Number-space mapping in human infants

The effect of spatial distance on numerical distance processing

The close relationship between numerical and spatial representation has been widely studied. However, little is known regarding the influence of spatial distance on the processing of numerical distance. The purpose of this study was to examine this relationship by employing a modified numerical Stroop task, in which the spatial distance was either congruent or incongruent with the numerical distance. That is, numerical and spatial distances were either compatible with each other or incompatible. Experiment 1 demonstrated that when participants were directly requested to assess the numerical distance, spatial distance influenced task performance, thereby revealing a novel effect-the spatial-numerical distance congruency effect. Experiment 2 demonstrated that these relations are asymmetrical and revealed that numerical distance did not influence spatial distance when the numerical distance was task-irrelevant. Experiment 3 revealed that the spatial-numerical distance congruency effect can also be obtained automatically by employing a numerical comparison task, which is considered a marker for indirect distance processing. In addition, also tested across the three experiments was whether spatial alignment on the screen (i.e., left, centre, and right) can influence the spatial-numerical distance congruency effect. Results revealed that when numbers were presented more naturally (on the left and centre of the screen), a larger effect was obtained compared with when stimuli were presented on the right side. Together, these findings shed new light regarding the relationship between numerical distance and spatial distance and whether and how these aspects influence each other.

Memory capacity as the core mechanism of the development of space-time interferences in children

This study investigated the development of spatiotemporal perceptual interactions in 5-to-7 years old children. Participants reproduced the temporal and spatial interval between sequentially presented visual stimuli. The time and spacing between stimuli were experimentally manipulated. In addition, cognitive capacities were assessed using neuropsychological tests. Results revealed that starting at 5 years old, children exhibited spatial biases in their time estimations and temporal biases in their spatial estimations, pointing at space-time interference. In line with developmental improvement of temporal and spatial abilities, these spatiotemporal biases decreased with age. Importantly, short-term memory capacity was a predictor of space-time interference pointing to shared cognitive mechanisms between time and space processing. Our results support the symmetrical hypothesis that proposes a common neurocognitive mechanism for processing time and space.

What makes different number-space mappings interact?

Models of numerical cognition consider a visuo-spatial representation to be at the core of numerical processing, the 'mental number line'. Two main interference effects between number and space have been described: the SNARC effect reflects a small number/left side and large number/right side association (number-location mapping); the size-congruity effect (SCE) reflects a small number/small size and large number/large size association (number-size mapping). Critically, a thorough investigation on the representational source for these two number-space mappings is lacking, leaving open the question of whether the same representation underlies both phenomena. Here, we build on a recent study (Viarouge and de Hevia in Front Hum Neurosci 15:750964, 2021) in order to address this question in three experiments, by systematically manipulating the presence of the two conditions that might elicit an interaction between SNARC and SCE: (i) an implicit task whereby numerical and spatial information are task-irrelevant, (ii) a design in which the number-space congruency relative to both mappings vary at the same level -either both within or between blocks. Experiment 1 replicated the interaction between the two mappings when both factors were present. Experiments 2 and 3 dissociated the two factors by varying the two mappings at the same level but using an explicit comparison task (Experiment 2), or by using an implicit task but with mappings varying at different levels (Experiment 3). We found that both factors, either in combination or used in isolation, drive the interaction between the two number-space mappings. These findings are discussed in terms of the weight given to each mapping, suggesting that a single representation encompassing both number-space mappings is therefore activated whenever both mappings are given equal weight through task requirements.

Intuitive mapping between nonsymbolic quantity and observed action across development

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.

The interplay between math performances, spatial abilities, and affective factors: The role of task

Many studies have suggested that cognitive and affective abilities (such as math anxiety- MA and math self-efficacy) explain individual differences in math.

PURPOSE

The present study explores the interplay between MA, math self-efficacy, spatial anxiety and spatial abilities in explaining individual differences on two complex math tasks.

PROCEDURES

Ninety-three college students took part in the experiment and completed 3 emotional questionnaires, in addition to 2 math tasks and a mental rotation task.

FINDINGS

The interplay between math performances and cognitive and affective factors is related to task demand. MA and spatial abilities affected math performances directly, regardless of task. Spatial anxiety had only an indirect effect on math performances via MA, regardless of task.

CONCLUSIONS

These finding suggest that for math performances, contrary to MA, real spatial abilities rather than perceived spatial anxiety play a significant role in explaining individual differences.  Hence, the present result dissociates cognitive and emotional factors.

Associations between physical size and space are strongly asymmetrical

The spatial-size association of response codes (SSARC) effect describes the phenomenon that left responses are faster and more accurate to small stimuli whereas right responses are faster and more accurate to large stimuli, as compared to the opposite mapping. The effect indicates associations between the mental representations of physical size and space. Importantly, the theoretical accounts of SSARC effects make different predictions about the reciprocity and/or symmetry of spatial-size associations. To investigate the reciprocity of SSARC effects, we compared compatibility effects in two verbal choice-response tasks: a size-location (typical SSARC) task and a location-size (reciprocal SSARC) task. In the size-location task, participants responded verbally to a small/large stimulus by saying "left"/"right". In the location-size task, participants responded verbally to a left-/right-side stimulus by saying "small"/"large". Participants completed both tasks with a compatible (small-left, large-right; left-small, right-large) and an incompatible (small-right, large-left; left-large, right-small) mapping. A regular SSARC effect emerged in the size-location task. However, no reciprocal SSARC effect emerged in the location-size task if outliers were excluded. If outliers were not excluded, small reciprocal SSARC effects occurred. Associations underlying the SSARC effect are thus strongly asymmetrical: Physical (stimulus) size can prime spatial responses much more strongly than spatial (stimulus) position can prime size-related responses. The finding of asymmetrical associations between size and space is in line with some theoretical accounts of the SSARC effect but at odds with others.

The transitive inference task to study the neuronal correlates of memory-driven decision making: A monkey neurophysiology perspective

A vast amount of literature agrees that rank-ordered information as A>B>C>D>E>F is mentally represented in spatially organized schemas after learning. This organization significantly influences the process of decision-making, using the acquired premises, i.e. deciding if B is higher than D is equivalent to comparing their position in this space. The implementation of non-verbal versions of the transitive inference task has provided the basis for ascertaining that different animal species explore a mental space when deciding among hierarchically organized memories. In the present work, we reviewed several studies of transitive inference that highlighted this ability in animals and, consequently, the animal models developed to study the underlying cognitive processes and the main neural structures supporting this ability. Further, we present the literature investigating which are the underlying neuronal mechanisms. Then we discuss how non-human primates represent an excellent model for future studies, providing ideal resources for better understanding the neuronal correlates of decision-making through transitive inference tasks.

Implicit Processing of Numerical Order: Evidence from a Continuous Interocular Flash Suppression Study

Processing the ordered relationships between sequential items is a key element in many cognitive abilities that are important for survival. Specifically, order may play a crucial role in numerical processing. Here, we assessed the existence of a cognitive system designed to implicitly evaluate numerical order, by combining continuous flash suppression with a priming method in a numerical enumeration task. In two experiments and diverse statistical analysis, targets that required numerical enumeration were preceded by an invisibly ordered or non-ordered numerical prime sequence. The results of both experiments showed that enumeration for targets that appeared after an ordered prime was significantly faster, while the ratio of the prime sequences produced no significant effect. The findings suggest that numerical order is processed implicitly and affects a basic cognitive ability: enumeration of quantities.

Spontaneous supra-modal encoding of number in the infant brain

The core knowledge hypothesis postulates that infants automatically analyze their environment along abstract dimensions, including numbers. According to this view, approximate numbers should be encoded quickly, pre-attentively, and in a supra-modal manner by the infant brain. Here, we directly tested this idea by submitting the neural responses of sleeping 3-month-old infants, measured with high-density electroencephalography (EEG), to decoders designed to disentangle numerical and non-numerical information. The results show the emergence, in approximately 400 ms, of a decodable number representation, independent of physical parameters, that separates auditory sequences of 4 vs. 12 tones and generalizes to visual arrays of 4 vs. 12 objects. Thus, the infant brain contains a number code that transcends sensory modality, sequential or simultaneous presentation, and arousal state.

Children grow upwards, and so does the number line: Evidence from a directional number line paradigm

Technological advancements give researchers the opportunity to explore the internal metric that allows to mentally place numbers in a spatial and ordered way to establish relationships between quantities. In this study, we implement the cMNL, an embodied number line paradigm to investigate the configuration of children's number space mappings under multiple conditions. A sample of 185 primary school children aged 8-10years old completed digitally an embodied number line task encompassing directionality and modality as variables. Contrary to the premise of a fixed internal number line moving from left to right in many Western scripts, our results suggest that children's number-space mapping is more robust along a vertical axis. In addition, children's embodied number line estimation differed depending on input modality. The findings provide insight into the variability in children's number line estimation, and the usability of digital assessment in understanding the mechanisms of the developing number-space system.

Electrophysiological Evidence for A Number-Action Mapping in Infancy

In the last decades, a growing body of literature has focused on the link between number and action. Many studies conducted on adult participants have provided evidence for a bidirectional influence between numerosity processing and grasping or reaching actions. However, it is not yet clear whether this link is functional in early infancy. Here, we used the event-related potential (ERP) technique to record electrical activity of the brain in response to number-hand pairings. We implemented a cueing paradigm where 3- to 4-month-old infants observed images showing either congruency (e.g., a large numerosity primed by a large hand opening) or incongruency (e.g., a large numerosity primed by a small hand opening). Infants' brain activity was modulated by the congruency of the pairings: amplitudes recorded over frontal and parietal-occipital scalp positions differed for congruent versus incongruent pairings. These findings suggest that the association between number and hand action processing is already functional early in life.

More linear than log? Non-symbolic number-line estimation in 3- to 5-year-old children

The number-line estimation task has become one of the most important methods in numerical cognition research. Originally applied as a direct measure of spatial number representation, it became also informative regarding various other aspects of number processing and associated strategies. However, most of this work and associated conclusions concerns processing numbers in a symbolic format, by school children and older subjects. Symbolic number system is formally taught and trained at school, and its basic mathematical properties (e.g., equidistance, ordinality) can easily be transferred into a spatial format of an oriented number line. This triggers the question on basic characteristics of number line estimation before children get fully familiar with the symbolic number system, i.e., when they mostly rely on approximate system for non-symbolic quantities. In our three studies, we examine therefore how preschool children (3–5-years old) estimate position of non-symbolic quantities on a line, and how this estimation is related to the developing symbolic number knowledge and cultural (left-to-right) directionality. The children were tested with the Give-a-number task, then they performed a computerized number-line task. In Experiment 1, lines bounded with sets of 1 and 20 elements going left-to-right or right-to-left were used. Even in the least numerically competent group, the linear model better fit the estimates than the logarithmic or cyclic power models. The line direction was irrelevant. In Experiment 2, a 1–9 left-to-right oriented line was used. Advantage of linear model was found at group level, and variance of estimates correlated with tested numerosities. In Experiment 3, a position-to-number procedure again revealed the advantage of the linear model, although the strategy of selecting an option more similar to the closer end of the line was prevalent. The precision of estimation increased with the mastery of counting principles in all three experiments. These results contradict the hypothesis of the log-to-linear shift in development of basic numerical representation, rather supporting the linear model with scalar variance. However, the important question remains whether the number-line task captures the nature of the basic numerical representation, or rather the strategies of mapping that representation to an external space.

Manipulation of Attention Affects Subitizing Performance: A Systematic Review and Meta-analysis

Subitizing is the fast and accurate enumeration of small sets. Whether attention is necessary for subitizing remains controversial considering (1) subitizing is claimed to be "pre-attentive", and (2) existing experimental methods and results are inconsistent. To determine whether manipulations to attention demonstratively affect subitizing, the current study comprises a systematic review and meta-analysis. Results from fourteen studies (22 experiments, 35 comparisons) suggest that changes to attentional demands interferes with enumeration of small sets; leading to slower response times, lower accuracy, and poorer Weber acuity (p <.010; p <.001; p <.001; respectively)-notwithstanding a potential publication bias. A unifying framework is proposed to explain the role of attention in visual enumeration, with progressively greater attentional involvement from estimation to subitizing to counting. Our findings suggest attention is integral for subitizing and highlights the need to emphasise attentional mechanisms into neurocognitive models of numerosity processing. We also discuss the possible role of attention in numerical processing difficulties (e.g., dyscalculia).

Fine motor skills and finger gnosia contribute to preschool children's numerical competencies

Facets of fine motor skills (FMS) and finger gnosia have been reported to predict young children's numerical competencies, possibly by affecting early finger counting experiences. Furthermore, neuronal connections between areas involved in finger motor movement, finger gnosia, and numerical processing have been posited. In this study, FMS and finger gnosia were investigated as predictors for preschool children's performance in numerical tasks. Preschool children (N = 153) completed FMS tasks measuring finger agility and finger dexterity as well as a non-motor finger gnosia task. Furthermore, children completed numerical tasks that involved finger use (i.e., finger counting and finger montring), and tasks that did not (i.e., picture-aided calculation and number line estimation). To control for possible confounding influences of domain general skills, we included measures of reasoning and spatial working memory. We found associations between FMS and both finger counting and calculation, but not finger montring. In contrast, finger gnosia was only associated with finger montring, but not finger counting and calculation. Surprisingly, there were no associations between FMS or finger gnosia with number line estimation. Findings highlight that the relationship between finger gnosia, FMS, and numerical skills is specific to task requirements. Possible implications are discussed.

Children perform better on left than right targets in an ordinal task

Francis Galton first reported that humans mentally organize numbers from left to right on a mental number line (1880). This spatial-numerical association was long considered to result from writing and reading habits. More recently though, newborns and animals showed a left-to-right oriented spatial numerical association challenging the primary role assigned to culture in determining the link between number and space. Despite growing evidence supporting the intrinsic association between number and space in different species, its adaptive value is still largely unknown. Here we tested for an advantage in identification of left versus right target positions in 3- to 6-year-old children. Children watched as a toy was hidden under one of 10 linearly arranged identical cups and were then asked to help a stuffed animal retrieve the toy. On each trial, the toy was hidden in the 2nd, 3rd, or 4th cup, from the left or right. To prevent children from staring at the target cup, they were asked to pick up the stuffed animal from under their chair after witnessing the hiding of the toy and then to help the stuffed animal find the toy. Older children were more accurate than younger children. Children exhibited a serial position effect, with performance higher for more exterior targets. Remarkably, children also showed a left bias: they remembered the left targets better than the right targets. Only the youngest children were dramatically influenced by the location of the experimenter during search. Additional analyses support the hypothesis that children used a left-to-right oriented searching strategy in this spatial/ordinal task.

The link between number and action in human infants

Humans' inborn ability to represent and manipulate numerical quantities is supported by the parietal cortex, which is also involved in a variety of spatial and motor abilities. While the behavioral links between numerical and spatial information have been extensively studied, little is known about the connection between number and action. Some studies in adults have shown a series of interference effects when simultaneously processing numerical and action information. We investigated the origins of this link by testing forty infants (7- to 9-month-old) in one of two experimental conditions: one group was habituated to congruent number-hand pairings, where the larger the number, the more open the hand-shape associated; the second group was habituated to incongruent number-hand pairings, where the larger the number, the more close the hand-shape associated. In test trials, both groups of infants were presented with congruent and incongruent pairings. We found that only infants habituated to congruency showed a significantly higher looking time to the test trial depicting incongruent pairings. These findings show for the first time that infants spontaneously associate magnitude-related changes across the dimensions of number and action-related information, thus offering support to the existence of an early, preverbal number-action link in the human mind.

Uncertainty and Prior Assumptions, Rather Than Innate Logarithmic Encoding, Explain Nonlinear Number-to-Space Mapping

Mapping number to space is natural and spontaneous but often nonveridical, showing a clear compressive nonlinearity that is thought to reflect intrinsic logarithmic encoding of numerical values. We asked 78 adult participants to map dot arrays onto a number line across nine trials. Combining participant data, we confirmed that on the first trial, mapping was heavily compressed along the number line, but it became more linear across trials. Responses were well described by logarithmic compression but also by a parameter-free Bayesian model of central tendency, which quantitatively predicted the relationship between nonlinearity and number acuity. To experimentally test the Bayesian hypothesis, we asked 90 new participants to complete a color-line task in which they mapped noise-perturbed color patches to a "color line." When there was more noise at the high end of the color line, the mapping was logarithmic, but it became exponential with noise at the low end. We conclude that the nonlinearity of both number and color mapping reflects contextual Bayesian inference processes rather than intrinsic logarithmic encoding.

Cultural factors weaken but do not reverse left-to-right spatial biases in numerosity processing: Data from Arabic and English monoliterates and Arabic-English biliterates

Directional response biases due to a conceptual link between space and number, such as a left-to-right hand bias for increasing numerical magnitude, are known as the SNARC (Spatial-Numerical Association of Response Codes) effect. We investigated how the SNARC effect for numerosities would be influenced by reading-writing direction, task instructions, and ambient visual environment in four literate populations exemplifying opposite reading-writing cultures-namely, Arabic (right-to-left script) and English (left-to-right script). Monoliterates and biliterates in Jordan and the U.S. completed a speeded numerosity comparison task to assess the directionality and magnitude of a SNARC effect in their numerosity processing. Monoliterates' results replicated previously documented effects of reading-writing direction and task instructions: the SNARC effect found in left-to-right readers was weakened in right-to-left readers, and the left-to-right group exhibited a task-dependency effect (SNARC effect in the smaller condition, reverse SNARC effect in the larger condition). Biliterates' results did not show a clear effect of environment; instead, both biliterate groups resembled English monoliterates in showing a left-to-right, task-dependent SNARC effect, albeit weaker than English monoliterates'. The absence of significant biases in all Arabic-reading groups (biliterates and Arabic monoliterates) points to a potential conflict between distinct spatial-numerical mapping codes. This view is explained in terms of the proposed Multiple Competing Codes Theory (MCCT), which posits three distinct spatial-numerical mapping codes (innate, cardinal, ordinal) during numerical processing-each involved at varying levels depending on individual and task factors.

Can a Single Representational Object Account for Different Number-Space Mappings?

Numbers are mapped onto space from birth on, as evidenced by a variety of interactions between the processing of numerical and spatial information. In particular, larger numbers are associated to larger spatial extents (number/spatial extent mapping) and to rightward spatial locations (number/location mapping), and smaller numbers are associated to smaller spatial extents and leftward spatial locations. These two main types of number/space mappings (number/spatial extent and number/location mappings) are usually assumed to reflect the fact that numbers are represented on an internal continuum: the mental number line. However, to date there is very little evidence that these two mappings actually reflect a single representational object. Across two experiments in adults, we investigated the interaction between number/location and number/spatial extent congruency effects, both when numbers were presented in a non-symbolic and in a symbolic format. We observed a significant interaction between the two mappings, but only in the context of an implicit numerical task. The results were unaffected by the format of presentation of numbers. We conclude that the number/location and the number/spatial extent mappings can stem from the activation of a single representational object, but only in specific experimental contexts.

Approach direction and accuracy, but not response times, show spatial-numerical association in chicks

Chicks trained to identify a target item in a sagittally-oriented series of identical items show a higher accuracy for the target on the left, rather than that on the right, at test when the series was rotated by 90°. Such bias seems to be due to a right hemispheric dominance in visuospatial tasks. Up to now, the bias was highlighted by looking at accuracy, the measure mostly used in non-human studies to detect spatial numerical association, SNA. In the present study, processing by each hemisphere was assessed by scoring three variables: accuracy, response times and direction of approach. Domestic chicks were tested under monocular vision conditions, as in the avian brain input to each eye is mostly processed by the contralateral hemisphere. Four-day-old chicks learnt to peck at the 4th element in a sagittal series of 10 identical elements. At test, when facing a series oriented fronto-parallel, birds confined their responses to the visible hemifield, with high accuracy for the 4th element. The first element in the series was also highly selected, suggesting an anchoring strategy to start the proto-counting at one end of the series. In the left monocular condition, chicks approached the series starting from the left, and in the right monocular condition, they started from the right. Both hemispheres appear to exploit the same strategy, scanning the series from the most lateral element in the clear hemifield. Remarkably, there was no effect in the response times: equal latency was scored for correct or incorrect and for left vs. right responses. Overall, these data indicate that the measures implying a direction of choice, accuracy and direction of approach, and not velocity, i.e., response times, can highlight SNA in this paradigm. We discuss the relevance of the selected measures to unveil SNA.

The relationship between mental rotation and arithmetic: do number line estimation, working memory, or place-value concept matter?

Mental rotation is positively related to arithmetic ability; however, the mechanism underlying this relationship remains unclear. The possible roles of working memory, place-value concept, and number line estimation in the correlation between mental rotation and whole-number computation were investigated. One hundred and fifty-five first-grade students were tested to determine their mental rotation ability, arithmetic ability, and non-verbal intelligence. One year later, their working memory, place-value concept, number line estimation, and overall arithmetic ability were assessed. After controlling for age, gender, and prior arithmetic ability, we found that mental rotation uniquely predicted arithmetic ability after one year. Further mediation analyses demonstrated that number line estimation significantly mediated the relationship between mental rotation and arithmetic ability. In contrast, neither working memory nor place-value concept significantly mediated the relationship between mental rotation and arithmetic ability. This study highlights that mental number line estimation is the most important element explaining the influence of a dynamic spatial skill, that is, mental rotation, on arithmetic ability among young Chinese children.

A left visual advantage for quantity processing in neonates

Forty-eight newborn infants were tested in one of three multimodal stimulus conditions, in which auditory quantities were presented alongside visual object arrays in two test trials. These tests varied with respect to which side (either left or right) numerically matched the auditory number. The infants looked longer to the test trials in which the left side of the visual display exhibited a quantity that matched the presented auditory quantity. This study provides the first evidence for an untrained, innate bias for humans to preferentially process quantity information presented in the left field of vision.

SNARC effect modulated by central executive control: revealed in a cue-based trisection task

People respond to small numbers faster with the left hand and respond to large numbers faster with the right hand, a phenomenon known as the Spatial-Numerical Association of Response Codes (SNARC) effect. Whether the SNARC effect originates from culturally determined long-term experience or the task-set-influenced temporary associations among spaces, locations, and numerical magnitudes in working memory (WM) is still controversial. In the present study, we used a trisection paradigm in which numbers were divided into three categories (small: 1, 2; middle: 4, 5, 6; and large: 8, 9) to explore whether the central executive control can modulate the SNARC effect. Participants were serially presented with a cue and a target number. The cue denoted a task rule, which informed participants to compare the target number with either 3 or 7. The cue was either switched or repeated across trials. We found that the SNARC effects were observed in the cue-switching condition. In the cue-repeat condition, the SNARC effect disappeared. These findings suggest that the SNARC effect is modulated by set-shifting-related central executive control in WM, supporting the view that the SNARC effect is WM-dependent.

Infants' sensitivity to shape changes in 2D visual forms

Research in developmental cognitive science reveals that human infants perceive shape changes in 2D visual forms that are repeatedly presented over long durations. Nevertheless, infants' sensitivity to shape under the brief conditions of natural viewing has been little studied. Three experiments tested for this sensitivity by presenting 128 seven-month-old infants with shapes for the briefer durations under which they might see them in dynamic scenes. The experiments probed infants' sensitivity to two fundamental geometric properties of scale- and orientation-invariant shape: relative length and angle. Infants detected shape changes in closed figures, which presented changes in both geometric properties. Infants also detected shape changes in open figures differing in angle when figures were presented at limited orientations. In contrast, when open figures were presented at unlimited orientations, infants detected changes in relative length but not in angle. The present research therefore suggests that, as infants look around at the cluttered and changing visual world, relative length is the primary geometric property by which they perceive scale- and orientation-invariant shape.

Food quantity discrimination in puppies (Canis lupus familiaris)

There is considerable evidence that animals are able to discriminate between quantities. Despite the fact that quantitative skills have been extensively studied in adult individuals, research on their development in early life is restricted to a limited number of species. We, therefore, investigated whether 2-month-old puppies could spontaneously discriminate between different quantities of food items. We used a simultaneous two-choice task in which puppies were presented with three numerical combinations of pieces of food (1 vs. 8, 1 vs. 6 and 1 vs. 4), and they were allowed to select only one option. The subjects chose the larger of the two quantities in the 1 vs. 8 and the 1 vs. 6 combinations but not in the 1 vs. 4 combination. Furthermore, the last quantity the puppies looked at before making their choice and the time spent looking at the larger/smaller amounts of food were predictive of the choices they made. Since adult dogs are capable of discriminating between more difficult numerical contrasts when tested with similar tasks, our findings suggest that the capacity to discriminate between quantities is already present at an early age, but that it is limited to very easy discriminations.

Hemispheric specialization in spatial versus ordinal processing in the day-old domestic chick (Gallus gallus)

Different species show an intriguing similarity in representing numerosity in space, starting from left to right. This bias has been attributed to a right hemisphere dominance in processing spatial information. Here, to disentangle the role of each hemisphere in dealing with spatial versus ordinal-numerical information, we tested domestic chicks during monocular versus binocular vision. In the avian brain, the contralateral hemisphere mainly processes the visual input from each eye. Four-day-old chicks learned to peck at the fourth element in a sagittal series of 10 identical elements. At testing, chicks faced a left-to-right-oriented series where the interelement distance was manipulated so that the third element was where the fourth had been at training; this compelled chicks to use either spatial or ordinal cues. Chicks tested binocularly selected both the fourth left and (to a lesser extent) right elements. Chicks tested monocularly chose the third and fourth elements on the seeing side equally. Interhemispheric cooperation resulted in the use of ordinal-numerical information, while each single hemisphere could rely on spatial or ordinal-numerical cue. Both hemispheres can process spatial and ordinal-numerical information, but their interaction results in the supremacy of processing the ordinal-numerical cue.

Functional lateralization of arithmetic processing in the intraparietal sulcus is associated with handedness

Functional lateralization is established for various cognitive functions, but was hardly ever investigated for arithmetic processing. Most neurocognitive models assume a central role of the bilateral intraparietal sulcus (IPS) in arithmetic processing and there is some evidence for more pronounced left-hemispheric activation for symbolic arithmetic. However, evidence was mainly obtained by studies in right-handers. Therefore, we conducted a functional near-infrared spectroscopy (fNIRS) study, in which IPS activation of left-handed adults was compared to right-handed adults in a symbolic approximate calculation task. The results showed that left-handers had a stronger functional right-lateralization in the IPS than right-handers. This finding has important consequences, as the bilateral IPS activation pattern for arithmetic processing seems to be shaped by functional lateralization and thus differs between left- and right-handers. We propose three possible accounts for the observed functional lateralization of arithmetic processing.

Discrimination of ordinal relationships in temporal sequences by 4-month-old infants

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.

The association of brightness with number/duration in human newborns

Human neonates spontaneously associate changes in magnitude across the dimensions of number, length, and duration. Do these particular associations generalize to other pairs of magnitudes in the same way at birth, or do they reflect an early predisposition to expect specific relations between spatial, temporal, and numerical representations? To begin to answer this question, we investigated how strongly newborns associated auditory sequences changing in number/duration with visual objects changing in levels of brightness. We tested forty-eight newborn infants in one of three, bimodal stimulus conditions in which auditory numbers/durations increased or decreased from a familiarization trial to the two test trials. Auditory numbers/durations were paired with visual objects in familiarization that remained the same on one test trial but changed in luminance/contrast or shape on the other. On average, results indicated that newborns looked longer when changes in brightness accompanied the number/duration change as compared to no change, a preference that was most consistent when the brightness change was congruent with the number/duration change. For incongruent changes, this preference depended on trial order. Critically, infants showed no preference for a shape change over no shape change, indicating that infants likely treated brightness differently than a generic feature. Though this performance pattern is somewhat similar to previously documented associations, these findings suggest that cross-magnitude associations among number, length, and duration may be more specialized at birth, rather than emerge gradually from postnatal experience or maturation.

Number, time, and space are not singularly represented: Evidence against a common magnitude system beyond early childhood

Our ability to represent temporal, spatial, and numerical information is critical for understanding the world around us. Given the prominence of quantitative representations in the natural world, numerous cognitive, neurobiological, and developmental models have been proposed as a means of describing how we track quantity. One prominent theory posits that time, space, and number are represented by a common magnitude system, or a common neural locus (i.e., Bonn & Cantlon in Cognitive Neuropsychology, 29(1/2), 149-173, 2012; Cantlon, Platt, & Brannon in Trends in Cognitive Sciences, 13(2), 83-91, 2009; Meck & Church in Animal Behavior Processes, 9(3), 320, 1983; Walsh in Trends in Cognitive Sciences, 7(11), 483-488, 2003). Despite numerous similarities in representations of time, space, and number, an increasing body of literature reveals striking dissociations in how each quantity is processed, particularly later in development. These findings have led many researchers to consider the possibility that separate systems may be responsible for processing each quantity. This review will analyze evidence in favor of a common magnitude system, particularly in infancy, which will be tempered by counter evidence, the majority of which comes from experiments with children and adult participants. After reviewing the current data, we argue that although the common magnitude system may account for quantity representations in infancy, the data do not provide support for this system throughout the life span. We also identify future directions for the field and discuss the likelihood of the developmental divergence model of quantity representation, like that of Newcombe (Ecological Psychology, 2, 147-157, 2014), as a more plausible account of quantity development.

Spatial metaphor and the development of cross-domain mappings in early childhood

Spatial language is often used metaphorically to describe other domains, including time (long sound) and pitch (high sound). How does experience with these metaphors shape the ability to associate space with other domains? Here, we tested 3- to 6-year-old English-speaking children and adults with a cross-domain matching task. We probed cross-domain relations that are expressed in English metaphors for time and pitch (length-time and height-pitch) as well as relations that are unconventional in English but expressed in other languages (size-time and thickness-pitch). Participants were tested with a perceptual matching task, in which they matched between spatial stimuli and sounds of different durations or pitches, and a linguistic matching task, in which they matched between a label denoting a spatial attribute, duration, or pitch and a picture or sound representing another dimension. Contrary to previous claims that experience with linguistic metaphors is necessary for children to make cross-domain mappings, children performed above chance for both familiar and unfamiliar relations in both tasks, as did adults. Children's performance was also better when a label was provided for one of the dimensions, but only when making length-time, size-time, and height-pitch mappings (not thickness-pitch mappings). These findings suggest that although experience with metaphorical language is not necessary to make cross-domain mappings, labels can promote these mappings, both when they have familiar metaphorical uses (e.g., English long denotes both length and duration) and when they describe dimensions that share a common ordinal reference frame (e.g., size and duration but not thickness and pitch). (PsycINFO Database Record

Development of a Possible General Magnitude System for Number and Space

There is strong evidence for a link between numerical and spatial processing. However, whether this association is based on a common general magnitude system is far from conclusive and the impact of development is not yet known. Hence, the present study aimed to investigate the association between discrete non-symbolic number processing (comparison of dot arrays) and continuous spatial processing (comparison of angle sizes) in children between the third and sixth grade (N = 367). Present findings suggest that the processing of comparisons of number of dots or angle are related to each other, but with angle processing developing earlier and being more easily comparable than discrete number representations for children of this age range. Accordingly, results favor the existence of a more complex underlying magnitude system consisting of dissociated but closely interacting representations for continuous and discrete magnitudes.

Compatibility between object size and response side in grasping: the left hand prefers smaller objects, the right hand prefers larger objects

It has been proposed that the brain processes quantities such as space, size, number, and other magnitudes using a common neural metric, and that this common representation system reflects a direct link to motor control, because the integration of spatial, temporal, and other quantity-related information is fundamental for sensorimotor transformation processes. In the present study, we examined compatibility effects between physical stimulus size and spatial (response) location during a sensorimotor task. Participants reached and grasped for a small or large object with either their non-dominant left or their dominant right hand. Our results revealed that participants initiated left hand movements faster when grasping the small cube compared to the large cube, whereas they initiated right hand movements faster when grasping the large cube compared to the small cube. Moreover, the compatibility effect influenced the timing of grip aperture kinematics. These findings indicate that the interaction between object size and response hand affects the planning of grasping movements and supports the notion of a strong link between the cognitive representation of (object) size, spatial (response) parameters, and sensorimotor control.

Dynamics and development in number-to-space mapping

Young children's estimates of numerical magnitude increase approximately logarithmically with actual magnitude. The conventional interpretation of this finding is that children's estimates reflect an innate logarithmic encoding of number. A recent set of findings, however, suggests that logarithmic number-line estimates emerge via a dynamic encoding mechanism that is sensitive to previously encountered stimuli. Here we examine trial-to-trial changes in logarithmicity of numerosity estimates to test an alternative dynamic model (D-MLLM) with both a strong logarithmic component and a weak response to previous stimuli. In support of D-MLLM, first-trial numerosity estimates in both adults (Study 1, 2, 3, and 4) and children (Study 4) were strongly logarithmic, despite zero previous stimuli. Additionally, although numerosity of a previous trial affected adults' estimates, the influence of previous numbers always accompanied the logarithmic-to-linear shift predicted by D-MLLM. We conclude that a dynamic encoding mechanism is not necessary for compressive mapping, but sequential effects on response scaling are a possible source of linearity in adults' numerosity estimation.

Spatial grounding of symbolic arithmetic: an investigation with optokinetic stimulation

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.

Non-adaptive strategy selection in adults with high mathematical anxiety

Participants with mathematical anxiety (MA) tend to show particular difficulty in mathematical operations with high working memory (WM) demands compared to operations with lower WM demands. Accordingly, we examined strategy selection to test the cognitive mechanism underlying the observed weakness of high MA participants in mathematical operations with high WM demands. We compared two groups of college students with high or low MA, in the solution of simple non-carry addition problems (e.g., 54 + 63) and complex carryover addition problems (e.g., 59 + 63). The results indicated that high MA participants showed particular difficulty in the harder carry condition. Testing the strategy selection mechanism among high MA participants, we found in the carry condition 1) they used the common strategy less often compared to low MA participants and 2) employed unusual strategies more often compared to low MA participants. Therefore, high MA participants were less efficient in their strategy selection, which may be due to weaker spatial representations, numerical difficulties, or less experience solving complex problems. These primitive representations are not adaptive, and can negatively impact performance in math tasks with high WM demands.

Hitting the Target: Mathematical Attainment in Children Is Related to Interceptive-Timing Ability

Interceptive timing is a fundamental ability underpinning numerous actions (e.g., ball catching), but its development and relationship with other cognitive functions remain poorly understood. Piaget suggested that children need to learn the physical rules that govern their environment before they can represent abstract concepts such as number and time. Thus, learning how objects move in space and time may underpin the development of related abstract representations (i.e., mathematics). To test this hypothesis, we captured objective measures of interceptive timing in 309 primary school children (5-11 years old), alongside scores for general motor skill and national standardized academic attainment. Bayesian estimation showed that interceptive timing (but not general motor capability) uniquely predicted mathematical ability even after we controlled for age, reading, and writing attainment. This finding demonstrates that interceptive timing is distinct from other motor skills with specificity in predicting childhood mathematical ability independently of other forms of attainment and motor capability.

On the genesis of spatial-numerical associations: Evolutionary and cultural factors co-construct the mental number line

Mapping numbers onto space is a common cognitive representation that has been explored in both behavioral and neuroimaging contexts. Empirical work probing the diverse nature of these spatial-numerical associations (SNAs) has led researchers to question 1) how the human brain links numbers with space, and 2) whether this link is biologically vs. culturally determined. We review the existing literature on the development of SNAs and situate that empirical work within cognitive and neuroscientific theoretical frameworks. We propose that an evolutionarily-ancient frontal-parietal circuit broadly tuned to multiple magnitude dimensions provides the phylogenetic substrate for SNAs, while enculturation and sensorimotor experience shape their specific profiles. We then use this perspective to discuss educational implications and highlight promising avenues for future research.

From What Age Is Mental Rotation Training Effective? Differences in Preschool Age but Not in Sex

Currently, there is evidence that spatial skills training leads to an improvement of such skills, although studies with children in the Preschool stage are very scarce. This paper aims to examine the effectiveness of mental rotation (MR) training and sex differences in preschool children. Two experiments were carried out. Experiment 1 included 59 children of 1st course (aged between 3 and 4 years) and Experiment 2, 61 children of 2nd course (aged between 4 and 5 years) of Preschool Education, distributed into control and training groups. The results showed a significant improvement in the MR ability of the training group (measured through a different test than the one used for training) only in the older children, and a tendency toward significance in the younger participants. Moreover, no sex differences in MR or group differences across age groups were found. These results regarding MR training support the malleability of spatial skills approach, particularly in 4–5 year-old preschoolers. This malleability should be enhanced in our educational system, as well as the implementation of educational and social policies that tend toward equality between sexes in the development of spatial skills. This can promote an equitable access to academic careers requiring high spatial skills such as engineering, science, technology or mathematics, in which nowadays women are underrepresented.