The spatial–numerical congruity effect in preschoolers

Development of number line estsimation in Chinese preschoolers: a comparison between numerical and non-numerical symbols

To examine the level of number line estimation (NLE) in Chinese children with respect to representations of both numerical (Arabic numerals) and non-numerical symbols (dots), a total of 192 Chinese preschoolers aged between 4 and 5 years participated in four different NLE tasks. These tasks were paired to evaluate the accuracy and patterns of children's estimations in both numerical and non-numerical symbol contexts. Our findings indicate that, for Chinese preschoolers, relatively precise numerical symbol representations begin to emerge as early as 4 years of age. The accuracy of number line estimates for both 4- and 5-year-old children gradually increases in tasks involving both numerical and non-numerical symbols. Additionally, the development and patterns observed in the number line estimates of 4- and 5-year-old Chinese preschoolers are similar in both numerical symbol and non-numerical symbol tasks. These results indicate that the initiation of relatively precise numerical symbol representation and the turning point in the developmental trajectory, where the relatively precise representation for numerical symbols surpasses that of non-numerical ones, occur earlier in Chinese children than in their Western counterparts.

Literacy overrides effects of animacy: A picture-naming study with pre-literate German children and adult speakers of German and Arabic

Animacy plays a key role for human cognition, which is also reflected in the way humans process language. However, while experiments on sentence processing show reliable effects of animacy on word order and grammatical function assignment, effects of animacy on conjoined noun phrases (e.g., fish and shoe vs. shoe and fish) have yielded inconsistent results. In the present study, we tested the possibility that effects of animacy are outranked by reading and writing habits. We examined adult speakers of German (left-to-right script) and speakers of Arabic (right-to-left script), as well as German preschool children who do not yet know how to read and write. Participants were tested in a picture naming task that presented an animate and an inanimate entity next to one another. On half of the trials, the animate entity was located on the left and, on the other half, it was located on the right side of the screen. We found that adult German and Arabic speakers differed in their order of naming. Whereas German speakers were much more likely to mention the animate entity first when it was presented on the left than on the right, a reverse tendency was observed for speakers of Arabic. Thus, in literate adults, the ordering of conjoined noun phrases was influenced by reading and writing habits rather than by the animacy status of an entity. By contrast, pre-literate children preferred to start their utterances with the animate entity regardless of position, suggesting that effects of animacy in adults have been overwritten by effects of literacy.

The importance of spatial language for early numerical development in preschool: Going beyond verbal number skills

Recent evidence suggests that spatial language in preschool positively affects the development of verbal number skills, as indexed by aggregated performances on counting and number naming tasks. We firstly aimed to specify whether spatial language (the knowledge of locative prepositions) significantly relates to both of these measures. In addition, we assessed whether the predictive value of spatial language extends beyond verbal number skills to numerical subdomains without explicit verbal component, such as number writing, symbolic magnitude classifications, ordinal judgments and numerosity comparisons. To determine the unique contributions of spatial language to these numerical skills, we controlled in our regression analyses for intrinsic and extrinsic spatial abilities, phonological awareness as well as age, socioeconomic status and home language. With respect to verbal number skills, it appeared that spatial language uniquely predicted forward and backward counting but not number naming, which was significantly affected only by phonological awareness. Regarding numerical tasks that do not contain explicit verbal components, spatial language did not relate to number writing or numerosity comparisons. Conversely, it explained unique variance in symbolic magnitude classifications and was the only predictor of ordinal judgments. These findings thus highlight the importance of spatial language for early numerical development beyond verbal number skills and suggest that the knowledge of spatial terms is especially relevant for processing cardinal and ordinal relations between symbolic numbers. Promoting spatial language in preschool might thus be an interesting avenue for fostering the acquisition of these symbolic numerical skills prior to formal schooling.

The temporal dynamics of emotion comparison depends on low-level attentional factors

Humans are predisposed to attend to emotions conveyed by facial expressions. However, compulsory attraction to emotions gets challenging when multiple emotional stimuli compete for attention, as in the emotion comparison task. In this task, participants are asked to choose which of two simultaneously presented faces displays the most positive (happiest) or negative (angriest) emotion. Participants usually respond faster to the face displaying the most intense emotion. This effect is stronger for face pairs that contain globally positive rather than negative emotional faces. Both effects are consistent with an attentional capture phenomenon driven by the perceptual salience of facial expressions. In the present experiment, we studied the temporal dynamics of attentional capture in the emotion comparison task by tracking participants' eye movements using gaze-contingent displays and responses. Our results show that, on the first fixation, participants were more accurate and dwelled longer on the left target face when it displayed the most intense emotion within the pair. On the second fixation, the pattern was reversed, with higher accuracy and longer gaze time on the right target face. Overall, our pattern of gazing behavior indicates that the typical results observed in the emotion comparison task arise from the optimal combination over time of two low-level attentional factors: the perceptual salience of emotional stimuli and the scanning habit of participants.

The plural counts: Inconsistent grammatical number hinders numerical development in preschoolers - A cross-linguistic study

The role of grammar in numerical development, and particularly the role of grammatical number inflection, has already been well-documented in toddlerhood. It is unclear, however, whether the influence of grammatical language structure further extends to more complex later stages of numerical development. Here, we addressed this question by exploiting differences between Polish, which has a complex grammatical number paradigm, leading to a partially inconsistent mapping between numerical quantities and grammatical number, and German, which has a comparatively easy verbal paradigm: 151 Polish-speaking and 123 German-speaking kindergarten children were tested using a symbolic numerical comparison task. Additionally, counting skills (Give-a-Number and count-list), and mapping between non-symbolic (dot sets) and symbolic representations of numbers, as well as working memory (Corsi blocks and Digit span) were assessed. Based on the Give-a-Number and mapping tasks, the children were divided into subset-knowers, CP-knowers-non-mappers, and CP-knowers-mappers. Linguistic background was related to performance in several ways: Polish-speaking children expectedly progressed to the CP-knowers stage later than German children, despite comparable non-numerical capabilities, and even after this stage was achieved, they fared worse in the numerical comparison task. There were also meaningful differences in spatial-numerical mapping between the Polish and German groups. Our findings are in line with the theory that grammatical number paradigms influence. the development of representations and processing of numbers, not only at the stage of acquiring the meaning of the first number-words but at later stages as well, when dealing with symbolic numbers.

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.

Developing mental number line games to improve young children's number knowledge and basic arithmetic skills

The learning of number knowledge in childhood may directly influence children's mathematics learning ability in subsequent periods. Previous studies also show that the difficulties in mathematics learning faced by schoolchildren are mainly rooted in the lack of number knowledge in early childhood. Focusing on the development of numerical knowledge and basic arithmetic skills in early childhood, this study designed a linear number line game based on the theory of the mental number line. Accordingly, this study examined the effectiveness of the linear number line game in children's learning of number concepts and arithmetic skills and compared the effectiveness of the linear number line game with that of two other games (a nonlinear number line game and a non-number-line game). This study adopted a quasi-experimental research design. A total of 140 young children from remote areas of eastern Taiwan participated and were divided into three experimental groups and one control group, and a pretest-posttest experiment was conducted. The experimental results showed that the linear number line game could help children to acquire numerical knowledge effectively, especially in number line estimation compared with other experimental groups. In terms of the learning effectiveness of basic arithmetic skills (e.g., addition, subtraction), the two number line games (linear and nonlinear number line games) are significantly superior to the non-number-line game (traditional number decomposition and synthesis game). This study recommends that preschool teachers use linear number line games to improve children's numerical knowledge and arithmetic skills.

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.

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.

Toddlers' interventions toward fair and unfair individuals

Cooperative societies rely on reward and punishment for norm enforcement. We examined the developmental origin of these interventions in the context of distributive fairness: past research has shown that infants expect resources to be distributed fairly, prefer to interact with fair distributors, and evaluate others based on their fair and unfair resource allocations. In order to determine whether infants would intervene in third-party resource distributions by use of reward and punishment we developed a novel task. Sixteen-month-old infants were taught that one side of a touch screen produces reward (vocal statements expressing praise; giving a cookie), whereas the other side produces punishment when touched (vocal statements expressing admonishment; taking away a cookie). After watching videos in which one actor distributed resources fairly and another actor distributed resources unfairly, participants' screen touches on the reward and punishment panels while the fair and unfair distributors appeared on screen were recorded. Infants touched the reward side significantly more than the punishment side when presented with the fair distributor but touched the screen sides equally when the unfair distributor was shown. Control experiments revealed no evidence of reward or punishment when infants saw food items they liked and disliked, or individuals uninvolved in the resource distribution events. These results provide the earliest evidence that infants are able to spontaneously intervene in socio-moral situations by rewarding positive actions.

Electrophysiological Evidence of Space-Number Associations in 9-Month-Old Infants

Infant research is providing accumulating evidence that number-space mappings appear early in development. Here, a Posner cueing paradigm was used to investigate the neural mechanisms underpinning the attentional bias induced by nonsymbolic numerical cues in 9-month-old infants (N = 32). Event-related potentials and saccadic reaction time were measured to the onset of a peripheral target flashing right after the offset of a centered small or large numerical cue, with the location of the target being either congruent or incongruent with the number's relative position on a left-to-right oriented representational continuum. Results indicated that the cueing effect induced by numbers on infants' orienting of eye gaze brings about sensory facilitation in processing visual information at the cued location.

Children's spatial-numerical associations on horizontal, vertical, and sagittal axes

There is substantial evidence linking numerical magnitude to the physical properties of space. The most influential support for this connection comes from the SNARC effect (spatial-numerical association of response codes), in which responses to small/large numbers are faster on the left/right side of space, respectively. The SNARC effect has been extensively replicated, and is understood as horizontal mapping of numerical magnitude. However, much less is known about how numbers are represented on the vertical and sagittal axes, and whether spatial-numerical associations on different axes emerge during childhood. To that end, we tested two groups of children, aged 5-7 years and 8 and 9 years, on a single-digit magnitude comparison task with response buttons positioned either upper/lower (vertical), left/right (horizontal) or near/far (sagittal). Our results provide evidence of spatial-numerical mapping on all three axes for both age groups that are similar in strength. This indicates that, even at an early stage of formal education, children can flexibly assign numerical magnitude to any spatial dimension. To examine the contribution of extracorporeal space and spatio-anatomical mapping to the SNARC effect across axes, these sources were pitted against each other by swapping the position of the response hands in Experiment 1b. Switching hand position did not reveal convincing evidence for SNARC effects on any axis. Results are discussed with respect to the utility of three-dimensional mental number lines, and potential avenues for future research are outlined.

Non-symbolic and symbolic number lines are dissociated

People use mental number lines for both symbolic numerals and numerosity, but little is known about how these two mental number lines are related. The current study investigated the association in effect size, directionality of the mental number line, and development between symbolic and non-symbolic mental number lines to determine if they were related to or independent from each other. We collected data from numerosity- and digit-matching tasks that used the following numbers: 11, 14, 17, 20, 23, 26, and 29. Tasks were performed by college undergraduates and the fifth-grade primary school students. The results showed that none of the effects for non-symbolic numbers was related to any of the effects for symbolic numbers, and vice versa, in both adults and children. Another notable finding was that the correlation between the SNARC (spatial-numerical association of response code) effect size and mathematical ability was negative in the adult group. These results are consistent with the dissociated processes hypothesis and suggest that mental number lines are notation-dependent. As shown by the SNARC effect, the mental number line might result in interference in the current task by an automatically activated spatial notation-dependent representation of numbers.

The importance of visuospatial abilities for verbal number skills in preschool: Adding spatial language to the equation

Children's verbal number skills set the foundation for mathematical development. Therefore, it is central to understand their cognitive origins. Evidence suggests that preschool children rely on visuospatial abilities when solving counting and number naming tasks despite their predominantly verbal nature. We aimed to replicate these findings when controlling for verbal abilities and sociodemographic factors. Moreover, we further characterized the relation between visuospatial abilities and verbal number skills by examining the role of spatial language. Because spatial language encompasses the verbalization of spatial thinking, it is a key candidate supporting the interplay between visuospatial and verbal processes. Regression analysis indicated that both visuospatial and verbal abilities, as assessed by spatial perception and phonological awareness, respectively, uniquely predicted verbal number skills when controlling for their respective influences, age, gender, and socioeconomic status. This confirms the spatial grounding of verbal number skills. Interestingly, adding spatial language to the model abolished the predictive effects of visuospatial and verbal abilities, whose influences were completely mediated by spatial language. Verbal number skills thus concurrently depend on specifically those visuospatial and verbal processes jointly indexed through spatial language. The knowledge of spatial terms might promote verbal number skills by advancing the understanding of the spatial relations between numerical magnitudes on the mental number line. Promoting spatial language in preschool thus might be a successful avenue for stimulating mathematical development prior to formal schooling. Moreover, measures of spatial language could become an additional promising tool to screen preschool children for potential upcoming difficulties with mathematical learning.

Moving attention along the mental number line in preschool age: Study of the operational momentum in 3- to 5-year-old children's non-symbolic arithmetic

People tend to underestimate subtraction and overestimate addition outcomes and to associate subtraction with the left side and addition with the right side. These two phenomena are collectively labeled 'operational momentum' (OM) and thought to have their origins in the same mechanism of 'moving attention along the mental number line'. OM in arithmetic has never been tested in children at the preschool age, which is critical for numerical development. In this study, 3-5 years old were tested with non-symbolic addition and subtraction tasks. Their level of understanding of counting principles (CP) was assessed using the give-a-number task. When the second operand's cardinality was 5 or 6 (Experiment 1), the child's reaction time was shorter in addition/subtraction tasks after cuing attention appropriately to the right/left. Adding/subtracting one element (Experiment 2) revealed a more complex developmental pattern. Before acquiring CP, the children showed generalized overestimation bias. Underestimation in addition and overestimation in subtraction emerged only after mastering CP. No clear spatial-directional OM pattern was found, however, the response time to rightward/leftward cues in addition/subtraction again depended on stage of mastering CP. Although the results support the hypothesis about engagement of spatial attention in early numerical processing, they point to at least partial independence of the spatial-directional and magnitude OM. This undermines the canonical version of the number line-based hypothesis. Mapping numerical magnitudes to space may be a complex process that undergoes reorganization during the period of acquisition of symbolic representations of numbers. Some hypotheses concerning the role of spatial-numerical associations in numerical development are proposed.

Spatial biases in mental arithmetic are independent of reading/writing habits: Evidence from French and Arabic speakers

The representation of numbers in human adults is linked to space. In Western cultures, small and large numbers are associated respectively with the left and right sides of space. An influential framework attributes the emergence of these spatial-numerical associations (SNAs) to cultural factors such as the direction of reading and writing, because SNAs were found to be reduced or inverted in right-to-left readers/writers (e.g., Arabic, Farsi, or Hebrew speakers). However, recent cross-cultural and animal studies cast doubt on the determining role of reading and writing directions on SNAs. In this study, we assessed this role in mental arithmetic, which requires explicit number manipulations and has revealed robust leftward or rightward biases in Western participants. We used a temporal order judgement task in French and Arabic speakers, two languages that have opposite reading/writing directions. Participants had to solve subtraction and addition problems presented auditorily while at the same time determining which of a left or right visual target appeared first on a screen. The results showed that the right target was favoured more often when solving additions than when solving subtractions both in the French- (n = 31) and Arabic-speaking (n = 25) groups. This was true even in Arabic-speaking participants whose preference for ordering of various series of numerical and non-numerical stimuli went from right to left (n = 10). These results indicate that SNAs in mental arithmetic cannot be explained by the direction of reading/writing habits and call for a reconsideration of current models to acknowledge the pervasive role of biological factors in SNAs in adults.

A gifted SNARC? Directional spatial-numerical associations in gifted children with high-level math skills do not differ from controls

The SNARC (Spatial-Numerical Association of Response Codes) effect (i.e., a tendency to associate small/large magnitude numbers with the left/right hand side) is prevalent across the whole lifespan. Because the ability to relate numbers to space has been viewed as a cornerstone in the development of mathematical skills, the relationship between the SNARC effect and math skills has been frequently examined. The results remain largely inconsistent. Studies testing groups of people with very low or very high skill levels in math sometimes found relationships between SNARC and math skills. So far, however, studies testing such extreme math skills level groups were mostly investigating the SNARC effect in individuals revealing math difficulties. Groups with above average math skills remain understudied, especially in regard to children. Here, we investigate the SNARC effect in gifted children, as compared to normally developing children (overall n = 165). Frequentist and Bayesian analysis suggested that the groups did not differ from each other in the SNARC effect. These results are the first to provide evidence for the SNARC effect in a relatively large sample of gifted (and mathematically highly skilled) children. In sum, our study provides another piece of evidence for no direct link between the SNARC effect and mathematical ability in childhood.

Large as being on top of the world and small as hitting the roof: a common magnitude representation for the comparison of emotions and numbers

Previous work on the direct speed-intensity association (SIA) on comparative judgement tasks involved spatially distributed responses over spatially distributed stimuli with high motivational significance like facial expressions of emotions. This raises the possibility that the inferred stimulus-driven regulation of lateralized motor reactivity described by SIA, which was against the one expected on the basis of a valence-specific lateral bias, was entirely due to attentional capture from motivational significance (beyond numerical cognition). In order to establish the relevance of numerical cognition on the regulation of attentional capture we ran two complementary experiments. These involved the same direct comparison task on stimulus pairs that were fully comparable in terms of their analog representation of intensity but with different representational domain and motivational significance: symbolic magnitudes with low motivational significance in experiment 1 vs. emotions with rather high motivational significance in experiment 2. The results reveal a general SIA and point to a general mechanism regulating comparative judgements. This is based on the way spatial attention is captured toward locations that contain the stimulus which is closest in term of relative intensity to the extremal values of the series, regardless from its representational domain being it symbolic or emotional.

Investigating the respective contribution of sensory modalities and spatial disposition in numerical training

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.

Compatibility between response position and either object typical size or semantic category: SNARC- and MARC-like effects in primary school children

In two experiments, we administered two binary classification tasks to third- to fifth-grade students and found that either the conceptual size (Experiment 1) or semantic category (Experiment 2) of the target picture interacted with response position: Participants emitted faster and/or more accurate right- and left-side responses to stimuli referring to typically large and small objects (i.e., a SNARC [spatial-numerical association of response codes]-like effect) or to living and nonliving objects (i.e., a MARC [markedness association of response codes]-like effect), respectively. The effect of either stimulus dimension was present only when this dimension was the task-relevant one. These findings may be accounted for by the polarity compatibility principle. In binary classification tasks, one of the two relevant stimulus values (i.e., the dominant one) and one of the two response values would be coded as having a positive polarity, whereas the other would be coded as having a negative polarity. Response selection would be faster and/or more accurate when stimulus and response polarities are compatible. According to a less parsimonious hypothesis, the polarity principle would only explain the effect of the stimulus semantic category in Experiment 2, whereas the effect of stimulus conceptual size in Experiment 1 might be traced back to the fact that children spatially code the typical size of stimulus referents (even if only when the task requires accessing this stimulus dimension). Small and large objects would be represented relatively on the left and right, respectively, which would result in faster and/or more accurate responses when response position is compatible with the stimulus referent's position in this spatial representation.

Non-symbolic numerosities do not automatically activate spatial-numerical associations: Evidence from the SNARC effect

The SNARC (spatial-numerical association of response codes) effect is the finding that people are generally faster to respond to smaller numbers with left-sided responses and larger numbers with right-sided responses. The SNARC effect has been widely reported for responses to symbolic representations of number such as digits. However, there is mixed evidence as to whether it occurs for non-symbolic representations of number, particularly when magnitude is irrelevant to the task. Mitchell et al. reported a SNARC effect when participants were asked to make orientation decisions to arrays of one-to-nine triangles (pointing upwards vs. pointing downwards) and concluded that SNARC effects occur for non-symbolic, non-canonical representations of number. They additionally reported that this effect was stronger in the subitising range. However, here we report four experiments that do not replicate either of these findings. Participants made upwards/inverted decisions to one-to-nine triangles where total surface area was either controlled across numerosities (Experiments 1, 2, and 4) or increased congruently with numerosity (Experiment 3). There was no evidence of a SNARC effect either across the full range or within the subset of the subitising range. The results of Experiment 4 (in which we presented the original stimuli of Mitchell et al.) suggested that visual properties of non-symbolic displays can prompt SNARC-like effects driven by visual cues rather than numerosity. Taken in the context of other recent findings, we argue that non-symbolic representations of number do not offer a direct and automatic route to numerical-spatial associations.

Limited evidence of number-space mapping in rhesus monkeys (Macaca mulatta) and capuchin monkeys (Sapajus apella)

Humans exhibit evidence of a mental number line that suggests a left-to-right, or sometimes right-to-left, representation of smaller to larger numbers. The Spatial Numerical Association of Response Codes (SNARC) effect is one example of this mental number line and has been investigated extensively in humans. Less research has been done with animals, and results have been inconclusive. Rugani, Vallortigara, Priftis, and Regolin (2015) found that young chicks showed a bias to respond to small quantities presented to their left and large quantities presented to their right when forced to move toward those stimuli to gain food reward. We replicated this design with rhesus macaques and capuchin monkeys using a computerized task, but we did not find this outcome. We also trained monkeys to choose between 2 arrays of dots, and then assessed biases in terms of choice location and response latency on trials with a numerical difference and on trials with equal numbers of items in both sets. There was no evidence of SNARC-like effects in equal trials, although when arrays differed in number, 12 of 19 monkeys showed differential performance depending on whether the smaller array was at the left or at the right onscreen. These results indicate that SNARC-like effects may not emerge in all contexts and may not be phylogenetically widespread. More effort is needed to broaden the number of species assessed and match other methods that are used with human participants so that we can better define the presence and extent of such effects. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Scanning of speechless comics changes spatial biases in mental model construction

The mental representation of both time and number shows lateral spatial biases, which can be affected by habitual reading and writing direction. However, this effect is in place before children begin to read. One potential early cause is the experiences of looking at picture books together with a carer, as those images also follow the directionality of the script. What is the underlying mechanism for this effect? In the present study, we test the possibility that such experiences induce spatial biases in mental model construction, a mechanism which is a good candidate to induce the biases observed with numbers and times. We presented a speechless comic in either standard (left-to-right) or mirror-reversed (right-to-left) form to adult Spanish participants. We then asked them to draw the scene depicted by sentences like 'the square is between the cross and the circle'. The position of the lateral objects in these drawings reveals the spatial biases at work when building mental models in working memory. Under conditions of highly consistent directionality, the mirror comic changed pre-existing lateral biases. Processes of mental model construction in working memory stand as a potential mechanism for the generation of spatial biases for time and number.This article is part of the theme issue 'Varieties of abstract concepts: development, use and representation in the brain'.

Emotional Semantic Congruency based on stimulus driven comparative judgements

A common cognitive process in everyday life consists in the comparative judgements of emotions given a pair of facial expressions and the choice of the most positive/negative among them. Results from three experiments on complete-facial expressions (happy/angry) and mixed-facial expressions (neutral/happy-or-angry) pairs viewed with (Experiment 1 and 3) or without (Experiment 2) foveation and performed in conditions in which valence was either task relevant (Experiment 1 and 2) or task irrelevant (Experiment 3), show that comparative judgements of emotions are stimulus driven. Judgements' speed increased as the target absolute emotion intensity grew larger together with the average emotion of the pair, irrespective of the compatibility between the valence and the side of motor response: a semantic congruency effect in the domain of emotion. This result undermines previous interpretation of results in the context of comparative judgements based on the lateralization of emotions (e.g., SNARC-like instructional flexibility), and is fully consistent with our formalization of emotional semantic congruency: the direct Speed-Intensity Association model.

Operational momentum for magnitude ordering in preschool children and adults

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.

The SNARC and MARC effects measured online: Large-scale assessment methods in flexible cognitive effects

The Spatial-Numerical Association of Response Codes (SNARC) effect (i.e., faster reactions to small/large numbers on the left-/right-hand side) is usually observed along with the linguistic Markedness of Response Codes (MARC) effect-that is, faster left-/right-hand responses to odd/even numbers. The SNARC effect is one of the most thoroughly investigated phenomena in numerical cognition. However, almost all SNARC and MARC studies to date were conducted with sample sizes smaller than 100. Here we report on a study with 1,156 participants from various linguistic and cultural backgrounds performing a typical parity judgment task. We investigated whether (1) the SNARC and MARC effects can be observed in an online setup, (2) the properties of these effects observed online are similar to those observed in laboratory setups, (3) the effects are reliable, and (4) they are valid. We found robust SNARC and MARC effects. Their magnitude and reliabilities were comparable to values previously reported in in-lab studies. Furthermore, we reproduced commonly observed validity correlations of the SNARC and MARC effects. Namely, SNARC and MARC correlated with mean reaction times and intraindividual variability in reaction times. Additionally, we found interindividual differences in the SNARC and MARC effects (e.g., finger-counting routines for the SNARC and handedness for the MARC). Large-scale testing via web-based data acquisition not only produces SNARC and MARC effects and validity correlations similar to those from small, in-lab studies, but also reveals substantial insights with regard to interindividual differences that usually cannot be revealed in the offline laboratory, due to power considerations.

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 Presentations, but Not Response Formats Influence Spatial-Numerical Associations in Adults

According to theories of embodied numerosity, processing of numerical magnitude is anchored in bodily experiences. In particular, spatial representations of number interact with movement in physical space, but it is still unclear whether the extent of the movement is relevant for this interaction. In this study, we compared spatial-numerical associations over response movements of differing spatial expansion. We expected spatial-numerical effects to increase with the extent of physical response movements. In addition, we hypothesized that these effects should be influenced by whether or not a spatial representation of numbers was presented. Adult participants performed two tasks: a magnitude classification (comparing numbers to the fixed standard 5), from which we calculated the Spatial Numerical Association of Response Codes (SNARC) effect; and a magnitude comparison task (comparing two numbers against each other), from which we calculated a relative numerical congruity effect (NCE), which describes that when two relatively small numbers are compared, responses to the smaller number are faster than responses to the larger number; and vice versa for large numbers. A SNARC effect was observed across all conditions and was not influenced by response movement extent but increased when a number line was presented. In contrast, an NCE was only observed when no number line was presented. This suggests that the SNARC effect and the NCE reflect two different processes. The SNARC effect seems to represent a highly automated classification of numbers as large or small, which is further emphasized by the presentation of a number line. In contrast, the NCE likely results from participants not only classifying numbers as small or large, but also processing their relative size within the relevant section of their mental number line representation. An additional external presentation of a number line might interfere with this process, resulting in overall slower responses. This study follows up on previous spatial-numerical training studies and has implications for future spatial-numerical trainings. Specifically, similar studies with children showed contrasting results, in that response format but not number line presentation influenced spatial-numerical associations. Accordingly, during development, the relative relevance of physical experiences and presentation format for spatial-numerical associations might change.

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.

Spatial order relates to the exact numerical magnitude of digits in young children

Spatial representation of numbers has been repeatedly associated with the development of numerical and mathematical skills. However, few studies have explored the contribution of spatial mapping to exact number representation in young children. Here we designed a novel task that allows a detailed analysis of direction, ordinality, and accuracy of spatial mapping. Preschool children, who were classified as competent counters (cardinal principle knowers), placed triplets of sequentially presented digits on the visual line. The ability to correctly order triplets tended to decrease with the larger digits. When triplets were correctly ordered, the direction of spatial mapping was predominantly oriented from left to right and the positioning of the target digits was characterized by a pattern of underestimation with no evidence of logarithmic compression. Crucially, only ordinality was associated with performance in a digit comparison task. Our results suggest that the spatial (ordinal) arrangement of digits is a powerful source of information that young children can use to construct the representation of exact numbers. Therefore, digits may acquire numerical meaning based on their spatial order on the number line.

Non-symbolic magnitudes are represented spatially: Evidence from a non-symbolic SNARC task

A core proposition in numerical cognition is numbers are represented spatially. Evidence for this proposition comes from the "spatial numerical association of response codes" effect (SNARC) in which faster responses are made by the left/right hand judging whether one of a pair of Arabic digits is smaller/larger than the other. Less is known if a similar SNARC effect exists for non-symbolic magnitudes; and research that has been conducted used stimuli which could be translated into symbolic terms. To overcome this limitation, we employed a referent-to-target judgment paradigm in which a referent dot array (n = 30 dots) was follow by a second array of dots (e.g., n = 45 or 15 dots)-participants judged if the second array contained fewer or more dots than the referent array. Dot arrays with fewer dots were judged more quickly with the left hand compared to the right hand (i.e., a SNARC effect). Not all participants demonstrated a SNARC effect, however. Neither visuospatial working memory nor math ability was associated with the presence/absence of a non-symbolic SNARC effect. Implications of the non-symbolic SNARC effect for accounts of numerical cognition are discussed.

Number concepts: abstract and embodied

Numerical knowledge, including number concepts and arithmetic procedures, seems to be a clear-cut case for abstract symbol manipulation. Yet, evidence from perceptual and motor behaviour reveals that natural number knowledge and simple arithmetic also remain closely associated with modal experiences. Following a review of behavioural, animal and neuroscience studies of number processing, we propose a revised understanding of psychological number concepts as grounded in physical constraints, embodied in experience and situated through task-specific intentions. The idea that number concepts occupy a range of positions on the continuum between abstract and modal conceptual knowledge also accounts for systematic heuristics and biases in mental arithmetic, thus inviting psycho-logical approaches to the study of the mathematical mind.This article is part of the theme issue 'Varieties of abstract concepts: development, use and representation in the brain'.

The Developmental Trajectory of the Operational Momentum Effect

Mental calculation is thought to be tightly related to visuospatial abilities. One of the strongest evidence for this link is the widely replicated operational momentum (OM) effect: the tendency to overestimate the result of additions and to underestimate the result of subtractions. Although the OM effect has been found in both infants and adults, no study has directly investigated its developmental trajectory until now. However, to fully understand the cognitive mechanisms lying at the core of the OM effect it is important to investigate its developmental dynamics. In the present study, we investigated the development of the OM effect in a group of 162 children from 8 to 12 years old. Participants had to select among five response alternatives the correct result of approximate addition and subtraction problems. Response alternatives were simultaneously presented on the screen at different locations. While no effect was observed for the youngest age group, children aged 9 and older showed a clear OM effect. Interestingly, the OM effect monotonically increased with age. The increase of the OM effect was accompanied by an increase in overall accuracy. That is, while younger children made more and non-systematic errors, older children made less but systematic errors. This monotonous increase of the OM effect with age is not predicted by the compression account (i.e., linear calculation performed on a compressed code). The attentional shift account, however, provides a possible explanation of these results based on the functional relationship between visuospatial attention and mental calculation and on the influence of formal schooling. We propose that the acquisition of arithmetical skills could reinforce the systematic reliance on the spatial mental number line and attentional mechanisms that control the displacement along this metric. Our results provide a step in the understanding of the mechanisms underlying approximate calculation and an important empirical constraint for current accounts on the origin of the OM effect.

The Developing Mental Number Line: Does Its Directionality Relate to 5- to 7-Year-Old Children's Mathematical Abilities?

Spatial representations of number, such as a left-to-right oriented mental number line, are well documented in Western culture. Yet, the functional significance of such a representation remains unclear. To test the prominent hypothesis that a mental number line may support mathematical development, we examined the relation between spatial-numerical associations (SNAs) and math proficiency in 5- to 7-year-old children. We found evidence of SNAs with two tasks: a non-symbolic magnitude comparison task, and a symbolic "Where was the number?" (WTN) task. Further, we found a significant correlation between these two tasks, demonstrating convergent validity of the directional mental number line across numerical format. Although there were no significant correlations between children's SNAs on the WTN task and math ability, children's SNAs on the magnitude comparison task were negatively correlated with their performance on a measure of cross-modal arithmetic, suggesting that children with a stronger left-to-right oriented mental number line were less competent at cross-modal arithmetic, an effect that held when controlling for age and a set of general cognitive abilities. Despite some evidence for a negative relation between SNAs and math ability in adulthood, we argue that the effect here may reflect task demands specific to the magnitude comparison task, not necessarily an impediment of the mental number line to math performance. We conclude with a discussion of the different properties that characterize a mental number line and how these different properties may relate to mathematical ability.

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.

Spatial and Verbal Routes to Number Comparison in Young Children

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.

The mental timeline is gradually constructed in childhood

When reasoning about time, English-speaking adults often invoke a "mental timeline" stretching from left to right. Although the direction of the timeline varies across cultures, the tendency to represent time as a line has been argued to be ubiquitous and primitive. On this hypothesis, we might predict that children also spontaneously invoke a spatial timeline when reasoning about time. However, little is known about how and when the mental timeline develops, or to what extent it is variable and malleable in childhood. Here, we used a sticker placement task to test whether preschoolers and kindergarteners spontaneously map temporal events (breakfast, lunch, and dinner) and deictic time words (yesterday, today, tomorrow) onto lines, and to what degree their representations of time are adult-like. We found that, at age 4, preschoolers were able to arrange temporal items in lines with minimal spatial priming. However, unlike kindergarteners and adults, most preschoolers did not represent time as a line spontaneously, in the absence of priming, and did not prefer left-to-right over right-to-left lines. Furthermore, unlike most adults, children of all ages could be easily primed to adopt an unconventional vertical timeline. Our findings suggest that mappings between time and space in children are initially flexible, and become increasingly automatic and conventionalized in the early school years.

Developmental Changes in the Effect of Active Left and Right Head Rotation on Random Number Generation

Numbers are thought to be spatially organized along a left-to-right horizontal axis with small/large numbers on its left/right respectively. Behavioral evidence for this mental number line (MNL) comes from studies showing that the reallocation of spatial attention by active left/right head rotation facilitated the generation of small/large numbers respectively. While spatial biases in random number generation (RNG) during active movement are well established in adults, comparable evidence in children is lacking and it remains unclear whether and how children’s access to the MNL is affected by active head rotation. To get a better understanding of the development of embodied number processing, we investigated the effect of active head rotation on the mean of generated numbers as well as the mean difference between each number and its immediately preceding response (the first order difference; FOD) not only in adults (n = 24), but also in 7- to 11-year-old elementary school children (n = 70). Since the sign and absolute value of FODs carry distinct information regarding spatial attention shifts along the MNL, namely their direction (left/right) and size (narrow/wide) respectively, we additionally assessed the influence of rotation on the total of negative and positive FODs regardless of their numerical values as well as on their absolute values. In line with previous studies, adults produced on average smaller numbers and generated smaller mean FODs during left than right rotation. More concretely, they produced more negative/positive FODs during left/right rotation respectively and the size of negative FODs was larger (in terms of absolute value) during left than right rotation. Importantly, as opposed to adults, no significant differences in RNG between left and right head rotations were observed in children. Potential explanations for such age-related changes in the effect of active head rotation on RNG are discussed. Altogether, the present study confirms that numerical processing is spatially grounded in adults and suggests that its embodied aspect undergoes significant developmental changes.