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Solving arithmetic word problems requires individuals to create a correct mental representation, and this involves both text processing and number processing. The latter comprises understanding the semantic meaning of numbers (i.e., their magnitudes) and potentially executing the appropriate mathematical operation. However, it is not yet clear whether number processing occurs after text processing or both take place simultaneously. We hypothesize that number processing occurs early and simultaneously with other problem-solving processes such as text processing. To test this hypothesis, we created non-solvable word problems that do not require any number processing and we manipulated the calculation difficulty using carry/borrow vs. non-carry/non-borrow within addition and subtraction problems. According to a strictly sequential model, this manipulation should not matter, because when problems are non-solvable, no calculation is required. In contrast, according to an interactive model, attention to numbers would be higher when word problems require a carry/borrow compared to a non-carry/non-borrow operation. Eye-tracking was used to measure attention to numbers and text in 63 adults, operationalized by static (duration and count of fixations and regressions) and dynamic measures (count of transitions). An interaction between difficulty and operation was found for all static and dynamic eye-tracking variables as well as for response times and error rates. The observed number processing in non-solvable word problems, which indicates that it occurs simultaneously with text processing, is inconsistent with strictly sequential models., Competing Interests: Declarations. Confict of interest: The authors have no conflict of interest to be declared., (© 2025. The Author(s).)

Numbers are associated with space, but it is unclear how flexible these associations are. We investigated whether the SNARC effect (Spatial-Numerical Association of Response Codes; Dehaene et al . 1993 J. Exp. Psychol . 122 , 371-396. (doi:10.1037/0096-3445.122.3.371); i.e. faster responses to small/large number magnitude with the left/right hand, respectively) is fully flexible (depending only on relative magnitude within a stimulus set) or not (depending on absolute magnitude as well). Evidence for relative-magnitude dependency came from studies observing that numbers 4 and 5 were associated with the right in a 0-5 range but with the left in a 4-9 range (Dehaene et al . 1993; Fias et al . 1996 Math. Cogn . 2 , 95-110 (doi:10.1080/135467996387552). Within this Registered Report, we conducted two online experiments running Bayesian analyses with optional recruitment stopping at moderate evidence (BF 10 above 3 or below 1/3). Experiment 1 ( n = 200) replicated relative-magnitude dependency using the original stimuli. However, Experiment 2 ( n = 300) additionally demonstrated absolute-magnitude dependency, while considering recent advances in SNARC research using 1-5 excluding 3 and 4-8 excluding 6. In contrast to the frequently perpetuated notion of fully flexible Spatial-Numerical Associations, some fixed relation to absolute magnitude prevails. These findings have important consequences for understanding how Spatial-Numerical Associations might support numerical processing., Competing Interests: The authors declare they have no competing interests., (© 2024 The Author(s).)

Spatial-Numerical Associations (SNAs) refer to the demonstrations of spatial processing of numbers. The Mental Number Line (MNL) is a representation model describing numbers as aligning left-to-right (LR) and was suggested to account for directional biases in participants' responses during numerical tasks. One common behavioral demonstration of this is the Spatial-Numerical Associations of Response Codes (SNARC) effect, which describes faster left-/right-hand responses to smaller/larger numbers, respectively. The MNL, and, consequently, directional SNAs, show variabilities across different cultures. Reading direction is considered to be the main factor in explaining these differences. In line with this, individuals with right-to-left (RL) reading habits show a weaker or even reverse SNARC effect. In the present study, we investigated whether SNAs are influenced not only by reading direction, but also by cultural directional preferences such as drawing lines, arranging objects, imagining objects (i.e., rightward or leftward facing), or representing events in time (i.e., mentally representing the past/future on the left/right, respectively). To test this hypothesis, we measured the cultural directional preferences and the SNARC effect across three cultures in an online setup; German, Turkish, and Iranian. LR preferences in the Cultural Directional Preferences Questionnaire were most prominent in German participants, intermediate in Turkish participants, and least prominent in Iranian participants. In line with this, the LR SNARC effect was strongest in German, intermediate in Turkish, and weakest (but not RL) in Iranian culture. These findings suggest that cultural directional preferences are involved in the emergence of adult SNAs in addition to the reading direction., Competing Interests: Declarations. Conflict of Interest: The authors declare no competing interests., (© 2024. The Author(s).)

Research on arithmetic uses different experimental paradigms. So far, it is unclear whether these different paradigms lead to the same effects or comparable effect sizes. Therefore, this study explores how different experimental paradigms influence mental arithmetic performance, focusing on understanding the potential differences and similarities in cognitive processes between paradigms. Six paradigms were systematically compared: decision paradigms (verification, forced-choice, delayed forced-choice) and production paradigms (written production, verbal-keyboard production, and simple verbal production). The results show consistent arithmetic effects related to operation (addition vs. subtraction) and task difficulty (with or without carry/borrow) across all paradigms, particularly in reaction time measures. However, accuracy varied between paradigms, with verbal-keyboard production and simple verbal production paradigms showing higher effect sizes for accuracy measures. These findings underscore the importance of considering each paradigm's specific demands and characteristics in arithmetic research, suggesting that paradigm selection can influence the observed outcomes. Our study provides critical methodological insights that can guide future research in the design and interpretation of arithmetic tasks, enhancing the reliability and ecological validity of findings in numerical cognition., Competing Interests: Declaration of competing interest The authors declare no conflicts of interest., (Copyright © 2024. Published by Elsevier B.V.)

Neurodegenerative diseases such as Parkinson's disease (PD) have a huge impact on patients, caregivers, and the health care system. Until now, 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 mechanisms of both primary and secondary dyscalculia. The current study systematically investigated 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 consisted of patients with a diagnosis of PD, according to consensus guidelines, and healthy controls. PD patients were stratified into patients with normal cognition (PD-NC) or mild cognitive impairment (level I-PD-MCI based on cognitive screening). Basic number processing was assessed using transcoding, number line estimation, and (non-) symbolic number magnitude comparison tasks. Discriminant analysis was employed to assess whether basic number processing tasks can differentiate between a healthy control group and both PD groups. All participants were subjected to a comprehensive numerical and a neuropsychological test battery, as well as sociodemographic and clinical measures. Results indicate a profile of preserved (verbal representation) and impaired (magnitude representation, place × value activation) function in PD-MCI, hinting at basal ganglia dysfunction affecting numerical cognition in PD. Numerical deficits could not be explained by domain-general cognitive impairments, so that future research needs to incorporate domain-specific tasks of sufficient difficulty., (© 2024 The Author(s). Journal of Neuroscience Research published by Wiley Periodicals LLC.)

Introduction: Despite having sufficient formal education, a large group of people cannot complete everyday tasks like reading, writing, or making basic calculations. Regarding reading, millions of people are not able to understand more complex texts despite the ability to read simple words or sentences; they have low literacy skills. Even though this problem has been known for decades, the causes and predictors of their poor reading comprehension skills are not fully explored. Socioeconomic, sociodemographic, and reading-related (i.e., linguistic) factors, especially of English-speaking participants and thus users of an opaque orthography, were often assessed. The goal of this study was to examine which linguistic, domain-general, or numerical factors predict substandard complex text reading as the core symptom of low literacy skills in adulthood., Methods: To this end, we assessed a group of German-speaking participants-users of a transparent orthography-who are at risk for complex text reading deficits., Results: The results indicated that linguistic variables (reduced word/pseudoword reading, weaker oral semantic and grammatical comprehension), working memory, and age predicted lower performance in text comprehension. This model explained 73% of the total variance, indicating that most of the deficits in complex text reading can be explained by a group of basic underlying linguistic and domain-general factors., Discussion: We conclude that interventions for adults with low literacy skills and others at risk for complex text reading deficits should address word/pseudoword reading and focus on both written and oral comprehension., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The author(s) declared that they were an editorial board member of Frontiers, at the time of submission. This had no impact on the peer review process and the final decision., (Copyright © 2024 Vágvölgyi, Sahlender, Schröter, Nagengast, Dresler, Schrader and Nuerk.)

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 (M age  = 6.48 years, SD = 0.35) completed a finger-based training (18 sessions of ∼ 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., (Copyright © 2024 The Author(s). Published by Elsevier Inc. All rights reserved.)

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., Competing Interests: Declaration of competing interest The authors declare no conflicts of interest with the content of this article., (Copyright © 2024 The Author(s). Published by Elsevier B.V. All rights reserved.)

While general cognitive skills decline during aging, numerical skills seem to be mainly preserved. Such skills are essential for an independent life up to old age, e.g., when dealing with money or time. Operating with numbers usually requires number magnitude and place-value processing. The question is whether these processes are negatively affected by aging due to the general cognitive decline or positively affected due to lifelong experience with numbers. Therefore, we investigated age-related changes in the distance and compatibility effects in single-digit, two-digit, and four-digit number comparison. On the one hand, older adults took longer for number processing and showed a smaller distance effect, indicating altered number magnitude representations. On the other hand, older adults were better in place-value processing as indicated by a smaller compatibility effect than in younger adults. We conclude that aging differentially affects basic numerical skills., (© 2024. The Author(s).)

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., (Copyright © 2024 International Federation of Clinical Neurophysiology. Published by Elsevier B.V. All rights reserved.)

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., (© 2024 The Authors. European Journal of Neuroscience published by Federation of European Neuroscience Societies and John Wiley & Sons Ltd.)

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., (© 2023. The Author(s).)

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., Competing Interests: Declaration of competing interest Authors declare no conflict of interest., (Copyright © 2023 The Authors. Published by Elsevier B.V. All rights reserved.)

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., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Bar-Kochva, Vágvölgyi, Schrader and Nuerk.)

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., (Copyright © 2023 The Authors. Published by Elsevier B.V. All rights reserved.)

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., Competing Interests: TS and HB are employees of Dopavision GmbH. HB is supported by and has financial interest in Dopavision GmbH. Remaining authors have no competing interest. This does not alter our adherence to PLOS ONE policies on sharing data and materials., (Copyright: © 2023 Schilling et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Background and Objectives: One-third of Parkinson disease (PD) patients with PD-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 quotient (cut-off ≥1), indicating more cognitive than motor-driven IADL impairment, defined cognitive IADL impairment status at baseline. Hazard ratios (HRs) 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 reassessed. 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 the 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 nonmotor burden, worse cognitive performance, and more severe IADL progression over the study period., Discussion: 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 the 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 MCI to dementia among patients with Parkinson disease., (Copyright © 2022 The Author(s). Published by Wolters Kluwer Health, Inc. on behalf of the American Academy of Neurology.)

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., (© 2022 The Authors. Annals of the New York Academy of Sciences published by Wiley Periodicals LLC on behalf of New York Academy of Sciences.)

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., (© 2022. The Author(s).)

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.

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., (© 2022. The Author(s).)

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., (© 2021 The Authors. Journal of Neuroscience Research published by Wiley Periodicals LLC.)

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.

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., Competing Interests: This study received funding from Janssen Research and Development, a division of Janssen Pharmaceutica N.V. The study is purely precompetitive. The funder was not involved in the study design and data collection. Additionally, the funder was not involved in the current analysis, interpretation of data, the writing of this article, or the decision to submit it for publication. The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Loenneker, Becker, Nussbaum, Nuerk and Liepelt-Scarfone.)

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.

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., (Copyright © 2020 Nemati, Gawrilow, Nuerk and Kühnhausen.)

Evidence from multiple studies conducted in the past few decades converges on the conclusion that numerical properties can be associated with specific directions in space. Such spatial-numerical associations (SNAs), as a signature of elementary number processing, seem to be a likely correlate of math skills. Nevertheless, almost three decades of research on the spatial-numerical association of response codes (SNARC) effect, the hallmark of SNAs, has not provided conclusive results on whether there is a relation with math skills. Here, going beyond reviewing the existing literature on the topic, we try to answer a more fundamental question about why the SNARC effect should (and should not) be related to math skills. We propose a multiroute model framework for a SNARC-math skills relationship. We conclude that the relationship is not straightforward and that several other factors should be considered, which under certain circumstances or in certain groups can cause effects of opposite directions. The model can account for conflicting results, and thus may be helpful for deriving predictions in future studies., (© 2020 The Authors. Annals of the New York Academy of Sciences published by Wiley Periodicals, LLC on behalf of New York Academy of Sciences.)

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.

It is widely accepted that finger and number representations are associated: many correlations (including longitudinal ones) between finger gnosis/counting and numerical/arithmetical abilities have been reported. However, such correlations do not necessarily imply causal influence of early finger-number training; even in longitudinal designs, mediating variables may be underlying such correlations. Therefore, we investigated whether there may be a causal relation by means of an extensive experimental intervention in which the impact of finger-number training on initial arithmetic skills was tested in kindergarteners to see whether they benefit from the intervention even before they start formal schooling. The experimental group received 50 training sessions altogether for 10 weeks on a daily basis. A control group received phonology training of a similar duration and intensity. All children improved in the arithmetic tasks. To our surprise and contrary to most accounts in the literature, the improvement shown by the experimental training group was not superior to that of the active control group. We discuss conceptual and methodological reasons why the finger-number training employed in this study did not increase the initial arithmetic skills beyond the unspecific effects of the control intervention., (Copyright © 2020 Schild, Bauch and Nuerk.)

Functional lateralization is established for various cognitive functions, but was hardly ever investigated for arithmetic processing. Most neurocognitive models assume a central role of the bilateral intraparietal sulcus (IPS) in arithmetic processing and there is some evidence for more pronounced left-hemispheric activation for symbolic arithmetic. However, evidence was mainly obtained by studies in right-handers. Therefore, we conducted a functional near-infrared spectroscopy (fNIRS) study, in which IPS activation of left-handed adults was compared to right-handed adults in a symbolic approximate calculation task. The results showed that left-handers had a stronger functional right-lateralization in the IPS than right-handers. This finding has important consequences, as the bilateral IPS activation pattern for arithmetic processing seems to be shaped by functional lateralization and thus differs between left- and right-handers. We propose three possible accounts for the observed functional lateralization of arithmetic processing.

Symbolic magnitude comparison is one of the most well-studied cognitive processes in research on numerical cognition. However, while the cognitive mechanisms of symbolic magnitude processing have been intensively studied, previous studies have paid less attention to individual differences influencing symbolic magnitude comparison. Employing a two-digit number comparison task in an online setting, we replicated previous effects, including the distance effect, the unit-decade compatibility effect, and the effect of cognitive control on the adaptation to filler items, in a large-scale study in 452 adults. Additionally, we observed that the most influential individual differences were participants' first language, time spent playing computer games and gender, followed by reported alcohol consumption, age and mathematical ability. Participants who used a first language with a left-to-right reading/writing direction were faster than those who read and wrote in the right-to-left direction. Reported playing time for computer games was correlated with faster reaction times. Female participants showed slower reaction times and a larger unit-decade compatibility effect than male participants. Participants who reported never consuming alcohol showed overall slower response times than others. Older participants were slower, but more accurate. Finally, higher grades in mathematics were associated with faster reaction times. We conclude that typical experiments on numerical cognition that employ a keyboard as an input device can also be run in an online setting. Moreover, while individual differences have no influence on domain-specific magnitude processing-apart from age, which increases the decade distance effect-they generally influence performance on a two-digit number comparison task.

The Spatial-Numerical Association of Response Codes (SNARC) effect (i.e., faster reactions to small/large numbers on the left-/right-hand side) is usually observed along with the linguistic Markedness of Response Codes (MARC) effect-that is, faster left-/right-hand responses to odd/even numbers. The SNARC effect is one of the most thoroughly investigated phenomena in numerical cognition. However, almost all SNARC and MARC studies to date were conducted with sample sizes smaller than 100. Here we report on a study with 1,156 participants from various linguistic and cultural backgrounds performing a typical parity judgment task. We investigated whether (1) the SNARC and MARC effects can be observed in an online setup, (2) the properties of these effects observed online are similar to those observed in laboratory setups, (3) the effects are reliable, and (4) they are valid. We found robust SNARC and MARC effects. Their magnitude and reliabilities were comparable to values previously reported in in-lab studies. Furthermore, we reproduced commonly observed validity correlations of the SNARC and MARC effects. Namely, SNARC and MARC correlated with mean reaction times and intraindividual variability in reaction times. Additionally, we found interindividual differences in the SNARC and MARC effects (e.g., finger-counting routines for the SNARC and handedness for the MARC). Large-scale testing via web-based data acquisition not only produces SNARC and MARC effects and validity correlations similar to those from small, in-lab studies, but also reveals substantial insights with regard to interindividual differences that usually cannot be revealed in the offline laboratory, due to power considerations.

Some individuals experience more difficulties with math than others, in particular when arithmetic problems get more complex. Math ability, on one hand, and arithmetic complexity, on the other hand, seem to partly share neural underpinnings. This study addresses the question of whether this leads to an interaction of math ability and arithmetic complexity for multiplication and division on behavioral and neural levels. Previously screened individuals with high and low math ability solved multiplication and division problems in a written production paradigm while brain activation was assessed by combined functional near-infrared spectroscopy (fNIRS) and electroencephalography (EEG). Arithmetic complexity was manipulated by using single-digit operands for simple multiplication problems and operands between 2 and 19 for complex multiplication problems and the corresponding division problems. On the behavioral level, individuals with low math ability needed more time for calculation, especially for complex arithmetic. On the neural level, fNIRS results revealed that these individuals showed less activation in the left supramarginal gyrus (SMG), superior temporal gyrus (STG) and inferior frontal gyrus (IFG) than individuals with high math ability when solving complex compared to simple arithmetic. This reflects the greater use of arithmetic fact retrieval and also the more efficient processing of arithmetic complexity by individuals with high math ability. Oscillatory EEG analysis generally revealed theta and alpha desynchronization with increasing arithmetic complexity but showed no interaction with math ability. Because of the discovered interaction for behavior and brain activation, we conclude that the consideration of individual differences is essential when investigating the neurocognitive processing of arithmetic.

In recent research, a systematic association of musical pitch with space has been described in the so-called Spatial-Pitch-Association-of-Response Codes-effect (SPARC). Typically, high pitch is associated with upper/right and low pitch with lower/left space. However, a theoretical classification of these associations regarding their experiential sources is difficult. Therefore, we applied a theoretical framework of numerical cognition classifying similar Space-Associated Response Codes (SARC) effects according to their groundedness, embodiedness and situatedness. We tested these attributes with a group of non-musicians and with a group of highly skilled cello players playing high tones with lower hand positions (i.e., reverse SPARC alignment) in a standard SPARC context of a piano and a reversed SPARC context of a cello. The results showed that SPARC is grounded, in general. However, for cello player SPARC is also situated and embodied. We conclude that groundedness, embodiedness and situatedness provide general characteristics of mapping cognitive representations to space.

Previous research has proposed that the approximate number system (ANS) constitutes a building block for later mathematical abilities. Therefore, numerous studies investigated the relationship between ANS acuity and mathematical performance, but results are inconsistent. Properties of the experimental design have been discussed as a potential explanation of these inconsistencies. In the present study, we investigated the influence of set size and presentation duration on the association between non-symbolic magnitude comparison and math performance. Moreover, we focused on strategies reported as an explanation for these inconsistencies. In particular, we employed a non-symbolic magnitude comparison task and asked participants how they solved the task. We observed that set size was a significant moderator of the relationship between non-symbolic magnitude comparison and math performance, whereas presentation duration of the stimuli did not moderate this relationship. This supports the notion that specific design characteristics contribute to the inconsistent results. Moreover, participants reported different strategies including numerosity-based, visual, counting, calculation-based, and subitizing strategies. Frequencies of these strategies differed between different set sizes and presentation durations. However, we found no specific strategy, which alone predicted arithmetic performance, but when considering the frequency of all reported strategies, arithmetic performance could be predicted. Visual strategies made the largest contribution to this prediction. To conclude, the present findings suggest that different design characteristics contribute to the inconsistent findings regarding the relationship between non-symbolic magnitude comparison and mathematical performance by inducing different strategies and additional processes.

Most studies have investigated brain activation changes after the course of arithmetic learning, and the question remains whether these changes are detectable during the course of learning, i.e., before memory consolidation. Twenty-four fifth graders solved multiplication problems while ongoing electroencephalography (EEG) was recorded. The arithmetic training revealed reduced errors together with a power increase in theta (4-7 Hz) but not in lower alpha (8-10 Hz) or upper alpha (10-13 Hz) bands. We conclude that increases in theta power subserved a shift from slow, procedural strategies to more efficient, automated procedural and retrieval strategies, which led to more efficient performance.

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).

According to theories of embodied numerosity, processing of numerical magnitude is anchored in bodily experiences. In particular, spatial representations of number interact with movement in physical space, but it is still unclear whether the extent of the movement is relevant for this interaction. In this study, we compared spatial-numerical associations over response movements of differing spatial expansion. We expected spatial-numerical effects to increase with the extent of physical response movements. In addition, we hypothesized that these effects should be influenced by whether or not a spatial representation of numbers was presented. Adult participants performed two tasks: a magnitude classification (comparing numbers to the fixed standard 5), from which we calculated the Spatial Numerical Association of Response Codes (SNARC) effect; and a magnitude comparison task (comparing two numbers against each other), from which we calculated a relative numerical congruity effect (NCE), which describes that when two relatively small numbers are compared, responses to the smaller number are faster than responses to the larger number; and vice versa for large numbers. A SNARC effect was observed across all conditions and was not influenced by response movement extent but increased when a number line was presented. In contrast, an NCE was only observed when no number line was presented. This suggests that the SNARC effect and the NCE reflect two different processes. The SNARC effect seems to represent a highly automated classification of numbers as large or small, which is further emphasized by the presentation of a number line. In contrast, the NCE likely results from participants not only classifying numbers as small or large, but also processing their relative size within the relevant section of their mental number line representation. An additional external presentation of a number line might interfere with this process, resulting in overall slower responses. This study follows up on previous spatial-numerical training studies and has implications for future spatial-numerical trainings. Specifically, similar studies with children showed contrasting results, in that response format but not number line presentation influenced spatial-numerical associations. Accordingly, during development, the relative relevance of physical experiences and presentation format for spatial-numerical associations might change.

A strong link between bodily activity and number processing has been established in recent years. Although numerous observations indicate that adults use finger counting (FC) in various contexts of everyday life for different purposes, existing knowledge of FC routines and their use is still limited. In particular, it remains unknown how stable the (default) FC habits are over time and how flexible they can be. To investigate these questions, 380 Polish participants completed a questionnaire on their FC routines, the stability of these routines, and the context of FC usage, preceded by the request to count on their fingers from 1 to 10. Next, the test-retest stability of FC habits was examined in 84 participants 2 months following the first session. To the best of our knowledge, such a study design has been adopted for the first time. The results indicate that default FC routines of the majority of participants (75%) are relatively stable over time. At the same time, FC routines can flexibly adapt according to the situation (e.g., when holding an object). As regards prevalence, almost all participants, in line with previous findings on Western individuals, declared starting from the closed palm and extending consecutive fingers. Furthermore, we observed relations between FC preferences and handedness (more left-handers start from the left hand) and that actual finger use is still widespread in healthy adults for a variety of activities (the most prevalent uses of FC are listing elements, presenting arguments and plans, and calendar calculations). In sum, the results show the practical relevance of FC in adulthood, the relative stability of preferences over time along with flexible adaptation to a current situation, as well as an association of FC routines with handedness. Taken together our results suggest that FC is the phenomenon, which is moderated or mediated by multiple embodied factors., Competing Interests: The authors declare that they have no competing interests.

Rumination is a perseverative thinking style that is associated with adverse mental and physical health. Stressful situations have been considered as a trigger for this kind of thinking. Until today, there are mixed findings with respect to the relations of functional connectivity (FC) and rumination. The study at hand aimed to investigate, in how far high and low ruminators would show elevated levels of state rumination after a stress induction and if these changes would show corresponding changes in FC in the cognitive control network (CCN) and dorsal attention network (DAN). 23 high and 22 low trait ruminators underwent resting-state measurements before and after a stress induction with the Trier Social Stress Test (TSST). Changes in rsFC through the TSST were measured with functional near-infrared spectroscopy within and between regions of the CCN. Stress successfully induced state rumination in both groups but stronger in the high trait ruminators. High trait ruminators showed elevated FC within the CCN at baseline, but attenuated increase in FC following the TSST. Increases in FC correlated negatively with state rumination. A lack of FC reactivity within the CCN in high ruminators might reflect reduced network integration between brain regions necessary for emotion regulation and cognitive control.

To investigate whether participants can activate only one spatially oriented number line at a time or multiple number lines simultaneously, they were asked to solve a unit magnitude comparison task (unit smaller/larger than 5) and a parity judgment task (even/odd) on two-digit numbers. In both these primary tasks, decades were irrelevant. After some of the primary task trials (randomly), participants were asked to additionally solve a secondary task based on the previously presented number. In Experiment 1, they had to decide whether the two-digit number presented for the primary task was larger or smaller than 50. Thus, for the secondary task decades were relevant. In contrast, in Experiment 2, the secondary task was a color judgment task, which means decades were irrelevant. In Experiment 1, decades' and units' magnitudes influenced the spatial association of numbers separately. In contrast, in Experiment 2, only the units were spatially associated with magnitude. It was concluded that multiple number lines (one for units and one for decades) can be activated if attention is focused on multiple, separate magnitude attributes.

Spatial attention in adults is characterized by systematic asymmetries across all three spatial dimensions. These asymmetries are evident when participants bisect horizontal, vertical, or radial lines and misplace their midpoints to the left, the top, or far from the body, respectively. However, bisection errors are rarely examined during early childhood. In this study, we examined the development of spatial-attentional asymmetries in three-dimensional (3D) space by asking preschool children (aged 3-6 years) to bisect horizontal, vertical, and radial lines. Children erred to the left with horizontal lines and to the top with vertical lines, consistent with the pattern reported in adults. These biases got stronger with age and were absent in the youngest preschoolers. However, by controlling for a possible failure in hitting the line, we observed an additional unpredicted pattern: Children's pointing systematically deviated away from the line to an empty space on its left side (for vertical and radial lines) or above it (for horizontal lines). Notably, this task-irrelevant deviation was pronounced in children as young as 3 or 4 years. We conclude that asymmetries in spatial-attentional functions should be measured not only in task-relevant dimensions but also in task-irrelevant dimensions because the latter may reveal biases in very young children not typically observed in task-relevant measures., (Copyright © 2018 Elsevier Inc. All rights reserved.)

Mathematical abilities are essential for an individual, as they predict career prospects among many other abilities. However, little is known about whether neural correlates of arithmetic problem difficulty differ between individuals with high and low math ability. For instance, the difficulty of two-digit addition and subtraction increases whenever a carry or borrow operation is required. Therefore, we systematically investigated the spatial and temporal neural correlates of the carry and borrow effects for high and low performers in a written production paradigm using combined functional near-infrared spectroscopy (fNIRS) and event-related potential (ERP) measurements. Effects of arithmetic difficulty interacted with an individual's math ability. High performers showed increased frontal activation especially in the left inferior frontal gyrus associated with the carry and borrow effects, whereas low performers did not. Furthermore, high and low performers even differed in their early processing of the borrow effect, as reflected by differences in slow waves at 1000-1500 ms at frontal sites. We conclude that the processing of arithmetic difficulty relies on an individual's mathematical ability, and suggest that individual differences should be taken into account when investigating mental arithmetic in an ecologically valid assessment.

Numerical categories such as parity, i.e., being odd or even, have frequently been shown to influence how particular numbers are processed. Mathematically, number parity is defined categorically. So far, cognitive, and psychological accounts have followed the mathematical definition and defined parity as a categorical psychological representation as well. In this manuscript, we wish to test the alternative account that cognitively, parity is represented in a more gradual manner such that some numbers are represented as "more odd" or "more even" than other odd or even numbers, respectively. Specifically, parity processing might be influenced by more specific properties such as whether a number is a prime, a square number, a power of 2, part of a multiplication table, divisible by 4 or by 5, and many others. We suggest that these properties can influence the psychologically represented parity of a number, making it more or less prototypical for odd- or evenness. In the present study, we tested the influence of these numerical properties in a bimanual parity judgment task with auditorily presented two-digit numbers. Additionally, we further investigated the interaction of these numerical properties with linguistic factors in three language groups (English, German, and Polish). Results show significant effects on reaction times of the congruity of parity status between decade and unit digits, even if numerical magnitude and word frequency are controlled. We also observed other effects of the above specific numerical properties, such as multiplication attributes, which facilitated or interfered with the speed of parity judgment. Based on these effects of specific numerical properties we proposed and elaborated a parity continuum account. However, our cross-lingual study also suggests that parity representation and/or access seem to depend on the linguistic properties of the respective language or education and culture. Overall, the results suggest that the "perceived" parity is not the same as objective parity, and some numbers are more prototypical exemplars of their categories.