with single-digit Arabic numbers. The groups did not differ with respect to symbolic numerical distance and size effects in either frequentist or Bayesian analyses. Moreover, we looked at their prevalence at the individual level using the bootstrapping method: while a reliable numerical distance effect was present in almost all participants, the prevalence of a reliable numerical size effect was much lower. Again, prevalence did not differ between groups. In summary, the phenomena were neither more pronounced nor more prevalent in mathematicians, suggesting that extremely high mathematical skills neither rely on nor have special consequences for analogue processing of symbolic numerical magnitudes.