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Adults' concurrent processing of numerical and action information yields bidirectional interference effects consistent with a cognitive link between these two systems of representation. This link is in place early in life: infants create expectations of congruency across numerical and action-related stimuli (i.e., a small [large] hand aperture associated with a smaller [larger] numerosity). Although these studies point to a developmental continuity of this mapping, little is known about the later development and thus how experience shapes such relationships. We explored how number-action intuitions develop across early and later childhood using the same methodology as in adults. We asked 3-, 6-, and 8-year-old children, as well as adults, to relate the magnitude of an observed action (a static hand shape, open vs. closed, in Experiment 1; a dynamic hand movement, opening vs. closing, in Experiment 2) to either a small or large nonsymbolic quantity (numerosity in Experiment 1 and numerosity and/or object size in Experiment 2). From 6 years of age, children started performing in a systematic congruent way in some conditions, but only 8-year-olds (added in Experiment 2) and adults performed reliably above chance in this task. We provide initial evidence that early intuitions guiding infants' mapping between magnitude across nonsymbolic number and observed action are used in an explicit way only from late childhood, with a mapping between action and size possibly being the most intuitive. An initial coarse mapping between number and action is likely modulated with extensive experience with grasping and related actions directed to both arrays and individual objects.

Adults present a large number of asymmetries in visuospatial behavior that are known to be supported by functional brain lateralization. Although there is evidence of lateralization for motor behavior and language processing in infancy, no study has explored visuospatial attention biases in the early stages of development. In this study, we tested for the presence of a leftward visuospatial bias (i.e., pseudoneglect) in 4- and 5-month-old infants using an adapted version of the line bisection task. Infants were trained to identify the center of a horizontal line (Experiment 1) while their eye gazes were monitored using a remote eyetracking procedure to measure their potential gazing error. Infants exhibited a robust pseudoneglect, gazing leftward with respect to the veridical midpoint of the horizontal line. To investigate whether infants’ pseudoneglect generalizes to any given object or is dependent on the horizontal dimension, in Experiment 2 we assessed infants’ gaze deployment in vertically oriented lines. No leftward bias was found, suggesting that early visuospatial attention biases in infancy are constrained by the orientation of the visual plane in which the information is organized. The interplay between biological and cultural factors that might contribute to the early establishment of the observed leftward bias in the allocation of visuospatial attention is discussed.

Developmental studies have shown that infants exploit ordinal information to extract and generalize repetition-based rules from a sequence of items. Within the visual modality, this ability is con-strained by the spatial layout within which items are delivered given that a left-to-right orientation boosts infants’ rule learning, whereas a right-to-left orientation hinders this ability. Infants’ rule learning operates across different domains and can also be transferred across modalities when learning is triggered by speech.However, no studies have investigated whether the transfer of rule learning occurs across different domains when language is not involved. Using a visual habituation procedure, we tested 7-month-old infants’ ability to extract rule-like patterns from numerical sequences and generalize them to non-numerical sequences of visual shapes and whether this ability is affected by the spatial orientation. Infants were first habituated to left-to-right or right-to-left oriented numerical sequences instantiating an ABB rule and were then tested with the familiar rule instantiated across sequences of single geometrical shapes and a novel (ABA) rule.Results showed a transfer of learning from number to visual shapes for left-to-right oriented sequences but not for right-to-left oriented ones (Experiment 1) even when the direction of the numerical change (increasing vs. decreasing) within the habituation sequences violated a small–left/large–right number–space association (Experiment 2). These results provide the first demonstration that visual rule learning mechanisms in infancy operate at a high level of abstraction and confirm earlier findings that left-to-right oriented directional cues facilitate infants’ representation of order.

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.

A wealth of studies show that human adults map ordered information onto a directional spatial continuum. We asked whether mapping ordinal information into a directional space constitutes an early predisposition, already functional prior to the acquisition of symbolic knowledge and language. While it is known that preverbal infants represent numerical order along a left-to-right spatial continuum, no studies have investigated yet whether infants, like adults, organize any kind of ordinal information onto a directional space. We investigated whether 7-month-olds' ability to learn high-order rule-like patterns from visual sequences of geometric shapes was affected by the spatial orientation of the sequences (left-to-right vs. right-to-left). Results showed that infants readily learn rule-like patterns when visual sequences were presented from left to right, but not when presented from right to left. This result provides evidence that spatial orientation critically determines preverbal infants' ability to perceive and learn ordered information in visual sequences, opening to the idea that a left-to-right spatially organized mental representation of ordered dimensions might be rooted in biologically-determined constraints on human brain development.

When adding or subtracting quantities, adults tend to overestimate addition outcomes and underestimate subtraction outcomes. They also shift visuospatial attention to the right when adding and to the left when subtracting. These operational momentum phenomena are thought to reflect an underlying representation in which small magnitudes are associated with the left side of space and large magnitudes with the right side of space. Currently, there is limited research on operational momentum in early childhood or for operations other than addition and subtraction. The current study tested whether English-speaking 3- and 4-year-old children and college-aged adults exhibit operational momentum when ordering quantities. Participants were presented with two experimental blocks. In one block of trials, they were tasked with choosing the same quantity they had previously seen three times; in the other block, they were asked to generate the next quantity in a doubling sequence composed of three ascending quantities. A bias to shift attention to the right after an ascending operation was found in both age groups, and a bias to overestimate the next sequential quantity during an ascending ordering operation was found in adults under conditions of uncertainty. These data suggest that, for children, the spatial biases during operating are more pronounced than the mis-estimation biases. These findings highlight the spatial underpinnings of operational momentum and suggest that both very young children and adults conceptualize quantity along a horizontal continuum during ordering operations, even before formal schooling.

An Operational Momentum (OM) effect is shown by 9-month-old infants during non-symbolic arithmetic, whereby they overestimate the outcomes to addition problems, and underestimate the outcomes to subtraction problems. Recent evidence has shown that this effect extends to ordering operations for size-based sequences in 12-month-olds. Here we provide evidence that OM occurs for ordering operations involving numerical sequences containing multiple quantity cues, but not size-based sequences, already at 4 months of age. Infants were tested in an ordinal task in which they detected and represented increasing or decreasing variations in physical and/or numerical size, and then responded to ordinal sequences that exhibited greater or lesser sizes/numerosities, thus following or violating the OM generated during habituation. Results showed that OM was absent during size ordering (Experiment 1), but was present when infants ordered arrays of discrete elements varying on numerical and non-numerical dimensions, if both number and continuous magnitudes were available cues to discriminate between with-OM and against-OM sequences during test trials (Experiments 2 vs. 3). The presence of momentum for ordering number only when provided with multiple cues of magnitude changes suggests that OM is a complex phenomenon that blends multiple representations of magnitude early in infancy

Ordinality is a fundamental aspect of numerical cognition. However, preverbal infants’ ability to represent numerical order is poorly understood. In the present study we extended the evidence provided by Macchi Cassia, Picozzi, Girelli, and de Hevia (2012), showing that 4-month-old infants detect ordinal relationships within size-based sequences, to numerical sequences. In three experiments, we showed that at 4 months of age infants fail to represent increasing and decreasing numerical order when numerosities differ by a 1:2 ratio (Experiment 1), but they succeed when numerosities differ by a 1:3 ratio (Experiments 2 and 3). Critically, infants showed the same behavioral signature (i.e., asymmetry) described by Macchi Cassia et al. for discrimination of ordinal changes in area: they succeed at detecting increasing but not decreasing order (Experiments 2 and 3). These results support the idea of a common (or at least parallel) development of ordinal representation for the two quantitative dimensions of size and number. Moreover, the finding that the asymmetry signature, previously reported for size-based sequences, extends to numerosity, points to the existence of a common constraint in ordinal magnitude processing in the first months of life. The present findings are discussed in the context of possible evolutionary and developmental sources of the ordinal asymmetry, as well as their implication for other related cognitive abilities.

Numbers are represented as ordered magnitudes along a spatially oriented number line. While culture and formal education modulate the direction of this number-space mapping, it is a matter of debate whether its emergence is entirely driven by cultural experience. By registering 8-9-month-old infants' eye movements, this study shows that numerical cues are critical in orienting infants' visual attention towards a peripheral region of space that is congruent with the number's relative position on a left-to-right oriented representational continuum. This finding provides the first direct evidence that, in humans, the association between numbers and oriented spatial codes occurs before the acquisition of symbols or exposure to formal education, suggesting that the number line is not merely a product of human invention. This work addresses the origins of the link between numbers and oriented spatial codes, as hypothesized under the'mental number line' model of numerical representation. Using a Posner-like task, we found that numerical (arrays of dots), but not non-numerical (size), cues orient 8-9 month-old infants' visual attention towards a peripheral region of space that is congruent with the number's relative position on a left-to-right oriented representational continuum. This evidence shows that a tendency to associate numbers onto spatial positions along a left-to-right oriented axis emerges before humans learn to read, write or count on their hands, and before acquisition of symbolic knowledge, supporting to the view that the number line is not merely a product of human invention.

Recent evidence has shown that, like adults and children, 9-month-old infants manifest an operational momentum (OM) effect during non-symbolic arithmetic, whereby they overestimate the outcomes to addition problems, and underestimate the outcomes to subtraction problems. Here we provide the first evidence that OM occurs for transformations of non-numerical magnitudes (i.e., spatial extent) during ordering operations. Twelve-month-old infants were tested in an ordinal task in which they detected and represented ascension or descension in physical size, and then responded to ordinal sequences that exhibited greater or lesser sizes. Infants displayed longer looking time to the size change whose direction violated the operational momentum experienced during habituation (i.e., the smaller sequence in the ascension condition and the larger sequence in the descension condition). The presence of momentum for ordering size during infancy suggests that continuous quantities are represented spatially during the first year of life.

A number of studies have shown strong relations between numbers and oriented spatial codes. For example, perceiving numbers causes spatial shifts of attention depending upon numbers’ magnitude, in a way suggestive of a spatially oriented, mental representation of numbers. Here, we investigated whether this phenomenon extends to non-symbolic numbers, as well as to the processing of the continuous dimensions of size and brightness, exploring whether different quantitative dimensions are equally mapped onto space. After a numerical (symbolic Arabic digits or non-symbolic arrays of dots; Experiment 1) or a non-numerical cue (shapes of different size or brightness level; Experiment 2) was presented, participants’ saccadic response to a target that could appear either on the left or the right side of the screen was registered using an automated eye-tracker system. Experiment 1 showed that, both in the case of Arabic digits and dot arrays, right targets were detected faster when preceded by large numbers, and left targets were detected faster when preceded by small numbers. Participants in Experiment 2 were faster at detecting right targets when cued by large-sized shapes and left targets when cued by small-sized shapes, whereas brightness cues did not modulate the detection of peripheral targets. These findings indicate that looking at a symbolic or a non-symbolic number induces attentional shifts to a peripheral region of space that is congruent with the numbers’ relative position on a mental number line, and that a similar shift in visual attention is induced by looking at shapes of different size. More specifically, results suggest that, while the dimensions of number and size spontaneously map onto an oriented space, the dimension of brightness seems to be independent at a certain level of magnitude elaboration from the dimensions of spatial extent and number, indicating that not all continuous dimensions are equally mapped onto space.

While associations between number and space, in the form of a spatially oriented numerical representation, have been extensively reported in human adults, the origins of this phenomenon are still poorly understood. The commonly accepted view is that this number-space association is a product of human invention, with accounts proposing that culture, symbolic knowledge, and mathematics education are at the roots of this phenomenon. Here we show that preverbal infants aged 7 months, who lack symbolic knowledge and mathematics education, show a preference for increasing magnitude displayed in a left-to-right spatial orientation. Infants habituated to left-to-right oriented increasing or decreasing numerical sequences showed an overall higher looking time to new left-to-right oriented increasing numerical sequences at test (Experiment 1). This pattern did not hold when infants were presented with the same ordinal numerical information displayed from right to left (Experiment 2). The different pattern of results was congruent with the presence of a malleable, context-dependent baseline preference for increasing, left-to-right oriented, numerosities (Experiment 3). These findings are suggestive of an early predisposition in humans to link numerical order with a left-to-right spatial orientation, which precedes the acquisition of symbolic abilities, mathematics education, and the acquisition of reading and writing skills.

The present study investigates basic numerical processing in deaf signers and hearing individuals by evaluating notational effects (Arabic digits vs Italian sign language number signs) and response modality (manual vs pedal) in a parity judgment task. Overall, a standard SNARC effect emerged in both groups, suggesting similar numerical representation in hearing and deaf individuals. With the exception of Italian sign language stimuli in the hearing group, this effect applied to all stimuli notations and to both response modalities. In line with the special status of signs, the visuospatial complexity of finger configurations (i.e. number of extended fingers) affected the performance of the hearing group to a greater extent. Finally, the SNARC effect emerged systematically across lateralized effectors (manual/pedal response), challenging the hypothesis that the stimulus-response compatibility effect is specific to the effectors associated with the production of written and sign language. As for parity processing, both groups were similarly influenced by the parity information conveyed by the dominant hand, indicating the compositional nature of number signs irrespective of the preferred language modality.

While infants’ ability to discriminate quantities has been extensively studied, showing that this competence is present even in neonates, the ability to compute ordinal relations between magnitudes has received much less attention. Here we show that the ability to represent ordinal information embedded in size-based sequences is apparent at 4 months of age, provided that magnitude changes involve increasing relations. Infants in Experiments 1A and 1B discriminated changes in ordinal relations after habituation to ascending sequences, but did not show evidence of discrimination after habituation to descending sequences. In Experiment 2 we replicated this asymmetry in magnitude discrimination even when additional cues known to boost ordinal competence were provided. The presence of an asymmetry between ascending vs. descending order during infancy suggests a developmental continuity in the underlying code used to represent magnitude, whereby the reported addition advantage in children and adults’ arithmetic performance emerges.

The interaction between numbers and action-related processes is currently one of the most investigated topics in numerical cognition. The present study contributes to this line of research by investigating, for the first time, the effects of number on an overlearned complex motor plan that does not require explicit lateralised movements or strict spatial constrains: spontaneous handwriting. In particular, we investigated whether the spatial mapping of numbers interferes with the motor planning involved in writing. To this aim, participants' spontaneous handwriting of single digits (Exp. 1) and letters (Exp. 2) was recorded with a digitising tablet. We show that the writing of numbers is characterised by a spatial dislocation of the digits as a function of their magnitude, i.e., small numbers were written leftwards relative to large numbers. In contrast, the writing of letters showed a null or marginal effect with respect to their dislocation on the writing area. These findings show that the automatic mapping of numbers into space interacts with action planning by modulating specific motor parameters in spontaneous handwriting

Previous evidence has shown that 11-month-olds represent ordinal relations between purely numerical values, whereas younger infants require a confluence of numerical and non-numerical cues. In this study, we show that when multiple featural cues (i.e., color and shape) are provided, 7-month-olds detect reversals in the ordinal direction of numerical sequences relying solely on number when non-numerical quantitative cues are controlled. These results provide evidence for the influence of featural information and multiple cue integration on infants' proneness to detect ordinal numerical information.

To detect an ordered sequence of quantities refers to the ability to appreciate ‘greater than’ and ‘less than’ relations and it represents one essential component of numerical knowledge that develops early in infancy. Brannon (2002) argued that by 11 months infants possess this ability for numerical values, and that it follows a sudden onset between 9 and 11 months. In fact, by 9 months infants succeed at discriminating the ordinal direction of a single square varying in size, but fail for numerical sequences, suggesting that the ability to represent the ordinal information embedded in non-numerical quantities develops earlier than for numerical values. Our study aims to track the emergence of the ability to encode ordinal relations between continuous, non-numerical quantities. We tested 4-month-old infants in their ability to discriminate ascending vs. descending sequences of the size of a single square. In Exp. 1, infants saw increasing (N=10) or decreasing (N=10) sequences of a single square that varied in size across 3 steps following a 1:2 ratio. After habituation, all infants saw six new trials, alternating between increasing vs. decreasing sequences of the single square varying in size in a 1:2 ratio. The direction of the first sequence was counterbalanced across participants. We found that 4-month-old infants successfully discriminated the ordinal direction, Familiar vs. Novel, p=.001, but this ability was present only for infants habituated to the increasing sequence, who displayed a preference for the novel vs. the familiar sequence (M=9.3 s vs. 5.3 s; p=.002 ). In contrast, infants habituated to the decreasing sequence did not discriminate the familiar vs. novel sequence (M=4.6 s vs. 5.3 s; p=.20). These results suggest that by 4 months infants are sensitive to the ordinal information contained in a sequence that varies along a continuous dimension, i.e., the area of a single element. However, this ability seems to apply only to sequences that vary in an

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. © 2008 Elsevier Ltd. All rights reserved.

In recent years, a growing amount of evidence concerning the relationships between numerical and spatial representations has been interpreted, by and large, in favour of the mental number line hypothesis--namely, the analogue continuum where numbers are spatially represented (Dehaene, 1992; Dehaene, Piazza, Pinel, & Cohen, 2003). This numerical representation is considered the core of number meaning and, accordingly, needs to be accessed whenever numbers are semantically processed. The present study explored, by means of a length reproduction task, whether besides the activation of lateralized spatial codes, numerical processing modulates the mental representation of a horizontal spatial extension. Mis-estimations of length induced by Arabic numbers are interpreted in terms of a cognitive illusion, according to which the elaboration of magnitude information brings about an expansion or compression of the mental representation of spatial extension. These results support the hypothesis that visuo-spatial resources are involved in the representation of numerical magnitude.

This study investigated the relationships between numerical and spatial representations by means of a bisection task, exploring the view that the core representation of number meaning is spatially organized as a mental number line. In Experiment nos. 1 (bisection of digit strings) and 2 (bisection of flanked lines) spatial biases towards the larger digit were found to be related only to processing of relative magnitude. Experiment nos. 3 (bisection of an unfilled space) and 4 (bisection of flanked lines/unfilled spaces) aimed at disclosing perceptual, attentional, and numerical constraints on the bias induced by the position of the larger digit. This effect is interpreted in terms of a cognitive illusion of length, whereby a spatial bias compensates for the numerical disparity. This seems to operate in a categorical fashion ("small/ large"), and to be congruent with the assumption that relatively large numbers are associated with the right side of a mental representational space. © Springer-Verlag 2005.