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In the study of numerical and arithmetical abilities, there is compelling evidence demonstrating that number and space representations are connected to one another. Historically the first source of support came more than a century ago, when Galton's investigations on mental imagery suggested that the internal representation of numbers may evoke a stable, linear space. In the past few decades, empirical evidence lent further support to the hypothesis that numerical representation is spatially coded into a non-verbal 'mental number line', which in turn lead to considering this representation as the core of number meaning. Visuo-spatial processing is intuitively involved in various aspects of number processing and calculation: For instance, the meaning of a digit in a multi-digit number is coded following spatial information, given its association to its relative position within the number; similarly, to solve a complex written multiplication one has to know the correct location of the intermediate results. In this review behavioral, neuropsychological, and neuroimaging data concerning the close relationship between numerical abilities and visuo-spatial processes are considered.

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... The present findings are potentially informative for the design and implementation of training studies. Previous research highlighted the positive role of spatial skills for basic number processing (Crollen & Noël, 2015;Thompson et al., 2013) and more complex mathematical calculations and/or mathematical expertise (Geary, Saults, Liu, & Hoard, 2000;Sella, Sader, Lolliot, & Cohen Kadosh, 2016;Wei, Yuan, Chen, & Zhou, 2012; see also review by de Hevia, Vallar, & Girelli, 2008). We show that spatial skills, notably mental rotation, are also important for basic arithmetic, especially at the stage of skill acquisition. ...

... Therefore, spatial training might not affect all aspects of arithmetic to an equal extent and differences between studies could partly rely on the choice of mathematical outcome measures (please note that Cheng &Mix, 2014, andHawes et al., 2015, used Several assumptions as to how better spatial skills may positively influence mathematical learning have been put forward. One assumption is the "mental number line hypothesis" (de Hevia et al., 2008). According to the latter, better spatial abilities induce a more fine-grained representation of numbers along a mental number line. ...

... A second assumption as to how spatial skills influence performance in arithmetic is through mental imagery (de Hevia et al., 2008), referring to an individual's visualization ability. Accordingly, the visualization of arithmetic problems might facilitate their resolution. ...

Considering the importance of arithmetic in school curricula, it is crucial to understand the cognitive processes underlying its successful acquisition. Previous research suggests the involvement of spatial skills, especially during arithmetic skill acquisition. We assessed the predictive effect of mental rotation on different arithmetic components in children halfway through elementary school. At this stage, additions and subtractions are already well mastered, while multiplications and divisions are newly acquired. Although mental rotation positively correlated with arithmetic performances regardless of operation, only multiplication, division and completion performances were significantly predicted by mental rotation when controlling for age, gender as well as domain-specific symbolic number skills and visuospatial short-term memory. This highlights the differential effects of mental rotation on arithmetic and suggests a particular importance for newly acquired arithmetic material. These findings extend previous research on the relation between spatial skills and arithmetic and yield practical information for mathematical education and instruction.

... Fischer et al., 2016). Many more findings from neuropsychological, neuroimaging, and behavioral research highlight the fundamental connection between spatial processes and magnitude representations (de Hevia et al., 2008). This might be explained by the fact that they share the property of transitivity. ...

... Codes (SNARC) in parity judgments induces faster responses to stimuli of small magnitude with the left hand and faster responses to stimuli of larger magnitude with the right hand (Dehaene et al., 1993) and was abundantly replicated . Other findings support the importance of spatial mental processes in magnitude processing and representation (for a review, see de Hevia et al., 2008). ...

... H.Fischer & Brugger, 2011). Many other findings from neuropsychological, neuroimaging, and behavioral research highlight the fundamental connection between spatial processes and magnitude representations(de Hevia, Girelli, & Macchi Cassia, 2012;de Hevia, Vallar, & Girelli, 2008;Thompson, Nuerk, Moeller, & Cohen Kadosh, 2013). ...

In this thesis is first considered how energy is taught and learned about in school, focusing on the discrepancies between a scientific definition of energy and a societal definition of energy, and discussing units of energy and the confusion they induce. Perspectives for education and energy management are provided. Then, focus is placed on the representations of energy provided in home energy management systems, seeking to propose an original classification based on educational strategies. The major obstacles met by designers reveal how energy management tools can be adapted to human cognition. Next, human numerical and magnitude processing abilities are discussed in depth, taking the viewpoint of grounded cognition and building a framework through which the impact of external representations of energy on learning and comparing can be established, understood, and predicted. This leads to two empirical studies. The first study tests the effect of external representation (symbolic or spatial) on recall and comparisons from memory. Accuracy and response time at comparisons are used as dependent variables. Results indicate analog processing of magnitude in both conditions, and show that external representation affects performance at both recall and comparison, with symbolic external representation increasing recall and comparison accuracy, and spatial external representation increasing comparison speed. The second study tests the effects of spatiality, groundedness, and physicality in external representations, also on recall and comparisons from memory, using the same dependent variables. Results indicate analog processing in all conditions. Spatiality decreases recall accuracy but increases comparison speed. Groundedness and physicality show no effect. Results are consistent with grounded cognition's mental simulations hypothesis (Barsalou, 1999, 2008; Wilson, 2002) as well as Dehaene's (1997) view on numerical cognition, in which number sense is based on a continuous accumulator that does not directly process discrete numbers. Theoretical implications and practical applications are discussed.

... There is a strong link between spatial processing and mathematics. For example, this has been demonstrated multiple times through the spatial numerical association of response codes effect (de Hevia et al., 2008;Hawes et al., 2015). This refers to the tendency to classify smaller numbers with 'left side' and larger numbers with 'right side'. ...

... de Hevia et al. (2008) reviewed the role of visuospatial processing and identified multiple neuroimaging techniques showing that the posterior parietal areas are activated when processing numerical or spatial information. Specifically, there is activation in the posterior parietal areas when processing simple multiplication, subtraction, and numerical tasks. ...

... However, in more complex mathematical problems neurological evidence suggests that a broader array of neural regions is activated. For example, pre-frontal regions are activated -which are typically involved in attention control, maintenance, and visuo-spatial WM processing (Postle, 2006;de Hevia et al., 2008); the inferior temporal gyrus is activated during mental imagery tasks, and the angular gyrus of the inferior parietal cortex is especially important for processing complex calculations when problems are presented visually. Taken together, there is a complex neurological network that is activated to process visual and spatial information as well as numerical information. ...

Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.

... This is in line with several neuropsychological studies that-starting with the seminal study by Hécaen, Angelergues, & Houillier (1961), who introduced the term "spatial acalculia"describe calculation deficits that are secondary to visuospatial ones (Ardila & Rosselli, 1994;Boller & Grafman, 1983;de Hevia, Vallar, & Girelli, 2008, for review). Typical errors of these patients include the incorrect alignment of numbers in column, difficulties in maintaining the decimal places, and so on, thus being at least partly dissociable from nonstrategic, approximation-related errors (Benavides-Varela et al., 2016;de Hevia et al., 2008). ...

... Therefore, the similarity between the pattern of procedural (positive decade errors for subtraction and negative decade errors for addition) and the pattern of estimation errors (overestimation for subtractions, underestimation for additions) does not imply a shared origin, and does not necessarily relate to the MNL framework. Dissociations between procedural and estimation strategies have been reported in neuropsychological studies (Ardila & Rosselli, 1994;Boller & Grafman, 1983;de Hevia, Vallar, & Girelli, 2008, for review) and indeed we observed one in the present study in terms of the modulating effect of OKS. ...

Growing evidence suggests that mental calculation might involve movements of attention along a spatial representation of numerical magnitude. Addition and subtraction on nonsymbolic numbers (numerosities) seem to induce a “momentum” effect, and have been linked to distinct patterns of neural activity in cortical regions subserving attention and eye movements. We investigated whether mental arithmetic on symbolic numbers, a cornerstone of abstract mathematical reasoning, can be affected by the manipulation of overt spatial attention induced by optokinetic stimulation (OKS). Participants performed additions or subtractions of auditory two-digit numbers during horizontal (experiment 1) or vertical OKS (experiment 2), and eye movements were concurrently recorded. In both experiments, the results of addition problems were underestimated, whereas results of subtractions were overestimated (a pattern that is opposite to the classic Operational Momentum effect). While this tendency was unaffected by OKS, vertical OKS modulated the occurrence of decade errors during subtractions (i.e., fewer during downward OKS and more frequent during upward OKS). Eye movements, on top of the classic effect induced by OKS, were affected by the type of operation during the calculation phase, with subtraction consistently leading to a downward shift of gaze position and addition leading to an upward shift. These results highlight the pervasive nature of spatial processing in mental arithmetic. Furthermore, the preeminent effect of vertical OKS is in line with the hypothesis that the vertical dimension of space–number associations is grounded in universal (physical) constraints and, thereby, more robust than situated and culture-dependent associations with the horizontal dimension.
Electronic supplementary material
The online version of this article (10.1007/s00426-018-1053-0) contains supplementary material, which is available to authorized users.

... La représentation mentale, spatialement organisée, des nombres qu'élabore un sujet tiendrait, outre à sa culture d'appartenance (sens de lecture et d'écriture), à une diversité de facteurs contextuels (De Hevia et al., 2008). Le fait d'habituer un sujet à se représenter les nombres sur une horloge à aiguilles qui lui fait face est ainsi de nature à susciter des effets SNARC inversés (sujets occidentaux) avec réponses plus rapide depuis le côté droit pour les plus petits nombres et réponses plus rapides depuis le côté gauche pour les plus grands nombres (Bächtold, Baumüller, & Brugger, 1998). ...

... OuvertureL'hypothèse d'une représentation analogique des nombres selon une ligne numérique mentale les classant par ordre croissant a été accréditée par une série de travaux : en particulier, un effet SNARC a été avéré à plusieurs reprises dans des tâches de classification numérique (e.g. : jugement de parité) avec réponse manuelle gauche et droite(De Hevia et al., 2008). De tels travaux ont ainsi suggéré un possible rôle déterminant de l'attention visuo-spatiale dans le traitement numérique et dans la réalisation de certaines tâches arithmétiques (e.g. ...

Les nombres et les opérations sur les nombres contribuent à structurer notre rapport au monde. Il est ainsi logique que plusieurs études aient tenté de clarifier les mécanismes sous-tendant la cognition numérique ou les mécanismes cérébraux responsables de la dyscalculie. Ces études ont suggéré que les représentations mathématiques pourraient s’ancrer dans des expériences corporelles et/ou que la cognition numérique et la préparation du mouvement pourraient être sous-tendues par des mécanismes cérébraux similaires. Plusieurs études ont suggéré que des mouvements segmentaires ou du corps dans sa globalité peuvent influer sur la performance de tâches numériques ou arithmétiques. L’effet de telles taches sur la performance motrice demeurait en revanche à examiner, en particulier dans le cas des mouvements à haute intensité. Cet éventuel effet a été examiné via deux études impliquant au total 206 étudiants de sexe masculin, en Licence à la faculté de santé publique de l’Université Libanaise (Beyrouth, Liban). Une première étude (deux séries de deux expérimentations) a examiné les effets de la lecture d’un nombre et de la soustraction mentale complexe sur la hauteur de saut en squat jump vertical (SJV) et sur le temps de réponse d’un mouvement de pointage manuel (MPM). Dans chaque série, ces effets ont été examinés dans le cas de nombres en chiffres arabes et de nombres écrits en toutes lettres. Une seconde étude a examiné l’effet de tâches d’arithmétique mentale sur le temps de réponse d’un MPM. Trois expérimentations (1-3) ont étudié l’effet de la soustraction (complexe) et, respectivement, de : (1) l’addition (simple ou complexe), (2) la multiplication (simple ou complexe) et (3) la comparaison d’ensembles de points et la comparaison de nombres. Tout nombre était écrit en chiffres arabes. Dans ces deux études, les données ont été analysées en recourant à un modèle linéaire multiniveaux à effets mixtes. Les résultats de la première étude ont avéré une amélioration modérée de la performance en SJV (statistiquement significative, p < 0,05) suite à la lecture d’un nombre écrit en toutes lettres et un net effet de la performance en SJV et en MPM après une soustraction mentale (complexe) avec nombres en chiffres arabes (p < 0,001). Les résultats de la seconde étude ont avéré une amélioration statistiquement significative de la performance en MPM suite aux seuls calculs complexes (p < 0,001) et à la seule comparaison de nombres (p < 0,003). Ces résultats suggèrent que la relation entre une tâche arithmétique et la performance d’un mouvement à haute intensité est influencée par le format numérique, le recours à des nombres en chiffres arabes (à la différence de celui à des nombres écrits en toutes lettres ou à des ensembles de points) s’avérant conditionner un effet positif sur la performance motrice. Ces résultats ont cependant montré que cette condition n’est pas suffisante, la performance motrice étant améliorée après les tâches arithmétiques (avec chiffres arabes) favorisant le recours à des stratégies procédurales plutôt que le recours à des stratégies par recouvrement (en mémoire) de faits arithmétiques. Au regard de la littérature, l’effet des calculs mentaux complexes (soustraction, addition et multiplication) et de la comparaison de nombres, en notation arabique, sur la performance motrice peut s’expliquer par différents mécanismes. Cet effet peut être lié à la mobilisation de mécanismes d’encodage et/ou de mémorisation spécifiques des chiffres arabes. L’addition et la multiplication complexes et, éventuellement, la comparaison de nombres, peuvent en outre avoir favorisé une attention à la trajectoire optimale du mouvement subséquent. L’influence des calculs complexes et de la comparaison de nombres, avec notation arabique, sur la performance motrice pourrait enfin tenir à l’implication de régions cérébrales motrices, mobilisées durant une activité effective de calcul ou de comparaison.

... In a review article by de Hevia, Vallar, & Girelli (2008), two accounts have been suggested for explaining the relation between spatial skills and different aspects of mathematical processing. The first explanative account, the "number line account", should explain the relation between spatial skills and basic number processing, whereas the second explanative account, the "visualization account" (or spatial imagery account), should explain the relation between spatial skills and calculation abilities. ...

... A predominant assumption relies on the spatial nature of numbers themselves: the mental number line (MNL). In western cultures, small numbers/magnitudes are associated with left side of space whereas large numbers/magnitudes are associated with right side of space (de Hevia et al., 2008;Fias & Fischer, 2005;Göbel et al., 2011;Hubbard et al., 2005). The systematic interaction between space and numbers is well established for healthy adults (Nuerk et al., 2005), and has recently been documented in young children (Hoffmann et al., 2013;Patro et al., 2016;Patro & Haman, 2012). ...

Early mathematical abilities, developed prior the onset of formal instruction, have been identified as a strong predictor of later mathematical achievement and numeracy, which goes along, in turn, with a variety of different life outcomes. Hence, unravelling the cognitive abilities associated with successful mathematical development is an important effort in the field of numerical cognition and developmental psychology. Abilities that are identified as predictors of mathematical development are potentially vital key targets of early interventions. By fostering these key abilities, children’s mathematical development should be positively influenced.
The present thesis pursues two major aims. The first aim is to identify key predictors of mathematical development. More precisely, the present thesis studies whether spatial skills fall within the category of key predictors in young children. Findings illustrate that different aspects of spatial skills emerge as strong predictors of mathematics (study I). Findings further highlight, that spatial skills hold a pivotal role for mathematical skills with a prominent verbal component (study II).
The second aim is concerned with the elaboration and scientific investigation of the effects of early interventions. A distinguishing feature of the present thesis is, that it is set in the Luxembourgish school setting. The latter is characterized by its heterogeneous student population from diverse language backgrounds. According to current statistics, around two-third of the children who attend Luxembourgish fundamental school do not speak Luxembourgish as a first language at home. Hence, an important number of children are not fluent in the language of instruction in preschool. Therefore, a central concern was to develop and implement early interventions that face the challenges posed by a multilingual school setting. For this reason, the language-neutral early mathematics training tool “MaGrid” was developed. MaGrid sets out to overcome the language-barrier in early mathematics education. On the content side, it encompasses a vast amount of number-specific and spatial training tasks. In the context of the present thesis two intervention studies (study III and study IV), including this tool, were run and yielded promising results. Results of these studies
further add to unravelling the relation between spatial skills and mathematics and answering the question, whether the (early) road to mathematics is spatial indeed.

... Consistent experimental evidence suggests that individuals tend to represent numerical and temporal information in a spatially organized manner. For instance, Western populations tend to represent number and time along a horizontal mental number line (MNL) and a horizontal mental time line (MTL), whereby smaller numbers or earlier events are associated with the left side of space, and larger numbers or later events are associated with the right side of space, respectively (for a review on the MNL, see de Hevia et al., 2008; for a review on the MTL, see Bonato et al., 2012). Similarly, in Western cultures, there is the tendency to maintain the temporal/serial order of events in working memory by activating a spatial representation such that temporal order is mapped from left to right (Abrahamse et al., 2014). ...

... In Western societies, the systematic tendency to map numerical magnitude onto a horizontal left-to-right axis has been widely documented and is supported by ample behavioural and neuropsychological data (see Fig. 1) (for a review, see de Hevia et al., 2008). However, only in the last decade have researchers looked at the potential contribution of visual experience in the development of the MNL. ...

The spatial representation of numerical and temporal information is thought to be rooted in our multisensory experiences. Accordingly, we may expect visual or auditory deprivation to affect the way we represent numerical magnitude and time spatially. Here, we systematically review recent findings on how blind and deaf individuals represent abstract concepts such as magnitude and time (e.g., past/future, serial order of events) in a spatial format. Interestingly, available evidence suggests that sensory deprivation does not prevent the spatial “re-mapping” of abstract information, but differences compared to normally sighted and hearing individuals may emerge depending on the specific dimension considered (i.e., numerical magnitude, time as past/future, serial order). Herein we discuss how the study of sensory deprived populations may shed light on the specific, and possibly distinct, mechanisms subserving the spatial representation of these concepts. Furthermore, we pinpoint unresolved issues that need to be addressed by future studies to grasp a full understanding of the spatial representation of abstract information associated with visual and auditory deprivation.

... The dependence of numerical discrimination on the ratio between the two quantities (Weber's Law, Dehaene 1992) in nonhumans implies that they also spatially represent quantities (de Hevia et al. 2008). In addition, both domestic chicks and rhesus monkeys show evidence for spatial mapping of quantities via position preferences (Drucker and Brannon 2014;Rugani et al. 2007). ...

... Our aim was first to evaluate the SNARC effect in American black bears and Western lowland gorillas using a similar methodology to Gazes et al. (2017) (Table 1). American black bears (Vonk and Beran 2012), like gorillas (Vonk et al. 2014), generally showed higher accuracy with smaller ratios in a quantity discrimination task, which implies spatial representation of magnitude (de Hevia et al. 2008). The ability to judge magnitudes may be useful to predators in discriminating groups of prey (e.g., Krusche et al. 2010;Panteleeva et al. 2013;Uller et al. 2003), and to non-predators for choosing sites with larger quantities of non-prey food items (e.g., Baker et al. 2011;Bánszegi et al. 2016;Evans et al. 2009;Hanus and Call 2007;Perdue et al. 2012;Ward and Smuts 2007). ...

The spatial-numerical association of response codes (SNARC) effect is the tendency for humans to respond faster to relatively larger numbers on the left or right (or with the left or right hand) and faster to relatively smaller numbers on the other side. This effect seems to occur due to a spatial representation of magnitude either in occurrence with a number line (wherein participants respond to relatively larger numbers faster on the right), other representations such as clock faces (responses are reversed from number lines), or culturally specific reading directions, begging the question as to whether the effect may be limited to humans. Given that a SNARC effect has emerged via a quantity judgement task in Western lowland gorillas and orangutans (Gazes et al., Cog 168:312–319, 2017), we examined patterns of response on a quantity discrimination task in American black bears, Western lowland gorillas, and humans for evidence of a SNARC effect. We found limited evidence for SNARC effect in American black bears and Western lowland gorillas. Furthermore, humans were inconsistent in direction and strength of effects, emphasizing the importance of standardizing methodology and analyses when comparing SNARC effects between species. These data reveal the importance of collecting data with humans in analogous procedures when testing nonhumans for effects assumed to bepresent in humans.

... One way to evaluate space estimates is by measuring distance predictions via numerical representation. The intricate relationship between spatial representations and numerical representations has been consistently referred in the literature (Arend, Naparstek, & Henik, 2013;DeHevia, Vallar, & Girelli, 2008;Van Dyck & Fias, 2011). In the last two decades, one of the most accepted hypothesis for the correlation between spatial representations and numerical spatial encoding is the Mental Number Line hypothesis (Dehaene, 1992;Dehaene & Cohen, 1997;Dehaene, Piazza, Pinel, & Cohen, 2003). ...

... Our results add a new finding regarding the correlation between proprioceptive distance predictions and spatial judgements in terms of numerical representation. Therefore, the results support the hypothesis of an intricate relationship between spatial representations and numerical representations (DeHevia et al., 2008). ...

Research has emphasized that the body's position in space and patterns of visual searching for stimuli are crucial variables to explain the ability to estimate distances numerically. In this paper, we tested the hypothesis that proprioception recalibration interferes in the ability to numerically estimate fixed peri-personal space. The Rubber Hand Illusion (RHI) experimental paradigm was applied as a tool to temporally manipulate the sense of proprioception in participant’s right hand. Seventeen college students were asked to estimate fixed horizontal spatial cues before and after two conditions of tactile stimulation within RHI (synchronous versus asynchronous stroking). Results evidenced that proprioceptive recalibration of the hand were temporally altered by both stroking patterns. However, the effects of numerically estimate fixed horizontal cues towards the body midline were only consistently observed in the synchronous stroking condition. Those findings suggest that numerical estimates of peri-personal fixed cues are strongly associated with proprioceptive recalibration, corroborating the literature on multisensory integration of perception.

... One way to evaluate space estimates is by measuring distance predictions via numerical representation. The intricate relationship between spatial representations and numerical representations has been consistently referred in the literature (Arend, Naparstek, & Henik, 2013;DeHevia, Vallar, & Girelli, 2008;Van Dyck & Fias, 2011). In the last two decades, one of the most accepted hypothesis for the correlation between spatial representations and numerical spatial encoding is the Mental Number Line hypothesis (Dehaene, 1992;Dehaene & Cohen, 1997;Dehaene, Piazza, Pinel, & Cohen, 2003). ...

... Our results add a new finding regarding the correlation between proprioceptive distance predictions and spatial judgements in terms of numerical representation. Therefore, the results support the hypothesis of an intricate relationship between spatial representations and numerical representations (DeHevia et al., 2008). ...

Research in cognitive psychology has emphasized that the body's position in space and patterns of visual searching for stimuli are crucial variables to explain the ability to estimate distances numerically. In this paper, we tested the hypothesis that proprioception recalibration interferes in the ability to numerically estimate fixed peri-personal space. The Rubber Hand Illusion (RHI) experimental paradigm was applied as a tool to temporally manipulate the sense of proprioception in participant's right hand. Seventeen college students were asked to estimate horizontal fixed spatial cues before and after two conditions of tactile stimulation within RHI (synchronous versus asynchronous stroking). Results evidenced that proprioceptive recalibration of the hand were temporally altered by both stroking patterns. However, the effects of numerically estimate fixed horizontal cues towards the body midline were only consistently observed in the synchronous stroking condition. These findings suggest that numerical estimates of peripersonal fixed cues are strongly associated with proprioceptive recalibration, corroborating the literature on multisensory integration of perception.

... A predominant assumption relies on the spatial nature of numbers themselves: the mental number line (MNL). In Western cultures, small numbers/magnitudes are associated with the left side of space, whereas large numbers/magnitudes are associated with the right side of space (de Hevia, Vallar, & Girelli, 2008;Fias & Fischer, 2005;Göbel, Shaki, & Fischer, 2011;Hubbard, Piazza, Pinel, & Dehaene, 2005). The systematic interaction between space and numbers is well established for healthy adults (Nuerk, Wood, & Willmes, 2005) and has recently been documented in young children (Hoffmann, Hornung, Martin, & Schiltz, 2013;Patro, Fischer, Nuerk, & Cress, 2016;Patro & Haman, 2012). ...

Children’s development of verbal number skills (i.e., counting abilities
and knowledge of the number names) presents a milestone in
mathematical development. Different factors such as visuo-spatial
and verbal abilities have been discussed as contributing to the
development of these foundational skills. To understand the cognitive
nature of verbal number skills in young children, the current
study assessed the relation of preschoolers’ verbal and visuospatial
abilities to their verbal number skills. In total, 141 children
aged 5 or 6 years participated in the current study. Verbal number
skills were regressed on vocabulary, phonological awareness and
visuo-spatial abilities, and verbal and visuo-spatial working memory
in a structural equation model. Only visuo-spatial abilities
emerged as a significant predictor of verbal number skills in the
estimated model. Our results suggest that visuo-spatial abilities
contribute to a larger extent to children’s verbal number skills than
verbal abilities. From a theoretical point of view, these results suggest
a visuo-spatial, rather than a verbal, grounding of verbal number
skills. These results are potentially informative for the
conception of early mathematics assessments and interventions.

... Over the past two decades, studies have converged over the idea that human adults conceptualize numbers in terms of space by translating them into corresponding spatial extensions and positions along a horizontal continuum, that is, the so-called mental number line (MNL; de Hevia, Vallar, & Girelli, 2008;Dehaene, Bossini, & Giraux, 1993;Hubbard, Piazza, Pinel, & Dehaene, 2005). This phenomenon, commonly referred to as number-space mapping, occurs automatically and accounts for various systematic behavioral effects in numerical and visuospatial tasks (for a review, see Fischer & Shaki, 2014). ...

There has been compelling evidence favoring the idea that human adults similarly represent number and time along a horizontal mental number line (MNL) and mental time line (MTL), respectively. Yet, analogies drawn between the MNL and MTL have been challenged by recent studies suggesting that adults' representations of number and time arise from different spatial frames of reference; whereas the MNL relies on both hand-centered and object-centered coordinates, the MTL appears to be exclusively anchored on object-centered coordinates. To directly test this possibility, here we explored the extent to which visual feedback and proprioceptive feedback affect children's performance in a Number Comparison task (Experiment 1) and a Time Comparison task (Experiment 2), in which participants needed to associate a lateralized key with numerical and temporal words, respectively. Children (5- and 6-year-olds) performed the task with their hands either uncrossed or crossed over the body midline (i.e., manipulation of proprioceptive feedback) and with either visual control over their hands allowed or precluded under blindfolds (i.e., manipulation of visual feedback). Results showed that children were facilitated in associating smaller/larger numbers with the left/right side of the external space, but only when hands were uncrossed and visual feedback was available. On the contrary, blindfolding and crossing their hands over the midline did not affect spatial time mapping, with 6-year-olds showing facilitation in associating words referring to the past/future with the left/right side of the external space irrespective of visual and proprioceptive feedback. This same effect was also present in 5-year-olds despite their difficulty in performing the Time Comparison task. Together, these findings show, for the first time, that-just like adults-young children (a) map temporal events onto space in a rightward direction as they do for numbers and (b) anchor their spatial representation of time and numbers to different spatial frames of reference.

... A major topic concerning spatial learning difficulties is troubled in basic spatial arrangement i.e. classification of objects according to their quantitative value [51]. This signifies that people dealing with dyscalculia have difficulties in comparing quantities and shape sizes [25]. ...

Learning difficulties research within the frame of dyscalculia has proceeded so far, nevertheless, they seem to fail in providing an overall conceptual map of the deficit. This paper objective is to propose a new classification in reference to dyscalculia features noticed at various ages. Although there are several approaches on dyscalculia features, algorithmic thinking ability deficits are not taken into consideration. Authors focus on problem solving and algorithmic thinking difficulties within the frame of dyscalculia

... A wealth of studies have established an intimate association between numbers and space (Hubbard et al., 2005;de Hevia et al., 2008;Nuerk et al., 2015;Patro et al., 2016). This association emerges early in development, as attested by the finding that 7 months-old infants display preferential looking for increasing numerical magnitude from left-to-right (De Hevia et al., 2014). ...

The ability to compare the numerical magnitude of symbolic numbers represents a milestone in the development of numerical skills. However, it remains unclear how basic numerical abilities contribute to the understanding of symbolic magnitude and whether the impact of these abilities may vary when symbolic numbers are presented as number words (e.g., “six vs. eight”) vs. Arabic numbers (e.g., 6 vs. 8). In the present study on preschool children, we show that comparison of number words is related to cardinality knowledge whereas the comparison of Arabic digits is related to both cardinality knowledge and the ability to spatially map numbers. We conclude that comparison of symbolic numbers in preschool children relies on multiple numerical skills and representations, which can be differentially weighted depending on the presentation format. In particular, the spatial arrangement of digits on the number line seems to scaffold the development of a “spatial route” to understanding the exact magnitude of numerals.

... Despite the numerous evidence suggesting a close link between numbers and space (see Crollen et al., 2017;de Hevia, Vallar, & Girelli, 2008 for reviews), our study failed to demonstrate an advantage of linear over nonlinear training in the arithmetic task. However, it has been shown that additions and subtractions involve movements on a spatial mental number line. ...

Recent studies suggested that multisensory training schemes could boost the development of abstract concepts. In the present study, we wanted to evaluate whether training arithmetic with a multisensory intervention could induce larger learning improvements than a visual intervention alone. Moreover, as a left-to-right oriented mental number line was for a long time considered as a core feature of numerical representation, we also wanted to compare left-to-right and non-linear arithmetic training. In order to do so, kindergarten children were trained to solve simple addition and subtraction operations. Four training-conditions were created according to two factors: the perceptual modalities (multisensory vs. visual) and the spatial disposition of the materials used (linear vs. non-linear). While the effect of spatial disposition was not highlighted in the arithmetic task, the multisensory training method induced a larger improvement of arithmetic performance as compared to the visual training alone. These results support the idea that haptic manipulation provides a bridge between concrete referents and abstract concepts.

... The tendency to commit positive decade errors (operationally defined as a response larger than the correct result by a multiple of 10 units) was higher for subtractions with respect to additions, but downward OKS was found to abolish this feature. Results thereby suggest that this kind of procedural errors might rely, to some extent, on spatial processes, in fully agreement with neuropsychological observations (de Hevia et al., 2008), and that they are subserved by different cognitive mechanisms. ...

In this work I present several studies, which might appear rather heterogeneous for both experimental questions and methodological approaches, and yet are linked by a common leitmotiv: spatial attention. I will address issues related to the assessment of attentional asymmetries, in the healthy individual as in patients with neurological disorders, their role in various aspects of human cognition, and their neural underpinning, driven by the deep belief that spatial attention plays an important role in various mental processes that are not necessarily confined to perception.
What follows is organized into two distinct sections. In the first I will focus on the evaluation of visuospatial asymmetries, starting from the description of a new paradigm particularly suitable for this purpose. In the first chapter I will describe the effects of multitasking in a spatial monitoring test; the main result shows a striking decreasing in detection performance as a function of the introduced memory load. In the second chapter I will apply the same paradigm to a clinical population characterized by a brain lesion affecting the left hemisphere. Despite a standard neuropsychological battery failed to highlight any lateralized attentional deficit, I will show that exploiting concurrent demands might lead to enhanced sensitivity of diagnostic tests and consequently positive effects on patients’ diagnostic and therapeutic management. Finally, in the third chapter I will suggest, in light of preliminary data, that attentional asymmetries also occur along the sagittal axis; I will argue, in particular, that more attentional resources appear to be allocated around peripersonal space, the resulting benefits extending to various tasks (i.e., discrimination tasks).
Then, in the second section, I will follow a complementary approach: I will seek to induce attentional shifts in order to evaluate their role in different cognitive tasks. In the fourth and fifth chapters this will be pursued exploiting sensory stimulations: visual optokinetic stimulation and galvanic vestibular stimulation, respectively. In the fourth chapter I will show that spatial attention is highly involved in numerical cognition, this relationship being bidirectional. Specifically, I will show that optokinetic stimulation modulates the occurrence of procedural errors during mental arithmetics, and that calculation itself affects oculomotor behaviour in turn. In the fifth chapter I will examine the effects of galvanic vestibular stimulation, a particularly promising technique for the rehabilitation of lateralized attention disorders, on spatial representations. I will discuss critically a recent account for unilateral spatial neglect, suggesting that vestibular stimulations or disorders might indeed affect the metric representation of space, but not necessarily resulting in spatial unawareness. Finally, in the sixth chapter I will describe an attentional capture phenomenon by intrinsically rewarding distracters. I will seek, in particular, to predict the degree of attentional capture from resting-state functional magnetic resonance imaging data and the related brain connectivity pattern; I will report preliminary data focused on the importance of the cingulate-opercular network, and discuss the results through a parallel with clinical populations characterized by behavioural addictions.

... Neuroscientific measurement allows for objective imagery testing but can also lend validity to the results of subjective self-report scales. Further, brain scans can be used to draw inferences on the relationship between brain activation patterns and measures like mathematics tests (de Hevia, Vallar, & Girelli, 2008). ...

Mathematics education researchers have examined the relationship between visualization and mathematics for decades (e.g., Arcavi, 2003; Bishop, 1991; Duval, 1999; Fennema & Tartre, 1985; Presmeg, 1986). Studies have linked spatial visualization ability, such as measured in mental rotation tasks, directly to mathematics self-efficacy (Pajares & Kranzler, 1995; Weckbacher & Okamoto, 2014), which in turn influences mathematics achievement (Casey, Nuttall, & Pezaris, 1997). With the important role that spatial visualization plays in learning mathematics, the recent identification of congenital aphantasia (Zeman, Dewar, & Della Sala, 2015), which is the lack of mental imagery ability, has raised new questions for mathematics education researchers. This study investigated the differences in mental rotation test performance and vividness of spatial imagery between people who have aphantasia and people who do not as a first step toward examining how aphantasia may affect mathematics learning and education. Results confirmed prior aphantasia research showing that there was no significant difference in mental rotation test performance between people with aphantasia and those without aphantasia, despite people with aphantasia reporting significantly lower vividness of spatial imagery. Results also showed that there was less difference in mental rotation test performance between the genders for people with aphantasia, while gender played a significant role in mental rotation test performance for people without aphantasia. People with aphantasia also reported lower self-efficacy in the arts than people without aphantasia. Implications of these results will be discussed within the context of current research, and possible directions for future research will be offered.

... Our GMD results included differences between mathematicians and non-mathematicians in the right IPS and right SPL, but not in the contralateral hemisphere. This might suggest that these differences are rooted in visuo-spatial abilities that are more right-lateralised, especially with respect to the parietal cortex (de Hevia, Vallar, & Girelli, 2008;Miller et al., 2018). While this suggestion would need further validation, the current results do also suggest a tendency of higher usage of visuospatial strategies to solve arithmetic problems by mathematicians. ...

Studies in several domains of expertise have established that experience-dependent plasticity brings about both functional and anatomical changes. However, little is known about how such changes come to shape the brain in the case of expertise acquired by professional mathematicians. Here, we aimed to identify cognitive and brain-structural (grey and white matter) characteristics of mathematicians as compared to non-mathematicians. Mathematicians and non-mathematician academics from the University of Oxford underwent structural and diffusion MRI scans, and were tested on a cognitive battery assessing working memory, attention, IQ, numerical and social skills. At the behavioural level, mathematical expertise was associated with better performance in domain-general and domain-specific dimensions. At the grey matter level, in a whole-brain analysis, behavioural performance correlated with grey matter density in left superior frontal gyrus – positively for mathematicians but negatively for non-mathematicians; in a region of interest analysis, we found in mathematicians higher grey matter density in the right superior parietal lobule, but lower grey matter density in the right intraparietal sulcus and in the left inferior frontal gyrus. In terms of white matter, there were no significant group differences in fractional anisotropy or mean diffusivity. These results reveal new insights into the relationship between mathematical expertise and grey matter metrics in brain regions previously implicated in numerical cognition, as well as in regions that have so far received less attention in this field. Further studies, based on longitudinal designs and cognitive training, could examine the conjecture that such cross-sectional findings arise from a bidirectional link between experience and structural brain changes that is itself subject to change across the lifespan.

... What explains the math-space link? One popular theory posits that numbers are represented spatially (de Hevia, Vallar, & Girelli, 2008). That is, humans come to conceive of and arrange numbers along a "mental number line," with small numbers belonging to the left and larger numbers extending to the right (Dehaene, Bossini, & Giraux, 1993). ...

Current evidence suggests that numerical, spatial, and executive function (EF) skills each play critical and independent roles in the learning and performance of mathematics. However, these conclusions are largely based on isolated bodies of research and without measurement at the latent variable level. Thus, questions remain regarding the latent structure and potentially shared and unique relations between numerical, spatial, EF, and mathematics abilities. The purpose of the current study was to (i) confirm the latent structure of the hypothesized constructs of numerical, spatial, and EF skills and mathematics achievement, (ii) measure their unique and shared relations with one another, and (iii) test a set of novel hypotheses aimed to more closely reveal the underlying nature of the oft reported space-math association. Our analytical approach involved latent-variable analyses (structural equation modeling) with a sample of 4- to 11-year-old children (N=316, Mage =6.68 years). Results of a confirmatory factor analysis demonstrated that numerical, spatial, EF, and mathematics skills are highly related, yet separable, constructs. Follow-up structural analyses revealed that numerical, spatial, and EF latent variables explained 84% of children’s mathematics achievement scores, controlling for age. However, only numerical and spatial performance were unique predictors of mathematics achievement. The observed patterns of relations and developmental trajectories remained stable across age and grade (preschool – 4th grade). Follow-up mediation analyses revealed that numerical skills, but not EF skills, partially mediated the relation between spatial skills and mathematics achievement. Overall, our results point to spatial visualization as a unique and robust predictor of children’s mathematics achievement.

... We assessed children's VSWM and symbolic access ability since these abilities are often associated with magnitude representation and math abilities (De Smedt and Gilmore, 2011;Friso-Van Den Bos et al., 2013;Vanbinst et al., 2015b;Paul and Reeve, 2016). VSWM is thought to support numerical magnitude processing, predicated on the proposition that magnitude information is spatially organized (Dehaene, 1992;Dehaene and Cohen, 1997;Zorzi et al., 2002;Dehaene et al., 2003;de Hevia et al., 2008). The speed and accuracy naming numbers (Arabic digits) has been used to assess the ability to access number symbols information (i.e., symbolic number knowledge) which is often invoked as an explanation for differences in symbolic magnitude abilities and in turn, math abilities (Rousselle and Noël, 2007;Berteletti et al., 2010;De Smedt and Gilmore, 2011). ...

Non-symbolic magnitude abilities are often claimed to support the acquisition of symbolic magnitude abilities, which, in turn, are claimed to support emerging math abilities. However, not all studies find links between non-symbolic and symbolic magnitude abilities, or between them and math ability. To investigate possible reasons for these different findings, recent research has analyzed differences in non-symbolic/symbolic magnitude abilities using latent class modeling and has identified four different magnitude ability profiles residing within the general magnitude ability distribution that were differentially related to cognitive and math abilities. These findings may help explain the different patterns of findings observed in previous research. To further investigate this possibility, we (1) attempted to replicate earlier findings, (2) determine whether magnitude ability profiles remained stable or changed over 1 year; and (3) assessed the degree to which stability/change in profiles were related to cognitive and math abilities. We used latent transition analysis to investigate stability/changes in non-symbolic and symbolic magnitude abilities of 109 5- to 6-year olds twice in 1 year. At Time 1 and 2, non-symbolic and symbolic magnitude abilities, number transcoding and single-digit addition abilities were assessed. Visuospatial working memory (VSWM), naming numbers, non-verbal IQ, basic RT was also assessed at Time 1. Analysis showed stability in one profile and changes in the three others over 1 year. VSWM and naming numbers predicted profile membership at Time 1 and 2, and profile membership predicted math abilities at both time points. The findings confirm the existence of four different non-symbolic–symbolic magnitude ability profiles; we suggest the changes over time in them potentially reflect deficit, delay, and normal math developmental pathways.

... We also tend to bisect lines with flanking numbers on a bias towards the higher number. Recent research has focused on these numerous links between space and number, providing us with a substantial amount of behavioural (and some neuroimaging) evidence on the interactions between numerical and spatial representations (for earlier reviews, see de Hevia, Vallar, & Girelli, 2008;Fias & Fischer, 2005;Fias, van Dijck, & Gevers, 2011;Fischer & Shaki, 2014;Gevers & Lammertyn, 2005;Hubbard, Piazza, Pinel, & Dehaene, 2005;McCrink & Opfer, 2014;Rossetti et al., 2011;Rugani & de Hevia, 2017;Umilta, Priftis, & Zorzi, 2009;G. Wood, Willmes, Nuerk, & Fischer, 2008). ...

... We also tend to bisect lines with flanking numbers on a bias towards the higher number. Recent research has focused on these numerous links between space and number, providing us with a substantial amount of behavioural (and some neuroimaging) evidence on the interactions between numerical and spatial representations (for earlier reviews, see de Hevia, Vallar, & Girelli, 2008;Fias & Fischer, 2005;Fias, van Dijck, & Gevers, 2011;Fischer & Shaki, 2014;Gevers & Lammertyn, 2005;Hubbard, Piazza, Pinel, & Dehaene, 2005;McCrink & Opfer, 2014;Rossetti et al., 2011;Rugani & de Hevia, 2017;Umilta, Priftis, & Zorzi, 2009;G. Wood, Willmes, Nuerk, & Fischer, 2008). ...

During the last decades, there have been a large number of studies into the number-related abilities of humans. As a result, we know that humans and non-human animals have a system known as the approximate number system that allows them to distinguish between collections based on their number of items, separately from any counting procedures. Dehaene and others have argued for a model on which this system uses representations for numbers that are spatial in nature and are shared by our symbolic and non-symbolic processing of numbers. However, there is a conflicting theoretical perspective in which there are no representations of numbers underlying the approximate number system, but only quantity-related representations. This perspective would then suggest that there are no shared representations between symbolic and non-symbolic processing. We review the evidence on spatial biases resulting from the activation of numerical representations, for both non-symbolic and symbolic tests. These biases may help decide between the theoretical differences; shared representations are expected to lead to similar biases regardless of the format, whereas different representations more naturally explain differences in biases, and thus behaviour. The evidence is not yet decisive, as the behavioural evidence is split: we expect bisection tasks to eventually favour shared representations, whereas studies on the spatial–numerical association of response codes (SNARC) effect currently favour different representations. We discuss how this impasse may be resolved, in particular, by combining these behavioural studies with relevant neuroimaging data. If this approach is carried forward, then it may help decide which of these two theoretical perspectives on number representations is correct.

... Research suggests that other, less traditional academic abilities-also known as domain-general cognitive processes (Welsh, Nix, Blair, Bierman, & Nelson, 2010)-are strongly associated with later outcomes (Heckman, Stixrud, & Urzua, 2006), although they are rarely taught explicitly in classrooms. Two interrelated cognitive processes in particular are critical for children's mathematics achievement: executive functions (EFs) and visuospatial (VS) skills (e.g., Best, Miller, & Naglieri, 2011;Bull & Lee, 2014;Cragg & Gilmore, 2014;de Hevia, Vallar, & Girelli, 2008;Geary, Hoard, Byrd-Craven, Nugent, & Numtee, 2007;Monette, Bigras, & Guay, 2011;Uttal et al., 2013;Verdine, Irwin, Golinkoff, & Hirsh-Pasek, 2014). The role of EFs and VS skills, individually, in the development of mathematics skills is not new; however, their interplay is not as well understood. ...

The purpose of this article is to review the literature and apply a developmental neuroscience perspective in investigating the role of two interrelated cognitive processes—executive functions (EFs) and visuospatial (VS) skills—which have been empirically and theoretically linked to children’s mathematics achievement. To illustrate, we provide evidence of the importance of EFs and VS skills for mathematics learning by examining and comparing the distinct cognitive profiles of individuals with autism spectrum disorder and Williams syndrome. By simultaneously considering two cognitive processes that are implicated in mathematics, we offer insight into the underlying mechanisms by which EFs and VS skills support children’s learning and acquisition of mathematical skills, as well as how neuroscience research may successfully inform educational practice.

... Visuospatial abilities in the literature were strongly related with math abilities and with performance in probabilistic problems (de Hevia, Vallar, & Girelli, 2008;Feeney, Adams, Webber, & Ewbank, 2004). Their implication in this type of performance is founded on the skill in representing and transfiguring symbolic and nonlinguistic data (Gardner, 1993). ...

A cross-national comparison between Italy and Spain was conducted on probabilistic reasoning performance presented in verbal-numerical and graphical-pictorial formats. This study investigated the similarities and differences in Psychology undergraduates in these two countries (Italy n=290; Spain n=130) and attempted to identify aspects that might enhance the probability of a student belonging to one country. The findings underscored that Spanish students had higher levels of visuospatial abilities, more positive attitudes toward statistics, lower statistical anxiety, and higher confidence in the correctness of their responses. Additionally, they gave a higher number of correct responses to problems presented in a verbal-numerical format. These data suggest interesting insights and highlight the interactions among multiple layers of variables at the collective, contextual, and individual levels.

... Research has also shown that the mental representation of numbers involves a spatial component (Fias and Fischer, 2005;de Hevia et al., 2008;Wood et al., 2008;Fischer and Shaki, 2014). Importantly, neural circuits involved in both spatial attention and number representations are located in the parietal cortex (reviewed by Hubbard et al., 2005). ...

At least three well-documented phenomena indicate a relationship between numbers and the internal representation of space. They are shifting attention in accordance with the localization of numbers on the mental number line (MNL); the spatial‑numerical association of response codes (SNARC) effect, which manifests as faster responses to high numbers with the right hand than with the left, and vice versa for low numbers; and the processing of both numbers and space primarily in the parietal cortex. Some EEG studies have pointed to the response selection stage as a locus of this effect. However, this explanation has yet to be corroborated by the fMRI experiments. The goal of this study was to investigate the functional anatomy underlying response selection induced by SNARC‑congruent and SNARC‑incongruent stimuli in a spatial visual cueing task. Healthy adult volunteers responded to a pair of target stimuli consisting of digits, non‑digit symbols, or a mix of both. In each trial, the stimuli were preceded by a centrally presented numerical or non‑numerical cue stimulus which was required to be memorized. One of the target stimuli that then appeared would be identical to the cue; the task was to determine which side it was presented on, within the pair. In the case of numerical stimuli, the side was congruent with its localization on the MNL in one‑half of the trials. In the other half of the trials, it was incongruent. The behavioral results revealed the SNARC effect, as well as a faster reaction to low numbers than to high numbers. The fMRI responses to the target stimuli showed engagement of regions implicated in number processing but also in sensory‑motor areas. This suggests that the motor response selection or execution stage may be the locus of the SNARC effect. Yet, the activation pattern obtained in the congruent and incongruent conditions did not allow us to determine, indisputably, the neural correlates of the mechanisms involved in the SNARC effect. Moreover, we did not observe any stimulus-specific responses to cues.

... The overlap of VSWM and arithmetic in the IPS in this study and in others (Zago et al., 2008) also highlights the close relationship between visuospatial processing and numerical processing. Compelling neuropsychological and neuroimaging evidence has been provided to suggest that number and space are closely related to one another (Hubbard, Piazza, Pinel, & Dehaene, 2005) and, more importantly, that visuospatial processing is important for calculation (de Hevia, Vallar, & Girelli, 2008). Memory for visuospatial information has been shown to have retinotopic organization in the IPS (Silver & Kastner, 2009;Konen & Kastner, 2008). ...

Visuospatial working memory (VSWM) plays an important role in arithmetic problem solving, and the relationship between these two skills is thought to change over development. Even though neuroimaging studies have demonstrated that VSWM and arithmetic both recruit frontoparietal networks, inferences about common neural substrates have largely been made by comparisons across studies. Little work has examined how brain activation for VSWM and arithmetic converge within the same participants and whether there are age-related changes in the overlap of these neural networks. In this study, we examined how brain activity for VSWM and arithmetic overlap in 38 children and 26 adults. Although both children and adults recruited the intraparietal sulcus (IPS) for VSWM and arithmetic, children showed more focal activation within the right IPS, whereas adults recruited the bilateral IPS, superior frontal sulcus/middle frontal gyrus, and right insula. A comparison of the two groups revealed that adults recruited a more left-lateralized network of fronto-parietal regions for VSWM and arithmetic compared with children. Together, these findings suggest possible neurocognitive mechanisms underlying the strong relationship between VSWM and arithmetic and provide evidence that the association between VSWM and arithmetic networks changes with age.

... This model shed light on the close relationship between numerical and spatial skills at the neural level. De Hevia et al. (2008) synthesized behavioral, neuropsychological, and neuroimaging studies and reached the same conclusion as what Walsh's (2003) model would suggest, i.e., in the realm of numerical and spatial cognition research, there is compelling evidence demonstrating that numerical and spatial representations are closely related. Specifically, these researchers argued that number and space are linked at the neural level through an imaginary mental number line where numerical magnitude is mapped onto an analogue spatial representation. ...

In this review, findings from studies investigating gender differences in spatial ability, math anxiety, and math achievement, the relationship between spatial ability and math anxiety, between spatial ability and math achievement, and between math anxiety and math achievement are synthesized. As a result of this synthesis, a sequential mediation model that allows simultaneous testing of two mediational relationships has been derived. Within this model, paths from gender to spatial ability, from spatial ability to math anxiety, and from math anxiety to math achievement are more strongly supported by prior studies than the paths from gender to math anxiety, from gender to math achievement, and from math achievement to math anxiety.

... This numerical-spatial relationship is considered to be automatically activated during simple numerical processing operations (for instance when solving small calculations, number estimations or approximations, or in a parity task 1 ). This idea is also based on mathematicians' reports who describe the use of visuo-spatial imagery in mathematical reasoning and symbolic calculations (De Hevia et al., 2008;De Hevia and Spelke, 2010;Fitzgerald and James, 2007;Tall, 2005;Tall and Mejia-Ramos, 2006). In fact, many people describe anecdotal experiences of "vivid mental number lines" when imagining numbers. ...

The objective of this thesis is the study of bilingual mathematics within the scientific field of Numerical Cognition. The approach to how bilingual people represent and access magnitude is currently a matter of growing interest that responds to the need to understand the role that language plays in the early acquisition of mathematics. This importance is usually reflected in the context of education, where learning arithmetic and bilingualism come together naturally. Given the importance in our society of both, math competence and early learning of a second language, research from a Cognitive Neuroscience perspective is necessary to better understand the bilingual brain.

... In a seminal paper published almost 30 years ago, Dehaene et al. (1993) reported for the first time that adult participants tested in a parity judgment task of symbolic digits were faster to respond to small numbers with the left hand and to large numbers with the right hand. This effect has been taken as an empirical proof supporting the intuitive idea that numbers are spatially organized from left to right along a mental line (Galton, 1880a, b) and, beyond being replicated in various settings (e.g., Cipora et al., 2019), this phenomenon has inspired much subsequent work (de Hevia et al., 2008). Although originally reported with symbolic stimuli (e.g., Arabic digits or number words), similar spatial-numerical associations (SNAs) have been obtained also with nonsymbolic numerical stimuli (e.g., arrays of objects or sequences of tones) allowing replication in animal research (e.g., Rugani et al., 2015Rugani et al., , 2020 and in preliterate children (Bulf et al., 2016;de Hevia et al., 2014;de Hevia et al., 2017;Ebersbach et al., 2014), hence suggesting a biological foundation of this mapping. ...

There is an intense debate surrounding the origin of spatial-numerical associations (SNAs), according to which small numbers are mapped onto the left side of the space, whereas large numbers to the right. Despite large evidence suggests that SNAs would emerge as an innate predisposition to map numerical information onto a left-to-right spatially oriented mental representation, alternative accounts have challenged these proposals maintaining that such a mapping would be the result of a mere spatial frequency (SF) coding of any visual image. That is, any smaller or larger array of objects would naturally contain more low or high SFs information and, accordingly, each hemisphere would be preferentially tuned only for one SF range (e.g., right hemisphere tuned for low SF and left hemisphere tuned for high SF). This would determine the typical SNA (e.g., faster RTs for small numerical arrays with left hand). To directly probe the role of SF coding in SNAs, we tested participants in a typical dot-arrays comparison task with two numerical sets: one in which SF were confounded with numerosity (Experiment 1), and one in which the full SF power spectrum was equalized across all stimuli, keeping therefore this cue uninformative about numerosity (Experiment 2). We found that SNAs emerged in both experiments, hence independently of whether SF was confounded or not with numerosity. Taken together, these findings suggest that SNAs cannot simply originate from SF power spectrum alone and, thus, they rule out the brain’s asymmetric SF tuning as a primary cause of such effect.

... It proposes that numbers are represented on a left-to-right continuum. Moreover, numbers and space have a common brain basis in several cortical areas [15][16][17][18][19][20]. Accordingly, DD has been demonstrated to be due to anatomical and functional abnormalities in the regions that are pivotal for basic numerical abilities (e.g., [2][3][4][5][6]). ...

An ability that is impaired in developmental dyscalculia (DD) is related to number line estimation (NLE). However, due to variability in NLE task performance, group differences do not exemplify the real difficulty level observed in the DD population. Thirty-two of the fifty-two participants posing dyscalculia risk (DR) (mean age = 9.88) experienced difficulties in mathematics. All the children performed two number-to-position tasks and two tasks requiring a verbal estimation of a number indicated on a line, utilizing the ranges 0–100 and 0–1000. The results showed that the estimation error in the verbal task was greater in the DR group than in the typically developed (TD) group for the 0–1000 range. In the number-to-position task, group differences were found for both ranges and the variability within both groups was smaller than it was in the verbal tasks. Analyses of each of the 26 numerical magnitudes revealed a more comprehensive pattern. The majority of the group effects were related to the 0–1000 line. Therefore, considerable data variability, especially in the DD group, suggests this issue must be analyzed carefully in the case of other mathematical capacities. It also critically questions some well-established phenomena and norms in experimental and diagnostic practices.

... Given the strong asymmetry in the perception of vertical and horizontal sizes, it is reasonable to ask whether a similar effect could be identified in non-symbolic numerical estimation. The fact that a significant body of literature indicates a link between spatial and numerical abilities (e.g., de Hevia, Vallar, & Girelli, 2008;Krause, Bekkering, Pratt, & Lindemann, 2017) also legitimates such a question. Many studies suggest that non-symbolic numerical estimation is affected by continuous quantities, such as the cumulative surface area (sum of areas) or convex hull (overall space occupied by the most lateral items) of the stimuli (Gebuis & Reynvoet, 2012a, 2012bLeibovich, Katzin, Harel, & Henik, 2017;but see DeWind, Adams, Platt, & Brannon, 2015;Cicchini, Anobile, & Burr, 2016;Park, Dewind, Woldorff, & Brannon, 2016 for a different perspective). ...

Many studies have investigated whether numerical and spatial abilities share similar cognitive systems. A novel approach to this issue consists of investigating whether the same perceptual biases underlying size illusions can be identified in numerical estimation tasks. In this study, we required adult participants to estimate the number of white dots in arrays made of white and black dots displayed in such a way as to generate horizontal–vertical illusions with inverted T and L configurations. In agreement with previous literature, we found that participants tended to underestimate the target numbers. However, in the presence of the illusory patterns, participants were less inclined to underestimate the number of vertically aligned white dots. This reflects the perceptual biases underlying horizontal–vertical illusions. In addition, we identified an enhanced illusory effect when participants observed vertically aligned white dots in the T shape compared to the L shape, a result that resembles the length bisection bias reported in the spatial domain. Overall, we found the first evidence that numerical estimation differs as a function of the vertical or horizontal displacement of the stimuli. In addition, the involvement of the same perceptual biases observed in spatial tasks supports the idea that spatial and numerical abilities share similar cognitive processes.

... Much work in the past has been devoted to highlight the similarities in the processing of quantitative dimensions of number, space and time, providing strong evidence that these dimensions share functional similarities, are spontaneously mapped onto one another, and are mentally organized along a spatial continuum, in adults (e.g., Bonato, Zorzi, & Umiltà, 2012;Bueti & Walsh, 2009;de Hevia, 2016b;de Hevia, Vallar, & Girelli, 2008;Ren, Nicholls, Ma, & Chen, 2011;Sellaro, Treccani, Job, & Cubelli, 2015), children (e.g., de Hevia, Vanderslice, & Spelke, 2012;de Hevia & Spelke, 2010), infants (e.g., Bulf et al., 2016;de Hevia, 2016a;Feigenson, 2007), and non-human animals (e.g., Rugani & de Hevia, 2017). However, recent work is also disclosing the existence of differential cognitive attributes characterizing the processing of different magnitudes across the lifespan. ...

The ability to discriminate the ordinal information embedded in magnitude-based sequences has been shown in 4-month-old infants, both for numerical and size-based sequences. At this early age, however, this ability is confined to increasing sequences, with infants failing to extract and represent decreasing order. Here we investigate whether the ability to represent order extends to duration-based sequences in 4-month-old infants, and whether it also shows the asymmetry signature previously observed for number and size. Infants were tested in an order discrimination task in which they were habituated to either increasing or decreasing variations in temporal duration, and were then tested with novel sequences composed of new temporal items whose durations varied following the familiar and the novel orders in alternation. Across three experiments, we manipulated the duration of the single temporal items and therefore of the whole sequences, which resulted in imposing more or less constraints on infants' working memory, or general processing capacities. Results showed that infants failed at discriminating the ordinal direction in temporal sequences when the sequences had an overall long duration (Experiment 1), but succeeded when the duration of the sequences was shortened (Experiments 2 and 3). Moreover, there was no sign of the asymmetry signature previously reported for number and size, as successful discrimination was present for infants habituated to both increasing and decreasing sequences. These results suggest that sensitivity to temporal order is present very early in development, and that its functional properties are not shared with other magnitude dimensions, such as size and number.

... Numerical magnitudes have spatial representations, and this spatial grounding of numbers is based on the metaphor of the Mental Number Line (MNL) (Restle, 1970;Dehaene, 1997), which proposes that numbers are represented on a left-to-right continuum. Moreover, numbers and space are conjointly processed in the brain (Capeletti, Muggleton, Walsh, 2009;de Hevia, Vallar, & Girelli, 2008;Farnè, & Rossetti, 2006;Fischer & Shaki, 2014;Hubbard, Piazza, Pinel, & Dehaene, 2005;Göbel, Calabria, 2006;Sandrini & Rusconi, 2009). Importantly, the brain areas involved in this spatial-numerical processing reveal anatomical and functional abnormalities in dyscalculia (e.g. ...

The aim of the study was to examine the effect of cognitive deficits, which are present in mathematical learning disabilities (e.g. dyscalculia risk) on the mental number line processing with the use of the one-digit numbers range as well as their symbolic and non-symbolic format of presentation.

... Indeed, in a seminal paper published almost 30 years ago, Dehaene and colleagues (Dehaene, Bossini, & Giraux, 1993) reported for the first time that adult participants tested in a parity judgment task of symbolic digits were faster to respond to small numbers with the left hand and to large numbers with the right hand. This effect has been taken as an empirical proof supporting the intuitive idea that numbers are spatially organized from left-toright along a mental line (Galton, 1880a, b) and, beyond being replicated in various settings (e.g., Cipora, Soltanlou, Reips, & Nuerk, 2019), this phenomenon has inspired much subsequent work (de Hevia, Vallar, & Girelli, 2008). Although originally reported with symbolic stimuli (e.g., Arabic digits or number words), similar spatial-numerical associations (SNAs) have been obtained also with nonsymbolic numerical stimuli (e.g., arrays of objects or sequences of tones) allowing replication in animal research (e.g., Rugani, Vallortigara, Priftis, & Regolin, 2015) and in preliterate children (Bulf, de Hevia, & Macchi Cassia, 2016;de Hevia, Girelli, Addabbo, & Macchi Cassia, 2014;de Hevia, Veggiotti, Streri, & Bonn, 2017;Ebersbach, Luwel, & Verschaffel, 2014), hence suggesting a biological foundation of this mapping. ...

... Spatial ability is defined as "the ability to generate, retain, retrieve and transform well-structured visual images" (Lohman, 1994(Lohman, , p. 1000). The relation between math abilities and spatial skills is evident in both behavioral (for a review, see de Hevia, Vallar, & Girelli, 2008) and neuropsychological measures (e.g., Hubbard, Piazza, Pinel, & Dehaene, 2005;Pinel, Piazza, Le Bihan, & Dehaene, 2004). People with high spatial ability perform better on mathematical tests (Mix & Cheng, 2012), and important theories such as the triple-code model claim that participants rely on visuo-spatial processes when they are engaged in arithmetic and numerical processing (e.g., Dehaene, 1992). ...

Previous studies suggested that highly math-anxious (HMA) individuals invest more attentional resources than their low math-anxious (LMA) peers in numerical tasks, and have worse spatial skills. We aimed to explore whether they also need to apply more resources in spatial tasks. In this study, HMA and LMA individuals saw normal or mirror-reversed letters in six orientations and made mirror-normal decisions. In both groups, response times and errors increased with angular deviation from upright and the ERP mental rotation effect was found. However, HMAs were slower to respond than their LMA counterparts. Interestingly, the HMA group showed a larger P3b in greater deviations for normal letters and in all mirrored letters. Since P3b amplitude reflects the attentional resources invested in the categorization of relevant stimuli, HMA individuals may need to devote more processing effort than their LMA peers when performing mental rotation. This finding is consistent with the Attentional Control Theory.

... In arithmetic fact fluency it can be assumed that the increasing load of WM capacity might be related to greater usage of less sophisticated concrete strategies such as counting. These strategies might demand maintenance and manipulation of quantities through a mental visual imagery in the WM (de Hevia et al., 2008). ...

This study investigated the underlying cognitive abilities which are related to both fluency in reading and arithmetic across different developmental phases of their acquisition. An unselected sample of children in first (N = 83), second (N = 66), and third (N = 67) grades completed several reading and arithmetic fluency tasks, as well as rapid automatized naming (RAN), working memory (WM), and inhibition measures. The results of a stepwise regression analysis revealed differences in the predictive models of fluency in both academic domains in first grade. However, similar patterns were found in the second and third grades. Specifically, in first grade reading fluency was predicted by inhibition and WM, while arithmetic fact fluency was predicted by RAN and WM. In contrast, in second grade both types of fluency were predicted by RAN and WM, and in third grade only RAN was found to be a predictor. Alongside the gradual reduction in the cognitive components participating in reading and arithmetic fluency, the results of the present study suggest that both fluencies share the same underlying cognitive mechanisms. Practical implications of the current results are discussed.

... Mix et al. (2016) indicated that the spatial and mathematical skills are separate but closely related from kindergarten through sixth grade. Besides, robust evidence from research in cognitive neuroscience suggests that spatial processing is associated with math processing ( deHevia, Vallar, &Girelli, 2008 ;Hubbard, Piazza, Pinel, & Dehaene, 2005 ;Pinel, Piazza, Le Bihan, &Dehaene, 2004 ). For example, cognitive tasks that require spatial transformation and those that require numerical processing tend to activate the same structure within the parietal lobe ( Hubbard et al., 2005 ). ...

Children's early cognitive skills are believed to be associated with their later academic achievement and even lifelong success. Among various cognitive skills, spatial skills are considered a strong predictor of children's future math and reading performance. This study examined the relations between Chinese kindergarteners’ spatial skills and their subsequent math and reading achievement in second grade. Spatial skills (spatial perception, spatial visualization, and mental rotation), vocabulary, working memory, self-regulation ability, and academic competencies of 182 Chinese children were assessed in their last year of kindergarten. Follow up tests were then conducted on the children's academic competencies in math and reading in second grade. After controlling for demographics and a range of early domain-general and academic skill variables in a multilevel model, the unique associations between the children's early spatial skills and their academic achievement in second grade were assessed. The results showed that the children's spatial visualization ability in kindergarten was positively related to their math and reading performance in second grade. The children's spatial perception ability was also positively associated with their math performance in second grade. No association was found between early mental rotation and academic performance in second grade. Overall, the findings suggest that early spatial skills may have long-term effects on children's academic achievement in primary school. The effects need to be understood in the Chinese sociocultural context. The implications of the findings are discussed.

Number interval bisection consists of estimating the mid-number within a pair (1–9=>5). Healthy adults and right-brain damage patients can show biased performance in this task, underestimating and overestimating the mid-number, respectively. The role of visuospatial attention during this task, and its interplay with other cognitive abilities (e.g., working memory) is still object of debate. In this study we explored the relation between visuospatial attention and individual differences in working memory and executive functions during number interval bisection. To manipulate the deployment of visuospatial attention, healthy participants tracked a dot moving to the left or moving to the right while bisecting numerical intervals. We also collected information concerning verbal and visuospatial short-term memory span, and concerning verbal and visuospatial fluency scores. Beside replicating what is typically observed in this task (e.g., underestimation bias), a correlation was observed between verbal short-term memory and bisection bias, and an interesting relation between performance in the number interval bisection, verbal short-term memory, and visuospatial attention. Specifically, performance of those participants with low verbal span was affected by the direction of the moving dot, underestimating at a larger extent when the dot moved leftward than rightward. Finally, it was also observed that participants’ verbal fluency ability contributed in the generation of biases in the numerical task. The finding of the involvement of abilities belonging to the verbal domain contributes to unveil the multi-componential nature of number interval bisection. Considering the debate on the nature of number interval bisection and its use in the clinical assessment of deficits following brain damage, this finding may be interesting also from a clinical perspective.

Arithmetical deficits in right-hemisphere damaged patients have been traditionally considered secondary to visuo-spatial impairments, although the exact relationship between the two deficits has rarely been assessed. The present study implemented a voxelwise lesion analysis among 30 right-hemisphere damaged patients and a controlled, matched-sample, cross-sectional analysis with 35 cognitively normal controls regressing three composite cognitive measures on standardized numerical measures. The results showed that patients and controls significantly differ in Number comprehension, Transcoding, and Written operations, particularly subtractions and multiplications. The percentage of patients performing below the cutoffs ranged between 27% and 47% across these tasks. Spatial errors were associated with extensive lesions in fronto-temporo-parietal regions -frequently leading to neglect-whereas pure arithmetical errors appeared related to more confined lesions in the right angular gyrus and its proximity. Stepwise regression models consistently revealed that spatial errors were primarily predicted by composite measures of visuo-spatial attention/neglect and representational abilities. Conversely, specific errors of arithmetic nature linked to representational abilities only. Crucially, the proportion of arithmetical errors (ranging from 65% to 100% across tasks) was higher than that of spatial ones. These findings thus suggest that unilateral right hemisphere lesions can directly affect core numerical/arithmetical processes, and that right-hemisphere acalculia is not only ascribable to visuo-spatial deficits as traditionally thought.

Spatial skills, the ability to encode, remember, and mentally manipulate the spatial features and relations of objects or space, are central to our daily functioning. They allow us to recall the location of car keys, navigate a route to work, and provide directions to the nearest restaurant or café. Spatial skills also are pivotal for academic achievement (e.g., Delgado & Prieto, 2004; Newcombe & Frick, 2010). They predict later math competence (e.g., Lauer & Lourenco, 2016; Mix et al., 2013, 2016; Verdine et al., 2014; Wang et al., 2021) and entry into the Science, Technology, Engineering and Mathematics (STEM) fields (e.g., Wai et al., 2009). Proficiency in visuospatial ability has long been associated with success in cognitively demanding educational tracks and occupations such as engineering, architecture, physics, chemistry, and surgery (e.g., Snow & Yalow, 1982; Sorby, 2001, 2009; Sorby & Baartmans, 2000) and is a salient characteristic of physical scientists (Gohm et al., 1998; Humphreys et al., 1993).

Objective
Engaging in a healthy diet and positive lifestyle behaviors have been shown to improve cognitive functioning in children and older adults, however, few have examined these factors in college-aged students. Participants: A diverse sample of 115 college students were recruited on two university campuses. Method: Completed computerized cognitive testing and an online survey about diet and lifestyle behaviors. Results: All analyses were conducted with Pearson’s correlations. Higher fruit consumption was correlated with better visual memory scores. Higher seafood consumption was correlated with better learning performance. Increased fast food consumption was correlated with poorer executive functioning in resident students and poorer visual memory performance in commuter students. Increased fluid intake on testing day was correlated with better visual memory and better verbal memory performance. Conclusions: Behavioral changes such as increasing hydration, eating more fruit and fish, and eating less fast food may improve cognitive performance in college students.

Previous studies showed that the magnitude information conveyed by sensory cues, such as length or surface, influences the ability to compare the numerosity of sets of objects. However, the perceptual nature of this representation and how it interacts with the processes involved in numerical judgements remain unclear. This study aims to address these issues by studying the interference of length on numerosity under different perceptual and response conditions. The first experiment shows that the influence of length does not depend on the actual length but on subjective values reflecting the way length is perceived in a given visual context. The Müller-Lyer illusion was used to manipulate the perceived length of two dot arrays independently of their actual length. When the length of two dot arrays was equal but perceived as different due to the illusion, participants erroneously reported differences in the number of dots contained in each array, evidencing a similar effect of Müller-Lyer illusion on length and numerosity comparison. This finding was replicated in a second experiment where participants had to give a verbal estimate of the number of dots contained in a given array, thereby eliminating the choice between a small or large response. Compared with a neutral condition, estimations were systematically larger than the actual number of dots as the illusory length increased. These results demonstrate that the illusory-induced experience of length influences numerosity estimation over and beyond objective cues and that this influence is not a response selection bias.

Space-number and space-time associations have been a timely topic in the cognitive sciences for years, but evidence from developmental populations is still scarce. In particular, it remains to be established whether space-number and space-time mappings are anchored onto the same spatial frame of reference across development. To explore this issue, we manipulated visual and proprioceptive feedback in a Number Comparison task (Experiment 1) and a Time Comparison task (Expriment 2), in which 6- and 10-year-old children had to classify numerical and temporal words by means of a lateralised response with or without a blindfold (visual manipulation), and with hands uncrossed or crossed over the body midline (proprioceptive manipulation). Results revealed that 10-year-old children were more efficient in associating smaller numbers and past events with the left key, and larger numbers and future events with the right key, irrespective of the visual and proprioceptive manipulations. On the contrary, younger children did so only in the Time Comparison task, but not in the Number Comparison task. In the latter task, 6-year-olds associated small/large numbers with the left/right side of space only in the presence of visual feedback, but not when blindfolded. Taken together, our findings unveil that in school-aged children the spatial representation of number and time develop on different spatial frames of reference: while space-time associations exclusively rely on external coordinates at age 6, space-number associations shift from mixed internal and external coordinates at age 6 to more adult-like external coordinates by age 10.

Recent studies have suggested that multisensory redundancy may improve cognitive learning. According to this view, information simultaneously available across two or more modalities is highly salient and, therefore, may be learned and remembered better than the same information presented to only one modality. In the current study, we wanted to evaluate whether training arithmetic with a multisensory intervention could induce larger learning improvements than a visual intervention alone. Moreover, because a left-to-right-oriented mental number line was for a long time considered as a core feature of numerical representation, we also wanted to compare left-to-right-organized and randomly organized arithmetic training. Therefore, five training programs were created and called (a) multisensory linear, (b) multisensory random, (c) visual linear, (d) visual random, and (e) control. A total of 85 preschoolers were randomly assigned to one of these five training conditions. Whereas children were trained to solve simple addition and subtraction operations in the first four training conditions, story understanding was the focus of the control training. Several numerical tasks (arithmetic, number-to-position, number comparison, counting, and subitizing) were used as pre- and post-test measures. Although the effect of spatial disposition was not significant, results demonstrated that the multisensory training condition led to a significantly larger performance improvement than the visual training and control conditions. This result was specific to the trained ability (arithmetic) and is discussed in light of the multisensory redundancy hypothesis.

Where and under what conditions do spatial and numerical skills converge and diverge in the brain? To address this question, we conducted a meta-analysis of brain regions associated with basic symbolic number processing, arithmetic, and mental rotation. We used Activation Likelihood Estimation (ALE) to construct quantitative meta-analytic maps synthesizing results from 86 neuroimaging papers (~ 30 studies/cognitive process). All three cognitive processes were found to activate bilateral parietal regions in and around the intraparietal sulcus (IPS); a finding consistent with shared processing accounts. Numerical and arithmetic processing were associated with overlap in the left angular gyrus, whereas mental rotation and arithmetic both showed activity in the middle frontal gyri. These patterns suggest regions of cortex potentially more specialized for symbolic number representation and domain-general mental manipulation, respectively. Additionally, arithmetic was associated with unique activity throughout the fronto-parietal network and mental rotation was associated with unique activity in the right superior parietal lobe. Overall, these results provide new insights into the intersection of numerical and spatial thought in the human brain.

In Western cultures, small-left and large-right spatial-numerical associations are constantly found in various simple number processing tasks. It has recently been suggested that spatial associations are also involved in more complex number processing, for example that individuals make rightward or upward “mental” movements along the number line during addition, and leftward or downward movements during subtraction. In line with this, it has been shown that participants' spontaneous eye movements on a blank screen during upward and downward counting follow such associations. The present research investigated whether eye movements along the number line are simply an epiphenomenon of the recruitment of a spatial reference frame, or whether they play a functional role for the arithmetic computation. This question was addressed by using multi-step problems (e.g., 59 + 5 + 4 + 3) that show a larger proportion of computation (vs. retrieval) when compared to single-step problems (e.g., 59 + 5), as confirmed in Pretest 1. Moreover, the question was addressed only for addition problems and vertical eye movements, because spatial-arithmetic associations were not found in the other conditions (subtraction, horizontal eye movements) in Pretest 2. In the main experiment, participants (n = 29) solved addition problems while following a moving dot with their eyes (smooth pursuit) either in a congruent (upward) or incongruent (downward) direction, or while keeping their eyes fixated on to the center of the screen, or while moving their eyes freely on a blank screen. Arithmetic performance was faster in the congruent condition (upward eye movements) when compared to the other conditions (downward eye movements, central fixation, free viewing). These results suggest that vertical shifts in spatial attention along the mental number line are functionally involved in addition. The results support the view of shared mechanisms for directing spatial attention in external (visual) and representational (number space). Implications for embodied views of number processing are discussed.

Developmental dyscalculia is a neurodevelopmental disorder, influencing the learning of mathematics in developing children. In the last two decades, continuous growth of research has helped in the advancement of the state of knowledge of dyscalculia. This upsurge in the number of studies makes it relevant to conduct a systematic review, covering all the empirical evidence, but there is a dearth of review studies synthesizing findings of the studies in the recent past. Therefore, the current study aims to systematically review studies investigating the underlying cognitive causal factors associated with developmental dyscalculia in the last two decades. To investigate the underlying cognitive factors associated with dyscalculia, two prominent approaches have been used: domain-general and domain-specific. While the domain-general approach argues for the deficit in general cognitive abilities, the domain-specific approach argues for the deficit in core numerical abilities. In the present review, the PRISMA method is followed. Articles were searched using two methods: firstly, through database sources of Google Scholar, Web of Science, and ScienceDirect, 1738 abstracts were screened, of which 46 articles met the specific inclusion criteria; and secondly, through recently published systematic reviews and meta-analyses, 29 studies were included. A total of 75 studies, 48 studies from domain-general and 27 studies from domain-specific approaches, have been selected. This review discusses domain-general and domain-specific approaches of developmental dyscalculia, along with specific theories associated with both approaches. Based on the discussed findings, visuospatial working memory and symbolic number processing abilities emerged as the best predictor of math ability in children with dyscalculia.

It has been shown repeatedly that relatively small numbers are responded to faster with the left hand and relatively large numbers are responded to faster with the right hand. This so-called SNARC effect (Dehaene, Bossini, & Giraux, 1993) is thought to arise through activation of irrelevant spatial codes associated with the magnitude of the number. This conflict between irrelevant magnitude information and the response is conceptually similar to the well-known Simon effect. Recently, both Mapelli, Rusconi, and Umiltà (2003) and Keus and Schwarz (in press) directly compared both effects in a single task within the framework of the additive factor method (Sternberg, 1969). While Mapelli et al. found additive effects of SNARC and Simon levels, suggesting different processing stages, Keus and Schwarz found that the SNARC effect depended on the compatibility level of the Simon task leading them to propose a common origin at the response selection stage. In the present study we demonstrate in 2 experiments that the relationship between Simon and SNARC depends on the relevance of the magnitude code, thereby violating one of the core assumptions of the AFM. Instead we propose a temporal overlap model to interpret the relationship between these effects which allows to commensurate apparently divergent outcomes.

Models of human number representation are based mainly on evidence from indirect sources such as number comparison tasks and findings on acquired dyscalculia. Researchers have rarely looked at the processing times of individual numbers. The experiments described in this article indicate that this neglect may have been unwarranted because number reading times considerably constrain the range of acceptable theoretical models. In particular, it is found that the time to process an Arabic integer from 1 to 99 is a function of the logarithm of the number magnitude, the frequency of the number, and sometimes the syllable length of the number name. In addition, processing a number facilitates the processing of a subsequent number with a close value. The effects of number magnitude and number priming are found for number naming as well, indicating that phonological recoding in silent reading (as evidenced by the syllable-length effect) happens after the internal semantic numerical representation has been accessed. (PsycINFO Database Record (c) 2012 APA, all rights reserved)

Data on numerical processing by verbal (human) and non-verbal (animal and human) subjects are integrated by the hypothesis that a non-verbal counting process represents discrete (countable) quantities by means of magnitudes with scalar variability. These appear to be identical to the magnitudes that represent continuous (uncountable) quantities such as duration. The magnitudes representing countable quantity are generated by a discrete incrementing process, which defines next magnitudes and yields a discrete ordering. In the case of continuous quantities, the continuous accumulation process does not define next magnitudes, so the ordering is also continuous (‘dense’). The magnitudes representing both countable and uncountable quantity are arithmetically combined in, for example, the computation of the income to be expected from a foraging patch. Thus, on the hypothesis presented here, the primitive machinery for arithmetic processing works with real numbers (magnitudes).

Positron emission tomography was used to examine the cerebral networks underlying number comparison and multiplication in eight normal volunteers. Cerebral blood flow was measured within anatomical regions of interest defined in each subject using magnetic resonance imaging. Three conditions were used: rest with eyes closed, mental multiplication of pairs of arabic digits and larger-smaller comparison of the same pairs. Both multiplication and comparison activated the left and right lateral occipital cortices, the left precentral gyrus, and the supplementary motor area. Beyond these common activations, multiplication activated also the left and right inferior parietal gyri, the left fusiform and lingual gyri, and the right cuneus. Relative to comparison, multiplication also yielded superior activity in the left lenticular nucleus and in Brodmann's area 8, and induced a hemispheric asymmetry in the activation of the precentral and inferior frontal gyri. Conversely, relative to multiplication, comparison yielded superior activity in the right superior temporal gyrus, the left and right middle temporal gyri, the right superior frontal gyrus, and the right inferior frontal gyrus. These results underline the role of bilateral inferior parietal regions in number processing and suggest that multiplication and comparison may rest on partially distinct networks.

The area of cognitive arithmetic is concerned with the mental representation of number and arithmetic, and the processes and procedures that access and use this knowledge. In this article, I provide a tutorial review of the area, first discussing the four basic empirical effects that characterize the evidence on cognitive arithmetic: the effects of problem size or difficulty, errors, relatedness, and strategies of processing. I then review three current models of simple arithmetic processing and the empirical reports that support or challenge their explanations. The third section of the review discusses the relationship between basic fact retrieval and a rule-based component or system, and considers current evidence and proposals on the overall architecture of the cognitive arithmetic system. The review concludes with a final set of speculations about the all-pervasive problem difficulty effect, still a central puzzle in the field.

Nine experiments of timed odd-even judgments examined how parity and number magnitude are accessed from Arabic and verbal numerals. With Arabic numerals, Ss used the rightmost digit to access a store of semantic number knowledge. Verbal numerals went through an additional stage of transcoding to base 10. Magnitude information was automatically accessed from Arabic numerals. Large numbers preferentially elicited a rightward response, and small numbers a leftward response. The Spatial-Numerical Association of Response Codes (SNARC) effect depended only on relative number magnitude and was weaker or absent with letters or verbal numerals. Direction did not vary with handedness or hemispheric dominance but was linked to the direction of writing, as it faded or even reversed in right-to-left writing Iranian Ss. The results supported a modular architecture for number processing, with distinct but interconnected Arabic, verbal, and magnitude representations.

This book is the magnum opus of one of the most influential cognitive psychologists of the past 50 years. This new volume on the model he created (with Graham Hitch) discusses the developments that have occurred in the past 20 years, and places it within a broader context. Working memory is a temporary storage system that underpins onex' capacity for coherent thought. Some 30 years ago, Baddeley and Hitch proposed a way of thinking about working memory that has proved to be both valuable and influential in its application to practical problems. This book updates the theory, discussing both the evidence in its favour, and alternative approaches. In addition, it discusses the implications of the model for understanding social and emotional behaviour, concluding with an attempt to place working memory in a broader biological and philosophical context. Inside are chapters on the phonological loop, the visuo-spatial sketchpad, the central executive and the episodic buffer. There are also chapters on the relevance to working memory of studies of the recency effect, of work based on individual differences, and of neuroimaging research. The broader implications of the concept of working memory are discussed in the chapters on social psychology, anxiety, depression, consciousness, and on the control of action. Finally, the author discusses the relevance of a concept of working memory to the classic problems of consciousness and free will.

Do numbers presented in different formats activate exactly the same semantic representations? Results of 6 experiments argue in favor of the hypothesis according to which different intermediate representations are activated, depending on the lexico-syntactic structure of the numeral to be processed. First, equation verification is faster when the calculation mimics the structure of the roman numeral proposed as a solution (e.g., VII = 5 + 2). Second, comparing the magnitude of 2 verbal numerals is more rapid when the 2 items share the same lexico-syntactic structure (e.g., twelve hundred, fourteen hundred) than when they do not (e.g., twelve hundred, one thousand four hundred). Third, when calculating orally, participants tend to use the same verbal structure to express their response as the one used in the problem's addends. The implications of these results for the different views of numerical representations are discussed.

This paper presents a single-case study of a patient (NR) showing a very specific (though not isolated) disorder in Arabic number reading. The type of reading errors and the pattern of the results observed in tasks tapping different components of the number processing system support the hypothesis of a deficit in the syntactic module of the Arabic comprehension system (in McCloskey, Sokol, & Goodman's [1986] model). NR's deficit is also examined in the light of two other number reading models: Seron and Deloche (1984) and Cohen and Dehaene (1991). In addition, the opposition beween semantic and asemantic transcoding models is discussed. In tasks based on a representation of the quantity, NR's errors with Arabic forms seem to result from correct semantic processing based on the expected verbal transcoded forms; this is easily interpretable in the semantic transcoding model (e.g. McCloskey et al., 1986), whereas in asemantic perspectives (e.g. Seron & Deloche, 1984; Cohen & Dehaene, 1991) no direct explanation is proposed. In this respect, a “preferred entry code” hypothesis is developed.

This study investigated cognitive interactions between visuo-motor processing and numerical cognition. In a pointing task healthy participants moved their hand to a left or right target, depending on the parity of small or large digits (1, 2, 8, or 9) shown at central fixation. Movement execution was faster when left-responses were made to small digits and right-responses to large digits. These results extend the SNARC effect (spatial-numerical association of response codes) to manual pointing and support the notion of a spatially oriented mental number line.

This paper reports three experiments using the secondary task methodology of working memory, in the task analysis of a complex computer game, ‘SPACE FORTRESS’. Unlike traditional studies of working memory, the primary task relies on perceptual-motor skills and accurate timing of responses as well as short- and long-term strategic decisions. In experiment 1, highly trained game performance was affected by the requirement to generate concurrent, paced responses and by concurrent loads on working memory, but not by the requirement to produce a vocal or a tapping response to a secondary stimulus. In experiment 2, expert performance was substantially affected by secondary tasks which had high visuo-spatial or verbal cognitive processing loads, but was not contingent upon the nature (verbal or visuo-spatial) of the processing requirement. In experiment 3, subjects were tested on dual-task performance after only 3 hours practice on Space Fortress, and again after a further five hours practice on the game. Early in training, paced generation of responses had very little effect on game performance. Game performance was affected by general working memory load, but an analysis of component measures showed that a wider range and rather different aspects of performance were disrupted by a visuo-spatial memory load than were affected by a secondary verbal load. With further training this pattern changed such that the differential nature of the disruption by a secondary visuo-spatial task was much reduced. Also, paced generation of responses had a small effect on game performance. However the disruption was not as dramatic as that shown for expert players. Subjective ratings of task difficulty were poor predictors of performance in all of the three experiments. These results suggested that general working memory load was an important aspect of performance at all levels

This paper is concerned with the syndrome, described by me some years ago, of finger agnosia, disorientation for right and left, agraphia and acalculia, appearing as a result of a cerebral lesion located in the transitional area of the lower parietal and the middle occipital convolution.In 1924 I first described the symptom of primary elective disability for recognizing, naming, selecting, differentiating and indicating the individual fingers of either hand, the patient's own as well as those of other persons, and called the condition "finger agnosia." Subsequent to this gnostic disorientation with respect to the fingers, restriction in their separate kinetic realization not infrequently occurs. I also showed that the symptom of finger agnosia is characteristically associated with disorientation for right and left in respect to the patient's own body, as well as that of other persons, with special reference to the hands and fingers. The symptoms tend to appear

Nine experiments of timed odd–even judgments examined how parity and number magnitude are accessed from Arabic and verbal numerals. With Arabic numerals, Ss used the rightmost digit to access a store of semantic number knowledge. Verbal numerals went through an additional stage of transcoding to base 10. Magnitude information was automatically accessed from Arabic numerals. Large numbers preferentially elicited a rightward response, and small numbers a leftward response. The Spatial–Numerical Association of Response Codes effect depended only on relative number magnitude and was weaker or absent with letters or verbal numerals. Direction did not vary with handedness or hemispheric dominance but was linked to the direction of writing, as it faded or even reversed in right-to-left writing Iranian Ss. The results supported a modular architecture for number processing, with distinct but interconnected Arabic, verbal, and magnitude representations. (PsycINFO Database Record (c) 2012 APA, all rights reserved)

The current investigations coordinate math cognition and cultural approaches to numeric thinking to examine the linkages between numeric and spatial processes, and how these linkages are modified by the cultural artifact of writing. Previous research in the adult numeric cognition literature has shown that English monoliterates have a spatialised mental number line which is oriented from left-to-right with smaller magnitudes associated with the left side of space and larger magnitudes are associated with the right side of space. These associations between number and space have been termed the Spatial Numeric Association Response Code Effect (SNARC effect, Dehaene, 1992). The current study investigates the spatial orientation of the mental number line in the following groups: English monoliterates, Arabic monoliterates who use only the right-left writing system, Arabic-English biliterates, and illiterate Arabic speakers who only read numerals. Current results indicate, for the first time, a Reverse SNARC effect for Arabic monoliterates, such that the mental number line had a right-to-left directionality. Furthermore, a weakened Reverse SNARC was observed for Arabic-English biliterates, and no effect was observed among Illiterate Arabic speakers. These findings are especially notable since left-right biases are neurologically supported and are observed in pre-literate children regardless of which writing system is used by adults. The broader implications of how cultural artifacts affect basic numeric cognition will be discussed.

This chapter discusses the role of notation-related imagery in mathematical problem solving. It explores the extent to which visual imagery penetrates into the structure of the problem solving process. The chapter presents work that is a mixture of subjective and objective methodologies. It discusses eight small empirical studies that constitute a tentative and incomplete exploration into the role of visual imagery in solving elementary mathematical problems. The investigation began with a protocol study in which people were asked to report on their use of visual imagery in the solution of elementary mathematical problems. Study 2 proved the striking spatial integration of image with stimulus reported by subjects in Study 1. Studies 3 and 4 were concerned with the temporal duration of images, Studies 5 and 6 with the relation of generated images to memory for specific visual formats, and Studies 7 and 8 with further spatial properties of generated images.

Presented to 38 undergraduates a series of problems consisting of 2 numbers to be added (A+B) and a comparison number (C) ranging from 13-153. They were to choose the larger, A+B or C, as rapidly as possible. Errors and latency increased with size of numbers, except when A+B and C were on opposite sides of 100. Speed and accuracy increased with the difference between A and B, but were also high when A = B. Errors and latency increased when the absolute difference between A+B and C was relatively small, requiring high accuracy on the part of S. Results were interpreted in terms of an analog operation in which Ss place the magnitudes symbolized by numbers on the number line (an imaginary analog) for manipulating and judging. (PsycINFO Database Record (c) 2012 APA, all rights reserved)

early concepts of dyscalculia--phenomenology and developmental aspects
association of spatial disorders and deficits in written calculation / hypothetical manifestations and error types / clinical observations
recent statistical research on the implicit nature of calculation deficits / observations on the cerebral localization of spatial dyscalculia (PsycINFO Database Record (c) 2012 APA, all rights reserved)

Do numbers presented in different formats activate exactly the same semantic representations? Results of 6 experiments argue in favor of the hypothesis according to which different intermediate representations are activated, depending on the lexico-syntactic structure of the numeral to be processed. First, equation verification is faster when the calculation mimics the structure of the roman numeral proposed as a solution (e.g.,
VII =
5 +
2). Second, comparing the magnitude of 2 verbal numerals is more rapid when the 2 items share the same lexico-syntactic structure (e.g.,
twelve hundred, fourteen hundred) than when they do not (e.g.,
twelve hundred, one thousand four hundred). Third, when calculating orally, participants tend to use the same verbal structure to express their response as the one used in the problem's addends. The implications of these results for the different views of numerical representations are discussed. (PsycINFO Database Record (c) 2012 APA, all rights reserved)

Examined the role of visuo-spatial working memory in the solution of mental addition problems in 3 experiments with a total of 12 adults. A standard task was devised in which Ss were required to mentally summate 2 3-digit addends presented either visually or auditorily. Exp 1 demonstrated that during mental addition both spatial interference and articulatory suppression were each capable of disrupting the working storage of initial problem information. While visual interference failed to disrupt performance in zero-carry problems, when the working retention of partial results and carrys was examined, evidence of selective interference was found. Results converge on the view that mental addition involves the deployment of a working memory constellation in which both the visuo-spatial scratch pad and the articulatory loop participate. (PsycINFO Database Record (c) 2012 APA, all rights reserved)

Reply by the current author to the comments made by T. J. Simon (see record
2006-00313-001) on the original article (see record
1999-05057-002). Simon's remarks bear on two theoretical issues. First, what is the specificity of the cerebral circuits for number processing? Second, how do numerical abilities emerge in the course of development? The answers are clear-cut: the brain's cerebral circuits are 'non-numerical', and the developmental foundations of numerical processing are to be found in 'a brain without numbers' which constructs itself through unspecified mechanisms of 'open-ended plasticity'. We disagree on all counts. Although those important issues are still open to scientific inquiry, there is already strong evidence that the numerical abilities of the human brain rest in part on specialized cerebral processes and follow a specific developmental time course that hints at an initial specialization. We share with him, the hypothesis that some mathematical abilities, particularly those that are evidently late cultural acquisitions, such as multiplication tables, do not rely on specific cerebral substrates. The unique and culture-specific features of human number knowledge nevertheless appear to build on a dedicated neural and cognitive system: a number sense that emerged early in vertebrate evolution, is present and functional early in human development, and resides in dedicated neural circuitry. (PsycINFO Database Record (c) 2012 APA, all rights reserved)

Two experiments were conducted to demonstrate that skilled soroban (Japanese abacus) operators can improve digit memory retention by manipulating the beads of a ‘mental soroban’ which is analogous to the actual one. In Experiment 1, soroban experts and control subjects were given two digit memory tasks. In one task, pictures of a soroban figure and in the other, pictures of digit sequences, were presented to the subjects during the retention interval. Soroban experts experienced greater interference from presentation of the soroban figures than the digits; on the other hand, the reverse was true in the control subjects. In Experiment 2, ther soroban experts and control subjects were given the same digit memory tasks under three conditions—soroban pictures, pictures of digit sequences, and human faces were presented to subjects during the retention period of 15 s. The soroban experts were more affected by the presentation of the soroban figures than by the faces or digits, whereas the controls showed more interference from the digits than by the presentation of faces or soroban pictures.

This paper presents a new conceptualization of the origins of numerical competence in humans. I first examine the existing claim that infants are innately provided with a system of specifically numerical knowledge, consisting of both cardinal and ordinal concepts. I suggest instead that the observed behaviors require only simple perceptual discriminations based on domain-independent competencies. At most, these involve the formal equivalent of cardinal information. Finally, I present a “non-numerical” account that characterizes infants competencies with regard to numerosity as emerging primarily from some general characteristics of the human perception and attention system.

Spatial stimulus—response (S-R) compatibility designates the observation that speeded reactions to unilateral stimuli are faster for the hand ipsilateral than for the hand contralateral to the sensory hemifield containing the stimulus. In two experiments involving presentation of the numbers 1 to 11 in the center of the visual field we show (1) a left-hand reaction time (RT) advantage for numerals <6 and a right-hand advantage for those >6 for subjects who conceive of the numbers as distances on a ruler, and (2) a reversal of this RT advantage for subjects who conceive of them as hours on a clock face. While the results in the first task (RULER) replicate a robust finding from the neuropsychology of number processing (the ‘‘SNARC effect’’) those in the second task (CLOCK) show that extension of the number scale from left to right in representational space cannot be the decisive factor for the observed interaction between hand and number size. Taken together, the findings in the two tasks are best accounted for in terms of an interaction between lateralized mental representations and lateralized motor outputs (i.e. an analog of traditional spatial S-R compatibility effects in representational space). We discuss potential clinical applications of the two tasks in patients with neglect of representational space.

Many subliminal priming experiments are thought to demonstrate unconscious access to semantics. However, most of them can be reinterpreted in a non-semantic framework that supposes only that subjects learn to map non-semantic visual features of the subliminal stimuli onto motor responses. In order to clarify this issue, we engaged subjects in a number comparison task in which the target number was preceded by another invisible masked number. We show that unconscious semantic priming occurs even for prime stimuli that are never presented as target stimuli, and for which no stimulus–response learning could conceivably occur. We also report analyses of the impact of the numerical relation between prime and target, and of the impact of learning on priming, all of which confirm that unconscious utilization of semantic information is indeed possible.