Search

It is debated whether the representation of numbers is endowed with a directional-spatial component so that perceiving small-magnitude numbers triggers leftward shifts of attention and perceiving large-magnitude numbers rightward shifts. Contrary to initial findings, recent investigations have demonstrated that centrally presented small-magnitude and large-magnitude Arabic numbers do not cause leftward and rightward shifts of attention, respectively. Here we verified whether perceiving small or large non-symbolic numerosities (i.e., clouds of dots) drives attention to the left or the right side of space, respectively. In experiment 1, participants were presented with central small (1, 2) vs large-numerosity (8, 9) clouds of dots followed by an imperative target in the left or right side of space. In experiment 2, a central cloud of dots (i.e., five dots) was followed by the simultaneous presentation of two identical dot-clouds, one on the left and one on the right side of space. Lateral clouds were both lower (1, 2) or higher in numerosity (8, 9) than the central cloud. After a variable delay, one of the two lateral clouds turned red and participants had to signal the colour change through a unimanual response. We found that (a) in Experiment 1, the small vs large numerosity of the central cloud of dots did not speed up the detection of left vs right targets, respectively, (b) in Experiment 2, the detection of colour change was not faster in the left side of space when lateral clouds were smaller in numerosity than the central reference and in the right side when clouds were larger in numerosity. These findings show that perceiving non-symbolic numerosity does not cause automatic shifts of spatial attention and suggests no inherent association between the representation of numerosity and that of directional space.

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.

Here we report the results of a speeded relative quantity task with Chinese participants. On each trial a single numeral (the probe) was presented and the instructions were to respond as to whether it signified a quantity less than or greater than five (the standard). In separate blocks of trials, the numerals were presented either in Mandarin or in Arabic number formats. In addition to the standard influence of numerical distance, a significant predictor of performance was the degree of physical similarity between the probe and the standard as depicted in Mandarin. Additionally, competing effects of physical similarity, defined in terms of the Arabic number format, were also found. Critically the size of these different effects of physical similarity varied systematically across individuals such that larger effects of one compensated for smaller effects of the other. It is argued that the data favor accounts of processing that assume that different number formats access different format-specific representations of quantities. Moreover, for Chinese participants the default is to translate numerals into a Mandarin format prior to accessing quantity information. The efficacy of this translation process is itself influenced by a competing tendency to carry out a translation into Arabic format.

By analyzing longitudinal data from the start to the end of primary education, we aimed to investigate whether symbolic numerical magnitude processing at the start of primary education predicted arithmetic at the end, and whether arithmetic at the start of primary education predicted later symbolic numerical magnitude processing skills at the end. In the first grade (start) and sixth grade (end) of primary education, the same group of children’s symbolic numerical magnitude processing skills and arithmetic competence were assessed. We were particularly interested in exploring the direction of the association between symbolic numerical magnitude processing and arithmetic and observed that this association was bi-directional across primary education. Symbolic numerical magnitude processing skills in first grade predicted arithmetic in sixth grade; but also the reversed direction turned out significant: Early arithmetic predicted later symbolic numerical magnitude processing skills. Both directions remained significant after controlling for motor speed and nonverbal reasoning. Critically, when controlling for auto-regressive effects of prior abilities, the symbolic comparison-arithmetic association was no longer significant, the reversed direction became marginally significant. This suggests that children’s arithmetic development across primary education to some extent strengthens their ability to process the numerical meaning of Arabic digits. ispartof: Journal of Numerical Cognition vol:5 issue:3 pages:358-370 status: published

In four experiments, we explore the role that verbal WM plays in numerical comparison. Experiment 1 demonstrates that verbal WM load differentially impacts the two most common variants of numerical comparison tasks, evidenced by distinct modulation of the size of the numerical distance effect (NDE). Specifically, when comparing one Arabic digit to a standard, the size of the NDE increases as a function of increased verbal WM load; however, when comparing two simultaneously presented Arabic digits, the size of the NDE decreases (and here is eliminated) as a function of an increased verbal WM load. Experiment 2, using the same task structure but different stimuli (physical size judgments), provides support for the notion that this pattern of results is unique to tasks employing numerical stimuli. Experiment 3 demonstrates that the patterns observed in Experiment 1 are not an artifact of the stimulus pairs used. Experiment 4 provides evidence that the differing pattern of results observed between Experiment 1 and Experiment 2 are due to differences in stimuli (numerical vs. non-numerical) rather than to other differences between tasks. These results are discussed in terms of current theories of numerical comparison.

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. 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.

Arabic and Hindi handwritten numeral detection and classification is one of the most popular fields in the automation research. It has many applications in different fields. Automatic detection and automatic classification of handwritten numerals have persistently received attention from researchers around the world due to the robotic revolution in the past decades. Therefore, many great efforts and contributions have been made to provide highly accurate detection and classification methodologies with high performance. In this paper, we propose a two-stage methodology for the detection and classification of Arabic and Hindi handwritten numerals. The classification was based on convolutional neural networks (CNNs). The first stage of the methodology is the detection of the input numeral to be either Arabic or Hindi. The second stage is to detect the input numeral according to the language it came from. The simulation results show very high performance, the recognition rate was close to 100%.

Can children solve Bayesian problems, given that these pose great difficulties even for most adults? We present an ecological framework in which Bayesian intuitions emerge from a match between children's numerical competencies and external representations of numerosity. Bayesian intuition is defined here as the ability to determine the exact Bayesian posterior probability by minds untutored in probability theory or in Bayes' rule. As we show, Bayesian intuitions do not require processing of probabilities or Arabic numbers, but basically the ability to count tokens in icon arrays and to understand what to count. A series of experiments demonstrates for the first time that icon arrays elicited Bayesian intuitions in children as young as second-graders for 22% to 32% of all problems; fourth-graders achieved 50% to 60%. Most surprisingly, icon arrays elicited Bayesian intuitions in children with dyscalculia, a specific learning disorder that has been attributed to genetic causes. These children could solve an impressive 50% of Bayesian problems, a level similar to that of children without dyscalculia. By seventh grade, children solved about two thirds of Bayesian problems with natural frequencies alone, without the additional help of icon arrays. We identify four non-Bayesian rules. On the basis of these results, we propose a common solution for the phylogenetic, the ontogenetic, and the 1970s puzzles in the Bayesian literature and argue for a revision of how to teach statistical thinking. In accordance with recent work on infants' numerical abilities, these findings indicate that children have more numerical ability than previously assumed. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Handwritten signatures widely exist in our daily lives. The main challenge of signal recognition on handwriting is in the development of approaches to obtain information effectively. External mechanical signals can be easily detected by triboelectric nanogenerators which can provide immediate opportunities for building new types of active sensors capable of recording handwritten signals. In this work, we report an intelligent human-machine interaction interface based on a triboelectric nanogenerator. Using the horizontal-vertical symmetrical electrode array, the handwritten triboelectric signal can be recorded without external energy supply. Combined with supervised machine learning methods, it can successfully recognize handwritten English letters, Chinese characters, and Arabic numerals. The principal component analysis algorithm preprocesses the triboelectric signal data to reduce the complexity of the neural network in the machine learning process. Further, it can realize the anticounterfeiting recognition of writing habits by controlling the samples input to the neural network. The results show that the intelligent human-computer interaction interface has broad application prospects in signature security and human-computer interaction.

Highlights • Overlapping neural responses to number discrimination tasks in adults and children. • Ontogenetic maturation of language regions may constrain verbal number processing. • Neural correlates of effortful number discrimination were similar across age groups. • Prefrontal activity attributed to children’s number processing was not replicated. • Results indicative of mature number discrimination abilities around 11 years of age., The triple code model of numerical cognition (TCM) details the neurocognitive mechanisms associated with perceiving and manipulating numerical information in exact symbolic (Arabic digits and number words) and approximate nonsymbolic numerical magnitude (e.g., dot arrays) representation codes. The current study provides a first empirical fMRI-based investigation into neurodevelopmental differences in 30 healthy children’s and 44 healthy adults’ recruitment of neural correlates associated with the Arabic digit, number word, and nonsymbolic magnitude codes. Differences between the two groups were found in cingulate regions commonly associated with domain-general aspects of cognitive control, as opposed to neural correlates of number processing per se. A primary developmental difference was identified in verbal number discrimination, where only adults recruited left-lateralized perisylvian language areas in accordance with the TCM. We therefore call for a revision of the verbal code and a formulation of separate child and adult-specific neurocognitive mechanisms associated with the discrimination of number words. Although further research is necessary, results indicate that numerical discrimination abilities in middle-school-aged children operate close to adult-level maturity. Neurodevelopmental differences may be more apparent in younger children, or on the level of functional network dynamics as opposed to a shift in recruited neural substrates.

Numbers can be presented in different notations and sensory modalities. It is currently debated to what extent these formats overlap onto a single representation. We asked whether such an overlap exists between symbolic numbers represented in two sensory modalities: Arabic digits and Braille numbers. A unique group of sighted Braille readers underwent extensive Braille reading training and was tested in an fMRI repetition-suppression paradigm with tactile Braille digit primes and visual Arabic digit targets. Our results reveal cross-modal priming: compared to repetition of two different quantities (e.g., Braille “5” and Arabic “2”), repetition of the same quantity presented in two modalities (e.g., Braille “5” and Arabic “5”) led to a reduction of activation in several sub-regions of the Intraparietal Sulcus (IPS), a key cortical region for magnitude processing. Thus, in sighted Braille readers, the representations of numbers read by sight and by touch overlap to a degree sufficient to cause repetition suppression. This effect was modulated by the numerical prime-probe distance. Altogether this indicates that the left parietal cortex hosts neural assemblies that are sensitive to numerical information from different notations (number words or Arabic digits) and modalities (tactile and visual).

The ability to choose the larger between two numbers reflects a mature understanding of the magnitude associated with numerical symbols. The present study explores how the knowledge of the number sequence and memory capacity (verbal and visuospatial) relate to number comparison skills while controlling for cardinal knowledge. Preschool children’s (N = 140, Mage‐in‐months = 58.9, range = 41–75) knowledge of the directional property of the counting list as well as the spatial mapping of digits on the visual line were assessed. The ability to order digits on the visual line mediated the relation between memory capacity and number comparison skills while controlling for cardinal knowledge. Beyond cardinality, the knowledge of the (spatial) order of numbers marks the understanding of the magnitude associated with numbers.

Debate continues on whether encoding of symbolic number is grounded in nonsymbolic numerical magnitudes. Nevertheless, fluency of perceiving both number formats, and translating between them, predicts math skills across the life span. Therefore, this study asked if numbers share cortical activation patterns across formats and tasks, and whether neural response to number predicts math-related behaviors. We analyzed patterns of neural activation using 7 Tesla functional magnetic resonance imaging in a sample of 39 healthy adults. Discrimination was successful between numerosities 2, 4, 6, and 8 dots and generalized to activation patterns of the same numerosities represented as Arabic digits in the bilateral parietal lobes and left inferior frontal gyrus (IFG) (and vice versa). This indicates that numerosity-specific neural resources are shared between formats. Generalization was also successful across tasks where participants either identified or compared numerosities in bilateral parietal lobes and IFG. Individual differences in decoding did not relate to performance on a number comparison task completed outside of the scanner, but generalization between formats and across tasks negatively related to math achievement in the parietal lobes. Together, these findings suggest that individual differences in representational specificity within format and task contexts relate to mathematical expertise.

Human adults are faster to respond to small/large numerals with their left/right hand when they judge the parity of numerals, which is known as the SNARC (spatial-numerical association of response codes) effect. It has been proposed that the size of the SNARC effect depends on response latencies. The current study introduced a perceptual orientation task, where participants were asked to judge the orientation of a digit or a frame surrounding the digit. The present study first confirmed the SNARC effect with native Chinese speakers (Experiment 1) using a parity task, and then examined whether the emergence and size of the SNARC effect depended on the response latencies (Experiments 2, 3, and 4) using a perceptual orientation judgment task. Our results suggested that (a) the automatic processing of response-related numerical-spatial information occurred with Chinese-speaking participants in the parity task; (b) the SNARC effect was also found when the task did not require semantic access; and (c) the size of the effect depended on the processing speed of the task-relevant dimension. Finally, we proposed an underlying mechanism to explain the SNARC effect in the perceptual orientation judgment task.

Understanding the cognitive underpinnings of children’s arithmetic development has great theoretical and educational importance. Recent research suggests symbolic and nonsymbolic representations of number influence arithmetic development before and after school entry. We assessed nonverbal ability and general language skills as well as nonsymbolic (numerosity) and symbolic (numeral) comparison skills, counting, and Arabic numeral knowledge (numeral reading, writing, and identification) in preschool children (4 years of age). At 6 years of age, we reassessed nonsymbolic (numerosity) and symbolic (numeral) comparison and arithmetic. A latent variable path model showed that Arabic numeral knowledge (defined by numeral reading, writing, and identification at 4 years of age) was the sole unique predictor of arithmetic at 6 years. We conclude that knowledge of the association between spoken and Arabic numerals is one critical foundation for the development of formal arithmetic.

Historical manuscripts and archival documentation are handwritten texts which are the backbone sources for historical inquiry. Recent developments in the digital humanities field and the need for extracting information from the historical documents have fastened the digitization processes. Cutting edge machine learning methods are applied to extract meaning from these documents. Page segmentation (layout analysis), keyword, number and symbol spotting, handwritten text recognition algorithms are tested on historical documents. For most of the languages, these techniques are widely studied and high performance techniques are developed. However, the properties of Arabic scripts (i.e., diacritics, varying script styles, diacritics, and ligatures) create additional problems for these algorithms and, therefore, the number of research is limited. In this research, we first automatically spotted the Arabic numerals from the very first series of population registers of the Ottoman Empire conducted in the mid-nineteenth century and recognized these numbers. They are important because they held information about the number of households, registered individuals and ages of individuals. We applied a red color filter to separate numerals from the document by taking advantage of the structure of the studied registers (numerals are written in red). We first used a CNN-based segmentation method for spotting these numerals. In the second part, we annotated a local Arabic handwritten digit dataset from the spotted numerals by selecting uni-digit ones and tested the Deep Transfer Learning method from large open Arabic handwritten digit datasets for digit recognition. We achieved promising results for recognizing digits in these historical documents., European Research Council (ERC) Project: "Industrialisation and Urban Growth from the mid-nineteenth century Ottoman Empire to Contemporary Turkey in a Comparative Perspective, 1850-2000" (; UrbanOccupationsOETR); European Union (European Union); Horizon 2020

In some languages the order of tens and units in number words is inverted compared with the symbolic digital notation (e.g., German 23 → “ dreiundzwanzig,” literally: “ three-and-twenty”). In other languages only teen-numbers are inverted (e.g., English 17 → “ seventeen”; Polish 17 → “ siedemnaście” literally “ seventeen”). Previous studies have focused on between group comparisons of inverted and non-inverted languages and showed that number word inversion impairs performance on basic numerical tasks and arithmetic. In two independent experiments, we investigated whether number word inversion affects addition performance within otherwise non-inverted languages (Exp. 1: English, Exp. 2: Polish). In particular, we focused on the influence of inverted ( I; English: teen-numbers ⩾ 13, Polish: numbers 11–19) and non-inverted ( N) summands with sums between 13 and 39. Accordingly, three categories of addition problems were created: N + N, N + I, and I + I with problem size matched across categories. Across both language groups, we observed that problems with results in the 20 and 30 number range were responded to faster when only non-inverted summands were part of the problems as opposed to problems with one or two inverted summands. In line with this, the cost of a carry procedure was the largest for two inverted summands. The results support the notion that both language-specific and language-invariant aspects contribute to addition problem-solving. In particular though, regarding language-specific aspects, the results indicate that inverted number word formation of teens influences place-value processing of Arabic digits even in otherwise non-inverted languages.

There is an ongoing debate concerning how numbers acquire numerical meaning. On the one hand, it has been argued that symbols acquire meaning via a mapping to external numerosities as represented by the approximate number system (ANS). On the other hand, it has been proposed that the initial mapping of small numerosities to the corresponding number words and the knowledge of the properties of counting list, especially the order relation between symbols, lead to the understanding of the exact numerical magnitude associated with numerical symbols. In the present study, we directly compared these two hypotheses in a group of preschool children who could proficiently count (most of the children were cardinal principle knowers). We used a numerosity estimation task to assess whether children have created a mapping between the ANS and the counting list (i.e., ANS-to-word mapping). Children also completed a direction task to assess their knowledge of the directional property of the counting list. That is, adding one item to a set leads to he next number word in the sequence (i.e., successor knowledge) whereas removing one item leads to the preceding number word (i.e., predecessor knowledge). Similarly, we used a visual order task to assess the knowledge that successive and preceding numbers occupy specific spatial positions on the visual number line (i.e., preceding: [?], [13], [14]; successive: [12], [13], [?]). Finally, children's performance in comparing the magnitude of number words and Arabic numbers indexed the knowledge of exact symbolic numerical magnitude. Approximately half of the children in our sample have created a mapping between the ANS and the counting list. Most of the children mastered the successor knowledge whereas few of them could master the predecessor knowledge. Children revealed a strong tendency to respond with the successive number in the counting list even when an item was removed from a set or the name of the preceding number on the number line was asked. Crucially, we found evidence that both the mastering of the predecessor knowledge and the ability to name the preceding number in the number line relate to the performance in number comparison tasks. Conversely, there was moderate/anecdotal evidence for a relation between the ANS-to-word mapping and number comparison skills. Non-rote access to the number sequence relates to knowledge of the exact magnitude associated with numerical symbols, beyond the mastering of the cardinality principle and domain-general factors.

Arabic digits (1–9) are everywhere in our daily lives. These symbols convey various semantic information, and numerate adults can easily extract from them several numerical features such as magnitude and parity. Nonetheless, since most studies used active processing tasks to assess these properties, it remains unclear whether and to what degree the access to magnitude and especially to parity is automatic. Here we investigated with EEG whether spontaneous processing of magnitude or parity can be recorded in a frequency-tagging approach, in which participants are passively stimulated by fast visual sequences of Arabic digits. We assessed automatic magnitude processing by presenting a stream of frequent small digit numbers mixed with deviant large digits (and the reverse) with a sinusoidal contrast modulation at the frequency of 10 Hz. We used the same paradigm to investigate numerical parity processing, contrasting odd digits to even digits. We found significant brain responses at the frequency of the fluctuating change and its harmonics, recorded on electrodes encompassing right occipitoparietal regions, in both conditions. Our findings indicate that both magnitude and parity are spontaneously and unintentionally extracted from Arabic digits, which supports that they are salient semantic features deeply associated to digit symbols in long-term memory., SCOPUS: ar.j, info:eu-repo/semantics/published

Number transcoding is a basic numerical processing task that demands verbal skills during its execution. The goal of this study was to investigate number transcoding ability in children with developmental dyslexia. Twenty-three children with typical development and twenty-six children with developmental dyslexia participated in this study. Results showed that children with dyslexia show a deficit in phonological processing as well as in number transcoding. Repeated-measures analysis of covariance indicated that the dyslexia group presented performance below the average in the number transcoding. Regression analyses indicated that short-term verbal memory, phoneme deletion, rhyme judgment task and automatized naming was a strong predictor of number transcoding difficulties. Children with dyslexia present number transcoding deficits regardless of age and educational level. Resumo A transcodificação numérica é uma tarefa do processamento numérico básico que demanda habilidades verbais durante a sua execução. O objetivo deste estudo foi investigar a habilidade de transcodificação numérica em crianças com dislexia do desenvolvimento. Participaram deste estudo 23 crianças com desenvolvimento escolar típico e 26 crianças com dislexia do desenvolvimento. Os resultados indicaram que crianças com dislexia apresentam um déficit no processamento fonológico e na transcodificação numérica ao longo de todas as séries escolares investigadas aqui. Uma análise de variância de medidas repetidas indicou que o grupo com dislexia apresentou desempenho abaixo da média na transcodificação numérica. Análises de regressão indicaram que a memória de curto prazo verbal, a supressão de fonemas, o julgamento de rimas e a tarefa de nomeação seriada rápida foram fortes preditores das dificuldades encontradas na transcodificação numérica. Crianças com dislexia apresentam déficits de transcodificação numérica independentemente da idade e nível de escolaridade.

The present study investigated the predictive role of spatial skills for arithmetic and number line estimation in kindergarten children (N = 125). Spatial skills are known to be related to mathematical development, but due to the construct’s non-unitary nature, different aspects of spatial skills need to be differentiated. In the present study, a spatial orientation task, a spatial visualization task and visuo-motor integration task were administered to assess three different aspects of spatial skills. Furthermore, we assessed counting abilities, knowledge of Arabic numerals, quantitative knowledge, as well as verbal working memory and verbal intelligence in kindergarten. Four months later, the same children performed an arithmetic and a number line estimation task to evaluate how the abilities measured at Time 1 predicted early mathematics outcomes. Hierarchical regression analysis revealed that children’s performance in arithmetic was predicted by their performance on the spatial orientation and visuo-motor integration task, as well as their knowledge of the Arabic numerals. Performance in number line estimation was significantly predicted by the children’s spatial orientation performance. Our findings emphasize the role of spatial skills, notably spatial orientation, in mathematical development. The relation between spatial orientation and arithmetic was partially mediated by the number line estimation task. Our results further show that some aspects of spatial skills might be more predictive of mathematical development than others, underlining the importance to differentiate within the construct of spatial skills when it comes to understanding numerical development.

What developmental roles do nonsymbolic (e.g., dot arrays) and symbolic (i.e., Arabic numerals) magnitude comparison skills play in children's mathematics? We assessed a large sample in kindergarten, grade 1 and 2 on two well-known nonsymbolic and symbolic magnitude comparison measures. We also assessed children's initial IQ and developing Working Memory (WM) capacities. Results demonstrated that symbolic and nonsymbolic comparison had different developmental trajectories; the first underwent larger developmental improvements. Both skills were longitudinal predictors of children's future mathematical achievement above and beyond IQ and WM. Nonsymbolic comparison was moderately predictive only in kindergarten. Symbolic comparison, however, was a robust and consistent predictor of future mathematics across all three years. It was a stronger predictor compared to nonsymbolic, and its predictive power at the early stages was even comparable to that of IQ. Furthermore, the present results raise several methodological implications regarding the role of different types of magnitude comparison measures.

Background: Based on the studies which have investigated conscious and unconscious processes, simple arithmetic operations such as addition and multiplication can be automatically processed in the brain and affect subsequent responses. However, most studies have focused on addition and multiplication of one-digit numbers. In this research we used subliminal priming paradigm to assess automatic retrieval of subtraction operation for the first time. Objectives: The aim of this study was to use a subliminal priming paradigm in a naming task and investigate the automatic and unconscious processing of the subtraction operation. Research of this kind can help us determine different levels of unconscious and conscious processing in the brain. Materials and Methods: Forty-five graduate student in psychology at the Faculty of Education and Psychology, University of Tabriz (between 18 and 25 years; mean 20.7, SD=2.7) participated in the experiment. For presenting the stimuli, an open-source software (DMDX) was used and presented on a 15-inch monitor. In the experiment, in the congruent condition, the prime was congruent with the target in terms of subtraction calculation result and in the incongruent condition there was no logical connection between the two stimuli. The vocal reaction time (RT) of participants was recorded and paired t-test analysis was conducted for comparison of the two conditions. Results: The data showed that naming the target by the participants is carried out faster when the two stimuli are congruent with each other in terms of the result of the operation. Conclusion: These findings may have implications on the levels of mathematical operations. In conclusion it seems that the calculation of one-digit numbers can happen at the level of simple neuronal circuits and may be carried out without conscious-awareness. The findings confirm the fact that calculating subtraction for one-digit numbers does not require conscious effort and can be processed automatically.

Synesthesia is a neurological phenomenon in which certain types of stimuli elicit involuntary perceptions in an unrelated pathway. A common type of synesthesia is grapheme-color synesthesia, in which the visual perception of letters and numbers stimulates the perception of a specific color. Previous studies have often collected relatively small numbers of grapheme-color associations per synesthete, but the accumulation of a large quantity of data has greater promise for uncovering the mechanisms underlying synesthetic association. In this study, we therefore collected large samples of data from a total of eight synesthetes. All told, we obtained over 1000 synesthetic colors associated with Japanese kanji characters from each of two synesthetes, over 100 synesthetic colors form each of three synesthetes, and about 80 synesthetic colors associated with Japanese hiragana, Latin letters, and Arabic numerals from each of three synesthetes. We then compiled the data into a database, called the KANJI-Synesthetic Colors Database (K-SCD), which has a total of 5122 colors for 483, 46, and 46 Japanese kanji, hiragana, and katakana characters, respectively, as well as for 26 Latin letters and ten Arabic numerals. In addition to introducing the K-SCD, this article demonstrates the database's merits by using two examples, in which two new rules for synesthetic association, "shape similarity" and "synesthetic color clustering, " were found. The K-SCD is publicly accessible ( www.cv.jinkan.kyoto-u.ac.jp/site/uploads/K-SCD.xlsm ) and will be a valuable resource for those who wish to conduct statistical analyses using a rich dataset in order to uncover the rules governing synesthetic association and to understand its mechanisms.

The current study is a first exploration of real-time self-regulation of functional magnetic resonance imaging (fMRI) activation based on several different visual neurofeedback presentations. Six healthy participants were engaged in self-regulation of regional fMRI activation in the posterior parietal cortex (PPC), by performing a mental calculation task. In different MR sessions, feedback was presented in the form of either a thermometer display (in vertical orientation), a circle display (increasing or decreasing in physical size), or a numbers display (Arabic digits). While self-regulation levels did differ between individuals, all six participants were able to significantly up-regulate their PPC activation with all three neurofeedback presentations. In addition to a successful general up-regulation, five out of six participants were furthermore capable of gradual self-regulation to multiple intensity levels. Taken together, the current study is a proof-of-concept demonstration of the feasibility of using multiple visual feedback presentations during gradual self-regulation of regional fMRI activation. Implications for future neurofeedback research and applications are discussed.

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 by 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.

In line with the suggestion that the strength of the spatial numerical association of response codes (SNARC) effect was time dependent, the aim of the present study was to assess whether the association strength depends on the processing time of numerical quantity and/or of the time to initiate responses. More specifically, we examined whether and how the SNARC effect could be modulated by number format and effector type. Experiment 1 compared the effect induced by Arabic numbers and number words on the basis of saccadic responses in a parity judgment task. Indeed, previous studies have shown that Arabic numbers lead to faster processing than number words. The results replicated the SNARC effect with Arabic numbers, but not with number words. Experiment 2 was similar to Experiment 1, but this time manual responses (i.e., responses far slower than saccadic ones) were recorded. A strong SNARC effect was observed for both number formats. Further analyses revealed a correlation between mean individual response times and the strength of the SNARC effect. We proposed that the initiation times for saccadic responses may be too short for the SNARC effect to appear, in particular with the written number format for which activation of magnitude takes time. We conclude in terms of time variations resulting from processing specificities related with number format, effector type and also individual reaction and processing speed.

Moving seamlessly between spoken number words and Arabic digits is common in everyday life. In this study, we systematically investigated the correspondence between auditory number words and visual Arabic digits in adults. Auditory number words and visual Arabic digits were presented concurrently or sequentially and participants had to indicate whether they described the same quantity. We manipulated the stimulus onset asynchronies (SOAs) between the two stimuli (Experiment 1: −500 ms to +500 ms; Experiment 2: −200 ms to +200 ms). In both experiments, we found a significant cross-modal distance effect. This effect was strongest for simultaneous stimulus presentation and decreased with increasing SOAs. Numerical distance emerged as the most consistent significant predictor overall, in particular for simultaneous presentation. However, physical similarity between the stimuli was often a significant predictor of response times in addition to numerical distance, and at longer SOAs, physical similarity between the stimuli was the only significant predictor. This shows that SOA modulates the extent to which participants access quantity representations. Our results thus support the idea that a semantic quantity representation of auditory and visual numerical symbols is activated when participants perform a concurrent matching task, while at longer SOAs participants are more likely to rely on physical similarity between the stimuli. We also investigated whether individual differences in the efficiency of the cross-modal processing were related to differences in mathematical performance. Our results are inconclusive about whether the efficiency of cross-format numerical correspondence is related to mathematical competence in adults.

According to the Triple Code Model, early arithmetic development depends on learning the mappings between non-verbal representations of magnitude (quantity) and symbolic verbal (number words) and visual (Arabic numerals) representations of number. We examined this hypothesis in a sample of 166 4- to 7-year old children. Children completed 4 paired-associate learning tasks and a broad range of measures assessing early numerical (symbolic and non-symbolic magnitude comparison, digit writing, arithmetic) and reading skills (letter-sound knowledge, phoneme awareness, rapid automatized naming, word reading). A path model showed that paired-associate learning tasks involving mapping magnitudes onto verbal or visual stimuli predicted arithmetic performance over and above other well-established predictors. This relationship was specific to arithmetic and, consistent with the Triple Code Model, highlights that mapping between non-symbolic magnitude representations and the corresponding symbolic forms (verbal and visual) is important to the development of arithmetic skills.

In this paper, we will present a novel and the first approach to transforming written Arabic numeral word format into a string of digits according to proposed Arabic numeral rules. In this work, we relied mainly on the Arabic stemmer to determine the digit number, where we proposed a set of stems for the main numbers. The proposed approach covers all problems associated with Arabic numeral texts, including different numeral word shapes and unordered sentences. That is, a textual number could be written in more than one format; moreover, we deal with Arabic accents. In addition, we propose to deal with simple spelling errors and using similarities to find the nearest correct word. The proposed approach covers all possible text numbers in the range of one to millions. Tests have been executed using a possible case from context numeral in the range above, and the experimental results have demonstrated that the proposed approach is promising in the sense that it provides an efficient and error-free transformation. Finally, we built an Android mobile-based application that uses the proposed approach to transform between three different formats: digits, numeral texts, and Abacus.