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One of the algorithms stored in natural intelligence is the writing of Arabic numerals in Indonesian words. Algorithms in naturals intelligence are not easy to find. This problem gave us an idea to create artificial intelligence that tries to mimic natural intelligence algorithms. The proposed algorithm for building artificial intelligence is an R-Z rule-based system. This rule-based system contains a knowledge base of R-Z rules and a knowledge base of facts. In the knowledge base, the R-Z rule provides the R rule and the Z rule, while the facts knowledge base provides facts in the form of a definite standard number and an affix word. R-Z rule-based system for reasoning writing Arabic numerals in Indonesian words uses forward chaining. Artificial intelligence designs that mimic naturals intelligence in writing numbers in Indonesian words were made in C using Borland C++ 5.02 software. The experimental results show that by applying the R's rule of seven rules and Z's of twenty-five rules, the R-Z rule-based system can write Arabic numerals in Indonesian words from Arabic numerals "0" to Arabic numerals "9999999". For example, to write the Arabic number "10" in Indonesian words, the R-Z rule-based system starts with the R2 rule. Rule R2 takes action on Z3 to create new facts about Arabic numerals in the Indonesian word, namely "SEPULUH."

Using Generative Adversarial Networks (GANs) have led to significant improvements in computer vision research filed. GANs are used to generate novel images by pitting two neural networks against each other, where a generator network generates images from a latent space and a discriminator network classifies the generated images. In our work, a number of different GANs is applied to generate handwritten Arabic digits in the Eastern Arabic numeral script and determine which GAN flavor preforms best. To generate these digits, we test the following types of GANs: a Basic GAN, Deep Convolutional GAN (DCGAN), Bidirectional GAN (BiGAN), VanillaGAN, and WassersteinGAN (WGAN). Then, a Frechet Inception Distance (FID) measurement tool along with native-Arabic human evaluation are carried out to evaluate the generated images. Experimental results show that DCGAN outperforms other employed GANs with respect to FID benchmark with a value of 96.815%. While DCGAN outperforms other GANs on FID, BiGAN obtains best performance with respect to native-Arabic human benchmark with a value of 69.93%. Our promising experimental results illustrate the ability of using GAN models to develop huge handwritten Arabic datasets with less efforts comparing with traditional methods of collecting data.

Text image comparison is a core component in web consistency testing across browsers. Previous studies mainly focused on general image comparison, which could not best suit the proposed task since text images share unique properties. In this paper, we introduce a novel Text-Image Matching Network (TimNet) to detect text differences in image pairs. A Multi-Stage Feature Extraction module (MFE) is integrated in TimNet to extract not only non-textual content features but also text-like features that are temporally aligned. Moreover, TimNet is composed of a Multi-Scale Metric module (MM) to measure the similarity between two text images with various scales and aspect ratios. Accordingly, a Text-Image Similarity Database (TISDB) consisting of 615.6 k text-image pairs of English characters, Chinese characters, and Arabic numbers was established. Extensive experiments were conducted to demonstrate that our TimNet outperforms existing state-of-the-art methods.

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.

Smart cards are a medium for children's learning that integrates interesting games, media creativity and promotes interaction between family members. This smart card has the theme of hijaiyah letters as an educational medium in learning Arabic numbers and letters during the pandemic that is happening in Indonesia. Now a lot of new innovations are created because of this pandemic period. This method is necessary because direct learning of Arabic letters and numbers is being avoided during the pandemic. This smart card is here to be an alternative for children to study at home. Based on the analysis conducted on the literature review, based on this incident led to the emergence of new obstacles in the way of educating children, namely the difficulty of parents in accompanying children to study at home due to a lack of understanding of the material by parents. With this smart card, it is hoped that children will have no difficulty in learning hijaiyah numbers and letters even though there is a companion

Computational estimation is seen as an important mathematical competence. Little is known, however, about the mathematical skills that are predictive of early computational estimation development. The current study longitudinally followed a group of about 350 children at four time points: second (K2, 4-year-olds) and third grades of kindergarten (K3, 5-year-olds) and first (P1, 6-year-olds) and second (P2, 7-year-olds) grades of primary school. The computational estimation task was administered in two variants: a nonverbal variant, in which the problems were presented with manipulatives and children also answered using manipulatives was administered in K3 and P1; and a verbal variant, in which the problems were presented with Arabic numerals and children had to answer verbally was administered in P1 and P2. Furthermore, children’s basic numerical skills and exact and approximate arithmetic skills were assessed in K2 and K3, respectively. Path analysis showed a positive autoregressive relationship between the verbal variants of the computational estimation task but not between the nonverbal ones. Basic numerical skills were important predictors for computational estimation at all time points. Approximate arithmetic positively contributed to nonverbal estimation, while exact arithmetic positively predicted verbal estimation. In sum, solid basic numerical and arithmetic skills support children when performing computational estimation. Future intervention research should further unravel the causal contribution of each of these basic numerical and arithmetic skills.

This article introduces a comparison between three different processing techniques for the selection of speech features. These features can be used for speaker recognition or speech recognition. A comparison between the performance of a system based on the linear prediction code, a system based on the cepstrum and a system based on the short time energy is introduced feature selection is very effective for recognition accuracy. This work illustrates where each of these features are more efficient for speaker recognition or for speech recognition. The results show that the short time energy in time domain is very effective for epeech recognition where its accuracy is found to be 92%. In speaker identification, the accuracy of identification for the features depending on energy in each frame is found to be 60%. It may be recommended that the features based on the capstrum given accuracy of 94% and 96% for speech recognition and speaker identification respectively. The accuracy of linear prediction code features depend on cepstrum may be recommended for speaker identifier or speech recognition. A recognition system for spoken digits are given using the above features with neural networks. The neural network has been used as a tool in this comparison.

For the first time, the article describes in detail the first Russian visual tutorial on arithmetic — a wall table created in 1705, the only copy of which is in the State Hermitage Museum in St. Petersburg. The manual was prepared on the basis of the first Russian textbook of arithmetic using Arabic numerals — the book of L. F. Magnitsky. A number of differences in the calculation methodology at the beginning of the 18th century from modern methods have been revealed. A comparative dictionary of modern mathematical terms and related terms used at the beginning of the 18th century was compiled. A number of errors and misprints were found in the table, they are given in the appendix to the article. The results obtained will be useful both to specialists and to everyone interested in the history of mathematics and informatics.

Gender polarity is an intriguing morphological phenomenon in Arabic. The numerals 3–10 take the gender opposite to that of their count nouns; that is, when the count noun is feminine, the numerals 3–10 appear in the masculine form, and vice versa. Earlier analyses (see, e.g., Alqassas 2013, 2017, Alqarni 2015) proposed that the numerals 3–10 bear an inherent feminine feature, which is deleted by an impoverishment rule in the presence of a feminine feature on the count noun, yielding gender polarity. This article provides empirical counterevidence to these analyses and the concept of gender polarity on the whole. It shows that the numerals 3–10 do not interact with the gender of the count noun; rather, they interact with the count noun’s morphology—that is, whether the count noun bears the morpheme /at/ or /a:tu/-/a:ti/ in its structure. These findings suggest that gender polarity in Arabic is a misnomer; the phenomenon should instead be termed morpheme polarity. Rather than implementing the impoverishment rules proposed in earlier analyses, this article uses readjustment rules to account for the morpheme polarity at hand.

The writing skills, which are crucial for learning in school, develop as the child gets older. They can be enhanced through various approaches. In this study, we aimed to examine the effects of motor games, which is a didactic approach, on learning how to spell Arabic numbers. Fifty-one pupils aged between 5 and 6 years old (age = 6.17 ± 0.33 years) took part in this study. They were divided into 3 different learning groups: 1) a control group that followed a classical learning (CG: n = 17) using visual and auditory modalities; 2) a second group that followed a multisensory learning modality (MSG: n = 17); and 3) a third group that followed a motor learning modality (MLG: n = 17). The digits spelling performances (from 0 to 9 in random orders) were assessed before and after 10 learning sessions. The retained parameters from the spelling test were the direction of the digits, the number of correct digits out of 10, and the number of non-mirrored digits out of 8. The results showed that the spelling test performance improved for all groups after the three learning modalities. However, the MLG showed the highest gains in plotting numbers performance (7.06 ± 1.25) compared to the CG (0.65 ± 2.32) and MSG (2.41 ± 2.15) (P

Melisa Vivanco objects to my theory of the Arabic numerals in Roads to Reference that the reference fixing procedure that I postulate doesn’t exploit the morphological structure of the Arabic numerals, but it should. Against Vivanco, I argue that the procedure in question does exploit the morphological structure of the numerals in an essential way.

The attentional boost effect (ABE) is a phenomenon in which in some dual tasks, increased attention to target detection causes an increase in memory performance related to items paired with the target. However, in previous studies concerning the ABE, the detection task objects usually reflected perceptual information. Whether the ABE could be observed if the task involves detecting semantic information is unclear. To answer this question, the present study adopted the classic dual-task paradigm of the ABE. Arabic numerals were used as semantic information stimuli in the detection tasks, and the degree of semantic processing in the detection task gradually increased over three experiments. The results showed that target detection with semantic information (i.e., digits) triggered the ABE (Experiment 1) and that the ABE was also generated under the semantic judgement-based detection task (i.e., odd–even detection task) regardless of whether the detection task used a single-target stimulus (Experiment 2) or a multi-target stimulus (Experiment 3). These findings indicate that an increased semantic load before the target decision in the detection task does not affect the ABE, and both perceptual detection and semantic detection can trigger the ABE.

Numbers are particularly interesting as they can be presented in different notations, for example, they can be represented as numerical digits or words. Moreover, many cultures around the world have different writing systems for representing number. Thai uses a more traditional Thai number system in conjunction with Arabic numbers. In the current study, we investigated the processing of numerical digits and words in unbalanced Thai-English bilinguals using a numerical parity judgment task. The flankers occurring on either side of the target were either congruent or incongruent with the target digit or word. In Experiment 1, we investigated the effects of Arabic digit and Thai digit flankers on English and Thai target number words and in Experiment 2, the effects of English and Thai number word flankers on Arabic and Thai digit targets. In Experiment 1, we found an interference effect from Thai digit flankers on Thai numerical words and in Experiment 2, an interference effect for Arabic digits from Thai word flankers. These results suggest that the first language is playing a greater contributing role than the second language and that numerical notation format contributes to the effect. Proficiency in the second language is likely to moderate this effect.

Children’s spontaneous focusing on Arabic number symbols (SFONS) has been identified as a relevant component of their early mathematical development. This study investigated whether SFONS is a sepa...

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.

Understanding of arithmetic students in Arabic learning is still low. This study aims to determine the effectiveness of the Direct Method in learning Arabic number material in Arabic understanding Arithmetic Students. The approach used is experimental research approach with Posttest-Only Control Design. The population and sample of the study were determined through the Random Sampling technique. Analysis of the data used included normality test, homogeneity test, average similarity test, completeness test, and comparative test. (1) the arithmetic understanding of students taught by the Direct Method in learning ‘Adad dan Ma’dud material can exceed the Standard of Minimum Mastery (KKM) of 76,87 , (2) the arithmetic understanding of students taught by the Direct Method is 76,87 higher than from the conventional models 65,32 . Then it can be concluded that the Direct Method is effective in understanding arithmetic in learning ‘Adad dan Ma’dud material. The novelty of this research is that using the Direct Method can facilitate a direct understanding of 'adad and ma'dud. This research contributes in Arabic teaching by using the Direct Method in the material 'Adad and Ma'dud to improve students' arithmetic understanding .

In this work, we propose a novel feature extraction algorithm that improves the robustness of automatic speech recognition (ASR) systems in the presence of various types of noise. The proposed algorithm uses a new cepstral technique based on the differential power spectrum (DPS) instead of the power spectrum (PS), the algorithm replaces the logarithmic non linearity by the power function. In order to reduce cepstral coefficients mismatches between training and testing conditions, we used the mean and variance normalization, then we apply auto-regression movingaverage filtering (MVA) in the cepstral domain. The ASR experiments were conducted using two databases, the first is LASA digit database designed for recognition the isolated Arabic digits in the presence of different types of noise. The second is Aurora 2 noisy speech database designed to recognize connected English digits in various operating environments. The experimental results show a substantial improvement from the proposed algorithm over the baseline Mel Frequency Cepstral Coefficients (MFCC), the relative improvement is the 28.92% for LASA database and is the 44.43% for aurora 2 database. The performance of our proposed algorithm was tested and verified by extensive comparisons with the state-of-the-art noise-robust features in aurora 2.

How are number symbols (e.g., Arabic digits) represented in the brain? Functional resonance imaging adaptation (fMRI‐A) research has indicated that the intraparietal sulcus (IPS) exhibits a decrease in activation with the repeated presentation of the same number, that is followed by a rebound effect with the presentation of a new number. This rebound effect is modulated by the numerical ratio or difference between presented numbers. It has been suggested that this ratio‐dependent rebound effect is reflective of a link between the symbolic numerical representation system and an approximate magnitude system. Experiment 1 used fMRI‐A to investigate an alternative hypothesis: that the rebound effect observed in the IPS is related to the ordinal relationships between symbols (e.g., 3 comes before 4; C after B). In Experiment 1, adult participants exhibited the predicted distance‐dependent parametric rebound effect bilaterally in the IPS for number symbols during a number adaptation task, however, the same effect was not found anywhere in the brain in response to letters. When numbers were contrasted with letters (numbers > letters), the left intraparietal lobule remained significant. Experiment 2 demonstrated that letter stimuli used in Experiment 1 generated a behavioral distance effect during an active ordinality task, despite the lack of a neural distance effect using fMRI‐A. The current study does not support the hypothesis that general ordinal mechanisms underpin the neural parametric recovery effect in the IPS in response to number symbols. Additional research is needed to further our understanding of mechanisms underlying symbolic numerical representation in the brain.

Numeral recognition is an important preliminary step for optical character recognition, document understanding and others. Deep learning based numeral recognition models have achieved huge popularity among the researchers around the world since last few years. Several convolutional neural network (CNN) based architectures have been proposed and many of those have achieved state-of-the-art results in numeral recognition. In this paper, we have explored CNN based architectures for handwritten Arabic numeral recognition. We have also developed a handwritten Arabic numerals dataset using various morphological operations on an existing dataset thus increasing the size of the dataset from 3000 to 72,000 images. A modification of previously proposed CNN architecture has given us an accuracy of 98.91% and our proposed architecture has produced 99.76%, which is comparable to state-of-the-art results found in the domain of handwritten Arabic numeral recognition.

A significant body of research links individual differences in symbolic numerical abilities, such as arithmetic, to number sense, the neurobiological system used to approximate and manipulate quantities without language or symbols. However, recent findings from cognitive neuroscience challenge this influential theory. Our current review presents an overview of evidence for the number sense account of symbolic numerical abilities and then reviews recent studies that challenge this account, organized around the following four assertions. (1) There is no number sense as traditionally conceived. (2) Neural substrates of number sense are more widely distributed than common consensus asserts, complicating the neurobiological evidence linking number sense to numerical abilities. (3) The most common measures of number sense are confounded by other cognitive demands, which drive key correlations. (4) Number sense and symbolic number systems (Arabic digits, number words, and so on) rely on distinct neural mechanisms and follow independent developmental trajectories. The review follows each assertion with comments on future directions that may bring resolution to these issues.

Numerosity estimation performance (e.g., how accurate, consistent, or proportionally spaced (linear) numerosity-numeral mappings are) has previously been associated with math competence. However, the specific mechanisms that underlie such a relation is unknown. One possible mechanism is the mapping process between numerical sets and symbolic numbers (e.g., Arabic numerals). The current study examined two hypothesized mechanisms of numerosity-numeral mappings (item-based “associative” and holistic “structural” mapping) and their roles in the estimation-and-math relation. Specifically, mappings for small numbers (e.g., 1–10) are thought to be associative and resistant to calibration (e.g., feedback on accuracy of estimates), whereas holistic “structural” mapping for larger numbers (e.g., beyond 10) may be supported by flexibly aligning a numeral “response grid” (akin to a ruler) to an analog “mental number line” upon calibration. In 57 adults, we used pre- and post-calibration estimates to measure the range of continuous associative mappings among small numbers (e.g., a base range of associative mappings from 1 to 10), and obtained measures of math competence and delayed multiple-choice strategy reports. Consistent with previous research, uncalibrated estimation performance correlated with calculation competence, controlling for reading fluency and working memory. However, having a higher base range of associative mappings was not related to estimation performance or any math competence measures. Critically, discontinuity in calibration effects was typical at the individual level, which calls into question the nature of “holistic structural mapping”. A parsimonious explanation to integrate previous and current findings is that estimation performance is likely optimized by dynamically constructing numerosity-numeral mappings through the use of multiple strategies from trial to trial.

Young children show large individual differences in their tendency to focus spontaneously on numerical aspects (e.g., numerosities or Arabic number symbols) of their everyday environment. The origins of these individual differences are unclear. Given the role of the home numeracy environment (HNE) in children’s early mathematical development and the assumed link between children’s spontaneous number focusing tendencies and their numerical behavior in everyday life, it is plausible that children’s spontaneous focusing tendencies are related to their HNE. The present study aimed to test this hypothesis by longitudinally investigating children’s spontaneous focusing on numerosity (SFON) and spontaneous focusing on Arabic number symbols (SFONS) in relation to their HNE. Participants were 128 children (4- to 5-year-olds), who were followed from the second until the third year of Flemish kindergarten. In both kindergarten years, children completed a SFON and SFONS Picture task while their parents completed a home numeracy questionnaire. Correlation analyses and structural equation modeling revealed no significant associations between children’s spontaneous number focusing tendencies and their HNE, neither in second nor in third year of kindergarten. This finding suggests that children’s spontaneous number focusing tendencies are not per se related to their HNE. Various possible explanations for this unexpected finding are discussed and directions for further research on this relationship are suggested. ispartof: ZDM Mathematics Education vol:52 issue:4 pages:729-749 status: published

Studies of brain activity during number processing suggest symbolic and nonsymbolic numerical stimuli (e.g., Arabic digits and dot arrays) engage both shared and distinct neural mechanisms. However, the extent to which number format influences large-scale functional network organization is unknown. In this study, using 7 Tesla MRI, we adopted a network neuroscience approach to characterize the whole-brain functional architecture supporting symbolic and nonsymbolic number comparison in 33 adults. Results showed the degree of global modularity was similar for both formats. The symbolic format, however, elicited stronger community membership among auditory regions, whereas for nonsymbolic, stronger membership was observed within and between cingulo-opercular/salience network and basal ganglia communities. The right posterior inferior temporal gyrus, left intraparietal sulcus, and two regions in the right ventromedial occipital cortex demonstrated robust differences between formats in terms of their community membership, supporting prior findings that these areas are differentially engaged based on number format. Furthermore, a unified fronto-parietal/dorsal attention community in the nonsymbolic condition was fractionated into two components in the symbolic condition. Taken together, these results reveal a pattern of overlapping and distinct network architectures for symbolic and nonsymbolic number processing., Author Summary Previous studies of local activity levels suggest that both shared and distinct neural mechanisms support the processing of symbolic (Arabic digits) and nonsymbolic (dot sets) number stimuli, involving regions distributed across frontal, temporal, and parietal cortices. Network-level characterizations of functional connectivity patterns underlying number processing have gone unexplored, however. In this study we examined the whole-brain functional architecture of symbolic and nonsymbolic number comparison. Stronger community membership was observed among auditory regions during symbolic processing, and among cingulo-opercular/salience and basal ganglia networks for nonsymbolic. A dual versus unified fronto-parietal/dorsal attention community organization was observed for symbolic and nonsymbolic formats, respectively. Finally, the inferior temporal gyrus and left intraparietal sulcus, both thought to be preferentially involved in processing number symbols, demonstrated robust differences in community membership between formats.

Contains fulltext : 236494.pdf (Publisher’s version ) (Open Access) Humans not only process and compare magnitude information such as size, duration, and number perceptually, but they also communicate about these properties using language. In this respect, a relevant class of lexical items are so-called scalar adjectives like "big," "long," "loud," and so on which refer to magnitude information. It has been proposed that humans use an amodal and abstract representation format shared by different dimensions, called the generalised magnitude system (GMS). In this paper, we test the hypothesis that scalar adjectives are symbolic references to GMS representations, and, therefore, GMS gets involved in processing their meaning. Previously, a parallel hypothesis on the relation between number symbols and GMS representations has been tested with the size congruity paradigm. The results of these experiments showed interference between the processing of number symbols and the processing of physical (font-) size. In the first three experiments of the present study (total N = 150), we used the size congruity paradigm and the same/different task to look at the potential interaction between physical size magnitude and numerical magnitude expressed by number words. In the subsequent three experiments (total N = 149), we looked at a parallel potential interaction between physical size magnitude and scalar adjective meaning. In the size congruity paradigm, we observed interference between the processing of the numerical value of number words and the meaning of scalar adjectives, on the one hand, and physical (font-) size, on the other hand, when participants had to judge the number words or the adjectives (while ignoring physical size). No interference was obtained for the reverse situation, i.e., when participants judged the physical font size (while ignoring numerical value or meaning). The results of the same/different task for both number words and scalar adjectives strongly suggested that the interference that was observed in the size congruity paradigm was likely due to a response conflict at the decision stage of processing rather than due to the recruitment of GMS representations. Taken together, it can be concluded that the size congruity paradigm does not provide evidence in support the hypothesis that GMS representations are used in the processing of number words or scalar adjectives. Nonetheless, the hypothesis we put forward about scalar adjectives is still is a promising potential line of research. We make a number of suggestions for how this hypothesis can be explored in future studies. 28 p.

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 size congruity effect in a numerical Stroop task shows that magnitude judgments of two numbers are faster and more accurate when the numerically larger number also appears in a physically larger size, indicating the interaction between numerical and physical magnitudes. It has recently been suggested that spatial shifts of attention between the two numbers may contribute to the size congruity effect. However, a complete line of evidence for the attentional attribution to the size congruity effect remains to be established. Therefore, the present study aimed to provide further demonstrations for the idea that spatial shifts of attention contribute to the size congruity effect during magnitude judgments regarding either the numerical or physical dimension of two numbers. Participants were sequentially or simultaneously presented with a pair of single-digit Arabic numbers whose numerical and physical magnitudes varied independently. They were instructed to perform a magnitude judgment regarding the numerical value or physical size of the paired numbers. Across three experiments, we consistently found that the size congruity effect was reduced or eliminated when number pairs were presented sequentially compared to when they were presented simultaneously. Because in the sequential presentation mode the paired numbers were successively presented at central fixation and therefore spatial attention shifts should be completely precluded by the central presentation of number stimuli, the present findings support the notion that spatial shifts of attention between numbers in the simultaneous presentation mode play an important role in generating the size congruity effect for both numerical and physical tasks.