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.

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.

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.

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.

Individual differences influence two-digit number processing, but not their analog magnitude processing: a large-scale online study.

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.

Set size influences the relationship between ANS acuity and math performance: a result of different strategies?

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.

Music-space associations are grounded, embodied and situated: examination of cello experts and non-musicians in a standard tone discrimination task.

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.

The SNARC and MARC effects measured online: Large-scale assessment methods in flexible cognitive effects.

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.

Cortical hemodynamic changes during the Trier Social Stress Test: An fNIRS study.

The study of the stress response has been of great interest in the last decades due to its relationship to physical and mental health. Along with the technological progress in the neurosciences, different methods of stress induction have been developed for the special requirements regarding the acquisition of neuroimaging data. However, these paradigms often differ from ecologically valid stress inductions such as the Trier Social Stress Test (TSST) in substantial ways. In the study at hand, we used the rather robust optical imaging method of functional Near-infrared Spectroscopy (fNIRS) to assess brain activation during the TSST and two non-stressful control conditions. Additionally, we measured other stress parameters including the cortisol response and subjective stress ratings. As expected we found significant increases in subjective and physiological stress measures during the TSST in comparison to the baseline and control conditions. We found higher activation in parts of the cognitive control network (CCN) and dorsal attention network (DAN) - comprising the dorsolateral prefrontal cortex, the inferior frontal gyrus and superior parietal cortex - during the performance of the TSST in comparison to the control conditions. Further, calculation errors during the TSST as well as subjective and physiological stress parameters correlated significantly with the activation in the CCN. Our study confirms the validity of previous neuroimaging data obtained from adapted stress procedures by providing cortical activation data during a classical stress induction paradigm (i.e., the TSST) for the first time.

Reduction of implicit cognitive bias with cathodal tDCS to the left prefrontal cortex.

Implicit associations can interfere with cognitive operations and behavioral decisions without direct intention. Enhancement of neural activity with anodal transcranial direct current stimulation (tDCS) was proposed to reduce implicit associations by means of improved cognitive control. However, a targeted reduction of distractive implicit associations by inhibitory cathodal tDCS, recently shown in spatial-numerical associations, provides an interesting alternative approach to support goal-directed behavior with transcranial brain stimulation. To test this rationale with a sham-controlled cross-over design, a standardized Implicit Association Test (IAT) was performed by 24 healthy participants parallel to 1 mA cathodal or sham tDCS to the left prefrontal cortex. In this double-classification task, insect versus flower pictures and negative versus positive words are mapped together onto two shared response keys with crossed response assignments in separate blocks. Responses were faster when insect + negative and flower + positive stimuli required the same answer (IAT effect). Most critically, the IAT effect was reduced during cathodal tDCS as compared to sham stimulation. Thus, results are consistent with the proposed stimulation rationale, with previous observations, and complementary to previous studies using different tDCS configurations.

The neural correlates of mental arithmetic in adolescents: a longitudinal fNIRS study.

BACKGROUND: Arithmetic processing in adults is known to rely on a frontal-parietal network. However, neurocognitive research focusing on the neural and behavioral correlates of arithmetic development has been scarce, even though the acquisition of arithmetic skills is accompanied by changes within the fronto-parietal network of the developing brain. Furthermore, experimental procedures are typically adjusted to constraints of functional magnetic resonance imaging, which may not reflect natural settings in which children and adolescents actually perform arithmetic. Therefore, we investigated the longitudinal neurocognitive development of processes involved in performing the four basic arithmetic operations in 19 adolescents. By using functional near-infrared spectroscopy, we were able to use an ecologically valid task, i.e., a written production paradigm. RESULTS: A common pattern of activation in the bilateral fronto-parietal network for arithmetic processing was found for all basic arithmetic operations. Moreover, evidence was obtained for decreasing activation during subtraction over the course of 1 year in middle and inferior frontal gyri, and increased activation during addition and multiplication in angular and middle temporal gyri. In the self-paced block design, parietal activation in multiplication and left angular and temporal activation in addition were observed to be higher for simple than for complex blocks, reflecting an inverse effect of arithmetic complexity. CONCLUSIONS: In general, the findings suggest that the brain network for arithmetic processing is already established in 12-14 year-old adolescents, but still undergoes developmental changes.

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

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

Visuospatial biases in preschool children: Evidence from line bisection in three-dimensional space.

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.

Increased arithmetic complexity is associated with domain-general but not domain-specific magnitude processing in children: A simultaneous fNIRS-EEG study.

The investigation of the neural underpinnings of increased arithmetic complexity in children is essential for developing educational and therapeutic approaches and might provide novel measures to assess the effects of interventions. Although a few studies in adults and children have revealed the activation of bilateral brain regions during more complex calculations, little is known about children. We investigated 24 children undergoing one-digit and two-digit multiplication tasks while simultaneously recording functional near-infrared spectroscopy (fNIRS) and electroencephalography (EEG) data. FNIRS data indicated that one-digit multiplication was associated with brain activity in the left superior parietal lobule (SPL) and intraparietal sulcus (IPS) extending to the left motor area, and two-digit multiplication was associated with activity in bilateral SPL, IPS, middle frontal gyrus (MFG), left inferior parietal lobule (IPL), and motor areas. Oscillatory EEG data indicated theta increase and alpha decrease in parieto-occipital sites for both one-digit and two-digit multiplication. The contrast of two-digit versus one-digit multiplication yielded greater activity in right MFG and greater theta increase in frontocentral sites. Activation in frontal areas and theta band data jointly indicate additional domain-general cognitive control and working memory demands for heightened arithmetic complexity in children. The similarity in parietal activation between conditions suggests that children rely on domain-specific magnitude processing not only for two-digit but-in contrast to adults-also for one-digit multiplication problem solving. We conclude that in children, increased arithmetic complexity tested in an ecologically valid setting is associated with domain-general processes but not with alteration of domain-specific magnitude processing.

Physiological threat responses predict number processing.

Being able to adequately process numbers is a key competency in everyday life. Yet, self-reported negative affective responses towards numbers are known to deteriorate numerical performance. Here, we investigated how physiological threat responses predict numerical performance. Physiological responses reflect whether individuals evaluate a task as exceeding or matching their resources and in turn experience either threat or challenge, which influences subsequent performance. We hypothesized that, the more individuals respond to a numerical task with physiological threat, the worse they would perform. Results of an experiment with cardiovascular indicators of threat/challenge corroborated this expectation. The findings thereby contribute to our understanding of the physiological mechanism underlying the influence of negative affective responses towards numbers on numerical performance.

Counteracting Implicit Conflicts by Electrical Inhibition of the Prefrontal Cortex.

Cognitive conflicts and distractions by task-irrelevant information often counteract effective and goal-directed behaviors. In some cases, conflicting information can even emerge implicitly, without an overt distractor, by the automatic activation of mental representations. For instance, during number processing, magnitude information automatically elicits spatial associations resembling a mental number line. This spatial-numerical association of response codes (SNARC) effect can modulate cognitive-behavioral performance but is also highly flexible and context-dependent, which points toward a critical involvement of working memory functions. Transcranial direct current stimulation to the PFC, in turn, has been effective in modulating working memory-related cognitive performance. In a series of experiments, we here demonstrate that decreasing activity of the left PFC by cathodal transcranial direct current stimulation consistently and specifically eliminates implicit cognitive conflicts based on the SNARC effect, but explicit conflicts based on visuospatial distraction remain unaffected. This dissociation is polarity-specific and appears unrelated to functional magnitude processing as classified by regular numerical distance effects. These data demonstrate a causal involvement of the left PFC in implicit cognitive conflicts based on the automatic activation of spatial-numerical processing. Corroborating the critical interaction of brain stimulation and neurocognitive functions, our findings suggest that distraction from goal-directed behavior by automatic activation of implicit, task-irrelevant information can be blocked by the inhibition of prefrontal activity.

How to rapidly construct a spatial-numerical representation in preliterate children (at least temporarily).

Spatial processing of numbers has emerged as one of the basic properties of humans' mathematical thinking. However, how and when number-space relations develop is a highly contested issue. One dominant view has been that a link between numbers and left/right spatial directions is constructed based on directional experience associated with reading and writing. However, some early forms of a number-space link have been observed in preschool children who cannot yet read and write. As literacy experience is evidently not necessary for number-space effects, we are searching for other potential sources of this association. Here we propose and test a hypothesis that the number-space link can be quickly constructed in preschool children's cognition on the basis of spatially oriented visuo-motor activities. We trained 3- and 4-year-old children with a non-numerical spatial movement task (left-to-right or right-to-left), where via touch screen children had to move a frog across a pond. After the training, children had to perform a numerosity comparison task. After left-to-right training, we observed a SNARC-like effect (reactions to smaller numbers were faster on the left side, and reactions to larger numbers on the right side), and after right-to-left training a reverse effect. These results are the first to show a causal link between visuo-motor activities and number-space associations in children before they learn to read and write. We argue that simple activities, such as manual games, dominant in a given society, might shape number-space associations in children in a way similar to lifelong reading training.

Finger gnosis predicts a unique but small part of variance in initial arithmetic performance.

Recent studies indicated that finger gnosis (i.e., the ability to perceive and differentiate one's own fingers) is associated reliably with basic numerical competencies. In this study, we aimed at examining whether finger gnosis is also a unique predictor for initial arithmetic competencies at the beginning of first grade-and thus before formal math instruction starts. Therefore, we controlled for influences of domain-specific numerical precursor competencies, domain-general cognitive ability, and natural variables such as gender and age. Results from 321 German first-graders revealed that finger gnosis indeed predicted a unique and relevant but nevertheless only small part of the variance in initial arithmetic performance (∼1%-2%) as compared with influences of general cognitive ability and numerical precursor competencies. Taken together, these results substantiated the notion of a unique association between finger gnosis and arithmetic and further corroborate the theoretical idea of finger-based representations contributing to numerical cognition. However, the only small part of variance explained by finger gnosis seems to limit its relevance for diagnostic purposes.

Processing multi-digit numbers: a translingual eye-tracking study.

The present study aimed at investigating the underlying cognitive processes and language specificities of three-digit number processing. More specifically, it was intended to clarify whether the single digits of three-digit numbers are processed in parallel and/or sequentially and whether processing strategies are influenced by the inversion of number words with respect to the Arabic digits [e.g., 43: dreiundvierzig ("three and forty")] and/or by differences in reading behavior of the respective first language. Therefore, English- and German-speaking adults had to complete a three-digit number comparison task while their eye-fixation behavior was recorded. Replicating previous results, reliable hundred-decade-compatibility effects (e.g., 742_896: hundred-decade compatible because 7 < 8 and 4 < 9; 362_517: hundred-decade incompatible because 3 < 5 but 6 > 1) for English- as well as hundred-unit-compatibility effects for English- and German-speaking participants were observed, indicating parallel processing strategies. While no indices of partial sequential processing were found for the English-speaking group, about half of the German-speaking participants showed an inverse hundred-decade-compatibility effect accompanied by longer inspection time on the hundred digit indicating additional sequential processes. Thereby, the present data revealed that in transition from two- to higher multi-digit numbers, the homogeneity of underlying processing strategies varies between language groups. The regular German orthography (allowing for letter-by-letter reading) and its associated more sequential reading behavior may have promoted sequential processing strategies in multi-digit number processing. Furthermore, these results indicated that the inversion of number words alone is not sufficient to explain all observed language differences in three-digit number processing.