Visual experience influences the interactions between fingers and numbers

A cross-cultural comparison of finger-based and symbolic number representations

The current study examined predictions from embodied cognition for effects of finger counting on number processing. Although finger counting is spontaneous and nearly universal, counting habits reflect learning and culture. European cultures use a sub-base-five system, requiring a full hand plus additional fingers to express numbers exceeding 5. Chinese culture requires only one hand to express such numbers. We investigated the differential impact of early-acquired finger-based number representations on adult symbolic number processing. In total, 53 European and 56 Chinese adults performed two versions of the magnitude classification task, where numbers were presented either as Arabic symbols or as finger configurations consistent with respective cultural finger-counting habits. Participants classified numbers as smaller/larger than 5 with horizontally aligned buttons. Finger-based size and distance effects were larger in Chinese compared with Europeans. These differences did not, however, induce reliably different symbol processing signatures. This dissociation challenges the idea that sensory and motor habits shape our conceptual representations and implies notation-specific processing patterns.

Enhancing mathematics learning through finger-counting: A study investigating tactile strategies in 2 visually impaired cases

Finger-counting plays a crucial role in grounding and establishing mathematics, one of the most abstract domains of human cognition. While the combination of visual and proprioceptive information enables the coordination of finger movements, it was recently suggested that the emergence of finger-counting primarily relies on visual cues. In this study, we aimed to directly test this assumption by examining whether explicit finger-counting training (through tactile stimulation) may assist visually impaired children in overcoming their difficulties in learning mathematics. Two visually impaired participants (2 boys of 8.5 and 7.5 years) were therefore trained to use their fingers to calculate. Their pre- and post-training performance were compared to two control groups of sighted children who underwent either the same finger counting training (8 boys, 10 girls, Mage = 5.9 years; 10 kindergarteners and eight 1st graders) or another control vocabulary training (10 boys, 8 girls, Mage = 5.9 years; 11 kindergarteners and seven 1st graders). Results demonstrated that sighted children's arithmetic performance improved much more after the finger training than after the vocabulary training. Importantly, the positive impact of the finger training was also observed in both visually impaired participants (for addition and subtraction in one child; only for addition in the other child). These results are discussed in relation to the sensory compensation hypothesis and emphasize the importance of early and appropriate instruction of finger-based representations in both sighted and visually impaired children.

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.

Geometry intuitions without vision? A study in blind children and adults

Geometry intuitions seem to be rooted in a non-verbal system that humans possess since early age. However, the mechanisms underlying the comprehension of basic geometric concepts remain elusive. Some authors have suggested that the starting point of geometry development could be found in the visual perception of specific features in our environment, thus conferring to vision a foundational role in the acquisition of geometric skills. To examine this assumption, a test probing intuitive understanding of basic geometric concepts was presented to congenitally blind children and adults. Participants had to detect the intruder among four different shapes, from which three instantiated a specific geometrical concept and one (the intruder) violated it. Although they performed above the chance level, the blind presented poorer performance than the sighted participants who did the task in the visual modality (i.e., with the eyes open), but performed equally well than the sighted who did the task in the tactile modality (i.e., with a blindfold). We therefore provide evidence that geometric abilities are impacted by the lack of vision.

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 Finger-Based Numerical Training Failed to Improve Arithmetic Skills in Kindergarten Children Beyond Effects of an Active Non-numerical Control Training

It is widely accepted that finger and number representations are associated: many correlations (including longitudinal ones) between finger gnosis/counting and numerical/arithmetical abilities have been reported. However, such correlations do not necessarily imply causal influence of early finger-number training; even in longitudinal designs, mediating variables may be underlying such correlations. Therefore, we investigated whether there may be a causal relation by means of an extensive experimental intervention in which the impact of finger-number training on initial arithmetic skills was tested in kindergarteners to see whether they benefit from the intervention even before they start formal schooling. The experimental group received 50 training sessions altogether for 10 weeks on a daily basis. A control group received phonology training of a similar duration and intensity. All children improved in the arithmetic tasks. To our surprise and contrary to most accounts in the literature, the improvement shown by the experimental training group was not superior to that of the active control group. We discuss conceptual and methodological reasons why the finger-number training employed in this study did not increase the initial arithmetic skills beyond the unspecific effects of the control intervention.

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.

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.

Finger posing primes number comprehension

Canonical finger postures, as used in counting, activate number knowledge, but the exact mechanism for this priming effect is unclear. Here we dissociated effects of visual versus motor priming of number concepts. In Experiment 1, participants were exposed either to pictures of canonical finger postures (visual priming) or actively produced the same finger postures (motor priming) and then used foot responses to rapidly classify auditory numbers (targets) as smaller or larger than 5. Classification times revealed that manually adopted but not visually perceived postures primed magnitude classifications. Experiment 2 obtained motor priming of number processing through finger postures also with vocal responses. Priming only occurred through canonical and not through non-canonical finger postures. Together, these results provide clear evidence for motor priming of number knowledge. Relative contributions of vision and action for embodied numerical cognition and the importance of canonicity of postures are discussed.

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.

A helping hand putting in order: Visuomotor routines organize numerical and non-numerical sequences in space

Theories of embodied cognition emphasize the importance of sensorimotor schemas linked to external world experience for representing conceptual knowledge. Accordingly, some researchers have proposed that the spatial representation of numerical and non-numerical sequences relies on visuomotor routines, like reading habit and finger counting. There is a growing interest in how these two routines contribute to the spatial representation of ordinal sequences, although no investigation has so far directly compared them. The present study aims to investigate how these routines contribute to represent ordinal information in space. To address this issue, bilingual participants reading either from left-to-right or right-to-left were required to map ordinal information to all fingers of their right dominant hand. Critically, we manipulated both the direction of the mapping and the language of the verbal information. More specifically, a finger-mapping compatibility task was adopted in three experiments to explore the spatial representation of numerical (digit numbers and number words) and non-numerical (days of the week, presented in Hebrew and in English) sequences. Results showed that numerical information was preferentially mapped according to participants' finger counting habits, regardless of hand posture (prone and supine), number notation and reading habit. However, for non-numerical ordinal sequences, reading and finger counting directions both contributed to determine a preferential spatial mapping. These findings indicate that abstract knowledge representation relies on multiple over-trained visuomotor routines. More generally, these results highlight the capacity of our cognitive system to flexibly represent abstract ordered information, by relying on different directional experiences (finger counting, reading direction) depending on the stimuli and on the task at hand.

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.