Embodied numbers: The role of vision in the development of number–space interactions

Stronger spatial bias induced more by numbers in mind than numbers in eye: Evidence from event-related potentials

The relationship between number and space is an important issue in numerical cognition. The spatial-numerical association of response codes (SNARC) effect is a classic example of the association between numbers and spaces. It refers to the phenomenon whereby left-handed responses occur faster to small number and right-handed responses occur faster to large number. The current study explored the shared and distinct neural correlates of the SNARC effect considering numbers in eye and numbers in mind, by using event-related potentials (ERPs) technology. In each trial of the task, participants were asked to press freely one of two keys as a response to a number presented visually (numbers in eye) or via imagination (numbers in mind). The behavioral results indicated that the free-choice key presses were affected by the magnitudes of the numbers either in eye or in mind. Electrophysiological results observed that the SNARC effect appeared only in the 110 - 140 ms time window for numbers in eye. In contrast, for numbers in mind, the SNARC effect appeared during a longer time window (110 - 330 ms). These results suggest that both, numbers in eye and numbers in mind, can induce spatial bias at the early stimulus-representation stage, but the time duration of the spatial bias is longer for numbers in mind than numbers in eye. This may reflect a closer connection between numbers in mind and mental number line.

Early visual deprivation disrupts the mental representation of numbers in visually impaired children

Several shreds of evidence indicate that visual deprivation does not alter numerical competence neither in adults nor in children. However, studies reporting non-impaired numerical abilities in the visually impaired population present some limitations: (a) they mainly assessed the ability to process numbers (e.g. mathematical competence) rather than represent numbers (e.g. mental number line); (b) they principally focused on positive rather than negative number estimates; (c) they investigated numerical abilities in adult individuals except one focusing on children (Crollen et al. in Cognition 210:104586, 2021). Overall, this could limit a comprehensive explanation of the role exerted by vision on numerical processing when vision is compromised. Here we investigated how congenital visual deprivation affects the ability to represent positive and negative numbers in horizontal and sagittal planes in visually impaired children (thirteen children with low vision, eight children with complete blindness, age range 6-15 years old). We adapted the number-to-position paradigm adopted by Crollen et al. (Cognition 210:104586, 2021), asking children to indicate the spatial position of positive and negative numbers on a graduated rule positioned horizontally or sagittally in the frontal plane. Results suggest that long-term visual deprivation alters the ability to identify the spatial position of numbers independently of the spatial plane and the number polarity. Moreover, results indicate that relying on poor visual acuity is detrimental for low vision children when asked to localize both positive and negative numbers in space, suggesting that visual experience might have a differential role in numerical processing depending on number polarity. Such findings add knowledge related to the impact of visual experience on numerical processing. Since both positive and negative numbers are fundamental aspects of learning mathematical principles, the outcomes of the present study inform about the need to implement early rehabilitation strategies to prevent the risk of numerical difficulties in visually impaired children.

Impact of deafness on numerical tasks implying visuospatial and verbal processes

The literature suggests that deaf individuals lag behind their hearing peers in terms of mathematical abilities. However, it is still unknown how unique sensorimotor experiences, like deafness, might shape number-space interactions. We still do not know either the spatial frame of reference deaf individuals use to map numbers onto space in different numerical tasks. To examine these issues, deaf, hearing signer and hearing control adults were asked to perform a number comparison and a parity judgment task with the hands uncrossed and crossed over the body midline. Deafness appears to selectively affect the performance of the numerical task relying on verbal processes while keeping intact the task relying on visuospatial processes. Indeed, while a classic SNARC effect was found in all groups and in both hand postures of the number comparison task, deaf adults did not show the SNARC effect in both hand postures of the parity judgment task. These results are discussed in light of the spatial component characterizing the counting system used in sign language.

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.

How visual is the « number sense »? Insights from the blind

Is vision a necessary building block for the foundations of mathematical cognition? A straightforward model to test the causal role visual experience plays in the development of numerical abilities is to study people born without sight. In this review we will demonstrate that congenitally blind people can develop numerical abilities that equal or even surpass those of sighted individuals, despite representing numbers using a qualitatively different representational format. We will also show that numerical thinking in blind people maps onto regions typically involved in visuo-spatial processing in the sighted, highlighting how intrinsic computational biases may constrain the reorganization of numerical networks in case of early visual deprivation. More generally, we will illustrate how the study of arithmetic abilities in congenitally blind people represents a compelling model to understand how sensory experience scaffolds the development of higher-level cognitive representations.

A biological foundation for spatial-numerical associations: the brain's asymmetric frequency tuning

"Left" and "right" coordinates control our spatial behavior and even influence abstract thoughts. For number concepts, horizontal spatial-numerical associations (SNAs) have been widely documented: we associate few with left and many with right. Importantly, increments are universally coded on the right side even in preverbal humans and nonhuman animals, thus questioning the fundamental role of directional cultural habits, such as reading or finger counting. Here, we propose a biological, nonnumerical mechanism for the origin of SNAs on the basis of asymmetric tuning of animal brains for different spatial frequencies (SFs). The resulting selective visual processing predicts both universal SNAs and their context-dependence. We support our proposal by analyzing the stimuli used to document SNAs in newborns for their SF content. As predicted, the SFs contained in visual patterns with few versus many elements preferentially engage right versus left brain hemispheres, respectively, thus predicting left-versus rightward behavioral biases. Our "brain's asymmetric frequency tuning" hypothesis explains the perceptual origin of horizontal SNAs for nonsymbolic visual numerosities and might be extensible to the auditory domain.

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.

The spatial representation of number, time, and serial order following sensory deprivation: A systematic review

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

Embodied Interaction Priority: Other's Body Part Affects Numeral-Space Mappings

Traditionally, the spatial-numerical association of response codes (SNARC) effect was presented in two-choice condition, in which only one individual reacted to both even (small) and odd (large) numbers. Few studies explored SNARC effect in a social situation. Moreover, there are many reference frames involved in SNARC effect, and it has not yet been investigated which reference frame is dominated when two participants perform the go-nogo task together. In the present study, we investigated which reference frame plays a primary role in SNARC effect when allocentric and egocentric reference frames were consistent or inconsistent in social settings. Furthermore, we explored how two actors corepresent number-space mapping interactively. Results of the two experiments demonstrated that egocentric reference frame was at work primarily when two reference frames were consistent and inconsistent. This shows that body-centered coordinate frames influence number-space mapping in social settings, and one actor may represent another actor's action and tasks.

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.

Blind readers break mirror invariance as sighted do

Mirror invariance refers to a predisposition of humans, including infants and animals, which urge them to consider mirrored images as corresponding to the same object. Yet in order to learn to read a written system that incorporates mirrored letters (e.g., <b> vs. <d> in the Latin alphabet), humans learn to break this perceptual bias. Here we examined the role visual experience and input modality play in the emergence of this bias. To this end, we tested congenital blind (CB) participants in two same-different tactile comparison tasks including pairs of mirrored and non-mirrored Braille letters as well as embossed unfamiliar geometric shapes and Latin letters, and compared their results to those of age-matched sighted participants involved in similar but visually-presented tasks. Sighted participants showed a classical pattern of results for their material of expertise, Latin letters. CB's results signed for their expertise with the Braille script compared to the other two materials that they processed according to an internal frame of reference. They also evidenced that they automatically break mirror invariance for different materials explored through the tactile modality, including Braille letters. Altogether, these results demonstrate that learning to read Braille through the tactile modality allows breaking mirror invariance in a comparable way to what is observed in sighted individuals for the mirrored letters of the Latin alphabet.

Visual Experience Shapes the Neural Networks Remapping Touch into External Space

Localizing touch relies on the activation of skin-based and externally defined spatial frames of reference. Psychophysical studies have demonstrated that early visual deprivation prevents the automatic remapping of touch into external space. We used fMRI to characterize how visual experience impacts the brain circuits dedicated to the spatial processing of touch. Sighted and congenitally blind humans performed a tactile temporal order judgment (TOJ) task, either with the hands uncrossed or crossed over the body midline. Behavioral data confirmed that crossing the hands has a detrimental effect on TOJ judgments in sighted but not in early blind people. Crucially, the crossed hand posture elicited enhanced activity, when compared with the uncrossed posture, in a frontoparietal network in the sighted group only. Psychophysiological interaction analysis revealed, however, that the congenitally blind showed enhanced functional connectivity between parietal and frontal regions in the crossed versus uncrossed hand postures. Our results demonstrate that visual experience scaffolds the neural implementation of the location of touch in space.SIGNIFICANCE STATEMENT In daily life, we seamlessly localize touch in external space for action planning toward a stimulus making contact with the body. For efficient sensorimotor integration, the brain has therefore to compute the current position of our limbs in the external world. In the present study, we demonstrate that early visual deprivation alters the brain activity in a dorsal parietofrontal network typically supporting touch localization in the sighted. Our results therefore conclusively demonstrate the intrinsic role that developmental vision plays in scaffolding the neural implementation of touch perception.

An Embodiment Perspective on Number-Space Mapping in 3.5-Year-Old Dutch Children

Previous research suggests that block adding, subtracting and counting direction are early forms of number–space mapping. In this study, an embodiment perspective on these skills was taken. Embodiment theory assumes that cognition emerges through sensory–motor interaction with the environment. In line with this assumption, it was investigated if counting and adding/subtracting direction in young children is related to the hand they use during task performance. Forty‐eight 3.5‐year‐old children completed a block adding, subtracting and counting task. They had to add and remove a block from a row of three blocks and count a row of five blocks. Adding, subtracting and counting direction were related to the hand the children used for task performance. Most children who used their right hand added, removed and started counting the blocks at the right side of the row. Most children who used their left hand added, removed and started counting the blocks at the left side of the row. It can be concluded that number–space mapping, as measured by direction of adding, subtracting and counting blocks, in young children is embodied: It is not fixed, but is related to the situation. © 2016 The Authors Infant and Child Development Published by John Wiley & Sons, Ltd.

How visual experience impacts the internal and external spatial mapping of sensorimotor functions

Tactile perception and motor production share the use of internally- and externally-defined coordinates. In order to examine how visual experience affects the internal/external coding of space for touch and movement, early blind (EB) and sighted controls (SC) took part in two experiments. In experiment 1, participants were required to perform a Temporal Order Judgment task (TOJ), either with their hands in parallel or crossed over the body midline. Confirming previous demonstration, crossing the hands led to a significant decrement in performance in SC but did not affect EB. In experiment 2, participants were trained to perform a sequence of five-finger movements. They were tested on their ability to produce, with the same hand but with the keypad turned upside down, the learned (internal) or the mirror (external) sequence. We observed significant transfer of motor sequence knowledge in both EB and SC irrespective of whether the representation of the sequence was internal or external. Together, these results demonstrate that visual experience differentially impacts the automatic weight attributed to internal versus external coordinates depending on task-specific spatial requirements.

Early but not late blindness leads to enhanced arithmetic and working memory abilities

Behavioural and neurophysiological evidence suggest that vision plays an important role in the emergence and development of arithmetic abilities. However, how visual deprivation impacts on the development of arithmetic processing remains poorly understood. We compared the performances of early (EB), late blind (LB) and sighted control (SC) individuals during various arithmetic tasks involving addition, subtraction and multiplication of various complexities. We also assessed working memory (WM) performances to determine if they relate to a blind person's arithmetic capacities. Results showed that EB participants performed better than LB and SC in arithmetic tasks, especially in conditions in which verbal routines and WM abilities are needed. Moreover, EB participants also showed higher WM abilities. Together, our findings demonstrate that the absence of developmental vision does not prevent the development of refined arithmetic skills and can even trigger the refinement of these abilities in specific tasks.

Rationale and design of a randomized controlled trial examining the effect of classroom-based physical activity on math achievement

Background

Integration of physical activity (PA) into the classroom may be an effective way of promoting the learning and academic achievement of children at elementary school. This paper describes the research design and methodology of an intervention study examining the effect of classroom-based PA on mathematical achievement, creativity, executive function, body mass index and aerobic fitness.

Methods

The study was designed as a school-based cluster-randomized controlled trial targeting schoolchildren in 1st grade, and was carried out between August 2012 and June 2013. Eligible schools in two municipalities in the Region of Southern Denmark were invited to participate in the study. After stratification by municipality, twelve schools were randomized to either an intervention group or a control group, comprising a total of 505 children with mean age 7.2 ± 0.3 years. The intervention was a 9-month classroom-based PA program that involved integration of PA into the math lessons delivered by the schools’ math teachers. The primary study outcome was change in math achievement, measured by a 45-minute standardized math test. Secondary outcomes were change in executive function (using a modified Eriksen flanker task and the Behavior Rating Inventory of Executive Function (BRIEF) questionnaire filled out by the parents), creativity (using the Torrance Tests of Creative Thinking, TTCT), aerobic fitness (by the Andersen intermittent shuttle-run test) and body mass index. PA during math lessons and total PA (including time spent outside school) were assessed using accelerometry. Math teachers used Short Message Service (SMS)-tracking to report on compliance with the PA intervention and on their motivation for implementing PA in math lessons. Parents used SMS-tracking to register their children’s PA behavior in leisure time.

Discussion

The results of this randomized controlled trial are expected to provide schools and policy-makers with significant new insights into the potential of classroom-based PA to improve cognition and academic achievement in children.

Trial registration

Clinicaltrials.gov: NCT02488460 (06/29/2015)

Spatial and numerical processing in children with non-verbal learning disabilities

Consistently with the idea that numbers and space interact with each other, the present paper aimed to investigate the impact of non-verbal learning disabilities (NVLD) on spatial and numerical processing. In order to do so, 15 NVLD and 15 control children were required to perform different spatial (the line bisection and Simon tasks) and numerical tasks (the number bisection, number-to-position and numerical comparison tasks). In every task, NVLD children presented lower accuracy scores than the control group. While both groups manifested similar pseudo-neglect and Simon effects, they however differed in the numerical comparison task: while control children presented the standard SNARC effect in the uncrossed and crossed postures, no SNARC effect was observed in the NVLD group. Our results therefore suggest that NVLD affects the accuracy and the nature of the mental number line by decreasing its precision and the saliency of its left-to-right orientation.

Constructing mental time without visual experience

Across many cultures, people create spatial representations of time. The direction of mental timelines often follows the direction of writing in a person's language. A new study demonstrates that blind participants (who read with their hands) also show mental timelines that follow reading direction.

The effect of hand movements on numerical bisection judgments in early blind and sighted individuals

Recent evidence suggests that in representing numbers blind individuals might be affected differently by proprioceptive cues (e.g., hand positions, head turns) than are sighted individuals. In this study, we asked a group of early blind and sighted individuals to perform a numerical bisection task while executing hand movements in left or right peripersonal space and with either hand. We found that in bisecting ascending numerical intervals, the hemi-space in which the hand was moved (but not the moved hand itself) influenced the bisection bias similarly in both early blind and sighted participants. However, when numerical intervals were presented in descending order, the moved hand (and not the hemi-space in which it was moved) affected the bisection bias in all participants. Overall, our data show that the operation to be performed on the mental number line affects the activated spatial reference frame, regardless of participants' previous visual experience. In particular, both sighted and early blind individuals' representation of numerical magnitude is mainly rooted in world-centered coordinates when numerical information is given in canonical orientation (i.e., from small to large), whereas hand-centered coordinates become more relevant when the scanning of the mental number line proceeds in non-canonical direction.

Development of Spatial-Numerical Associations

Links between spatial and numerical thinking are well established in studies of adult cognition. Here, we review recent research on the origins and development of these links, with an emphasis on the formative role of experience in typical development and on the theoretical insights to be gained from infant cognition. This research points to three important influences on the development of spatial-numerical associations: innate mechanisms linking space and nonsymbolic number, gross and fine motor activity that couples spatial location to both symbolic and nonsymbolic number, and culturally bound activities (e.g., reading, writing, and counting) that shape the relationship between spatial direction and symbolic number.

Neural substrates of numerosity estimation in autism

Visual skills, including numerosity estimation are reported to be superior in autism spectrum disorders (ASD). This phenomenon is attributed to individuals with ASD processing local features, rather than the Gestalt. We examined the neural correlates of numerosity estimation in adults with and without ASD, to disentangle perceptual atypicalities from numerosity processing. Fourteen adults with ASD and matched typically developed (TD) controls estimated the number of dots (80-150) arranged either randomly (local information) or in meaningful patterns (global information) while brain activity was recorded with magnetoencephalography (MEG). Behavioral results showed no significant group difference in the errors of estimation. However, numerical estimation in ASD was more variable across numerosities than TD and was not affected by the global arrangement of the dots. At 80-120 ms, MEG analyses revealed early significant differences (TD > ASD) in source amplitudes in visual areas, followed from 120 to 400 ms by group differences in temporal, and then parietal regions. After 400 ms, a source was found in the superior frontal gyrus in TD only. Activation in temporal areas was differently sensitive to the global arrangement of dots in TD and ASD. MEG data show that individuals with autism exhibit widespread functional abnormalities. Differences in temporal regions could be linked to atypical global perception. Occipital followed by parietal and frontal differences might be driven by abnormalities in the processing and conversion of visual input into a number-selective neural code and complex cognitive decisional stages. These results suggest overlapping atypicalities in sensory, perceptual and number-related processing during numerosity estimation in ASD.

Spatial Associations in Numerical Cognition—From Single Digits to Arithmetic

The literature on spatial associations during number processing is dominated by the SNARC (spatial–numerical association of response codes) effect. We describe spatial biases found for single digits and pairs of numbers, first in the “original” speeded parity task and then extending the scope to encompass different tasks, a range of measures, and various populations. Then we review theoretical accounts before surveying the emerging evidence for similar spatial associations during mental arithmetic. We conclude that the mental number line hypothesis and an embodied approach are useful frameworks for further studies.

Massive somatic deafferentation and motor deefferentation of the lower part of the body impair its visual recognition: a psychophysical study of patients with spinal cord injury

Embodied cognition theories postulate that perceiving and understanding the body states of other individuals are underpinned by the neural structures activated during first-hand experience of the same states. This suggests that one's own sensorimotor system may be used to identify the actions and sensations of others. Virtual and real brain lesion studies show that visual processing of body action and body form relies upon neural activity in the ventral premotor and the extrastriate body areas, respectively. We explored whether visual body perception may also be altered in the absence of damage to the above cortical regions by testing healthy controls and spinal cord injury (SCI) patients whose brain was unable to receive somatic information from and send motor commands to the lower limbs. Participants performed tasks investigating the ability to visually discriminate changes in the form or action of body parts affected by somatosensory and motor disconnection. SCI patients showed a specific, cross-modal deficit in the visual recognition of the disconnected lower body parts. This deficit affected both body action and body form perception, hinting at a pervasive influence of ongoing body signals on the brain network dedicated to visual body processing. Testing SCI patients who did or did not practise sports allowed us to test the influence of motor practice on visual body recognition. We found better upper body action recognition in sport-practising SCI patients, indicating that motor practice is useful for maintaining visual representation of actions after deafferentation and deefferentation. This may be a potential resource to be exploited for rehabilitation.