Nature or nurture in finger counting: a review on the determinants of the direction of number-finger mapping

Influences of hand action on the processing of symbolic numbers: A special role of pointing?

Embodied and grounded cognition theories state that cognitive processing is built upon sensorimotor systems. In the context of numerical cognition, support to this framework comes from the interactions between numerical processing and the hand actions of reaching and grasping documented in skilled adults. Accordingly, mechanisms for the processing of object size and location during reach and grasp actions might scaffold the development of mental representations of numerical magnitude. The present study exploited motor adaptation to test the hypothesis of a functional overlap between neurocognitive mechanisms of hand action and numerical processing. Participants performed repetitive grasping of an object, repetitive pointing, repetitive tapping, or passive viewing. Subsequently, they performed a symbolic number comparison task. Importantly, hand action and number comparison were functionally and temporally dissociated, thereby minimizing context-based effects. Results showed that executing the action of pointing slowed down the responses in number comparison. Moreover, the typical distance effect (faster responses for numbers far from the reference as compared to close ones) was not observed for small numbers after pointing, while it was enhanced by grasping. These findings confirm the functional link between hand action and numerical processing, and suggest new hypotheses on the role of pointing as a meaningful gesture in the development and embodiment of numerical skills.

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

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

Effect of Mental Calculation and Number Comparison on a Manual-Pointing Movement

The present study aimed at examining the effect of mental calculation and number comparison on motor performance measured as the movement time of a fast manual-pointing movement. Three experiments, involving a total number of 65 undergraduate subjects, examined the effect of mental subtraction (complex) and, respectively, of (a) mental addition (simple or complex), (b) mental multiplication (simple or complex), and (c) the comparison of dot sets and number comparison. Each number was written in Arabic. The movement times were analyzed by using a multilevel linear mixed-effect model. The results showed significant improvement of manual-pointing movement performance only after the complex calculations and after number comparison. Possible implication of attentional mechanisms specific to this arithmetical activity is further discussed.

Processing of numerical representation of fingers depends on their location in space

Fingers can express quantities and thus contribute to the acquisition and manipulation of numbers as well as the development of arithmetical skills. As embodied entities, the processing of finger numerical configurations should, therefore, be facilitated when they match shared cultural representations and are presented close to the body. To investigate these issues, the present study investigated whether canonical finger configurations are processed faster than noncanonical configurations or spatially matched dot configurations, taking into account their location in the peripersonal or the extrapersonal space. Analysis of verbal responses to the enumeration of small and large numerosities showed that participants (N = 30) processed small numerosities faster than large ones and dots faster than finger configurations despite visuo-spatial matching. Canonical configurations were also processed faster than noncanonical configurations but for finger numerical stimuli only. Furthermore, the difference in response time between dots and fingers processing was greater when the stimuli were located in the peripersonal space than in the extrapersonal space. As a whole, the data suggest that, due to their motor nature, finger numerical configurations are not processed as simple visual stimuli but in relation to corporal and cultural counting habits, in agreement with the embodied framework of numerical cognition.

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.

A large-scale survey on finger counting routines, their temporal stability and flexibility in educated adults

A strong link between bodily activity and number processing has been established in recent years. Although numerous observations indicate that adults use finger counting (FC) in various contexts of everyday life for different purposes, existing knowledge of FC routines and their use is still limited. In particular, it remains unknown how stable the (default) FC habits are over time and how flexible they can be. To investigate these questions, 380 Polish participants completed a questionnaire on their FC routines, the stability of these routines, and the context of FC usage, preceded by the request to count on their fingers from 1 to 10. Next, the test-retest stability of FC habits was examined in 84 participants 2 months following the first session. To the best of our knowledge, such a study design has been adopted for the first time. The results indicate that default FC routines of the majority of participants (75%) are relatively stable over time. At the same time, FC routines can flexibly adapt according to the situation (e.g., when holding an object). As regards prevalence, almost all participants, in line with previous findings on Western individuals, declared starting from the closed palm and extending consecutive fingers. Furthermore, we observed relations between FC preferences and handedness (more left-handers start from the left hand) and that actual finger use is still widespread in healthy adults for a variety of activities (the most prevalent uses of FC are listing elements, presenting arguments and plans, and calendar calculations). In sum, the results show the practical relevance of FC in adulthood, the relative stability of preferences over time along with flexible adaptation to a current situation, as well as an association of FC routines with handedness. Taken together our results suggest that FC is the phenomenon, which is moderated or mediated by multiple embodied factors.

The SNARC Effect in Chinese Numerals: Do Visual Properties of Characters and Hand Signs Influence Number Processing?

The SNARC effect refers to an association of numbers and spatial properties of responses that is commonly thought to be amodal and independent of stimulus notation. We tested for a horizontal SNARC effect using Arabic digits, simple-form Chinese characters and Chinese hand signs in participants from Mainland China. We found a horizontal SNARC effect in all notations. This is the first time that a horizontal SNARC effect has been demonstrated in Chinese characters and Chinese hand signs. We tested for the SNARC effect in two experiments (parity judgement and magnitude judgement). The parity judgement task yielded clear, consistent SNARC effects in all notations, whereas results were more mixed in magnitude judgement. Both Chinese characters and Chinese hand signs are represented non-symbolically for low numbers and symbolically for higher numbers, allowing us to contrast within the same notation the effects of heavily learned non-symbolic vs. symbolic representation on the processing of numbers. In addition to finding a horizontal SNARC effect, we also found a robust numerical distance effect in all notations. This is particularly interesting as it persisted when participants reported using purely visual features to solve the task, thereby suggesting that numbers were processed semantically even when the task could be solved without the semantic information.

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.

Numerical Magnitude Representation in Children With Mathematical Difficulties With or Without Reading Difficulties

This study aimed to explore the spatial numerical association of response codes (SNARC), the flanker, and the numerical distance effects in children with mathematical difficulties. From a sample of 720 third, fourth, and fifth graders, 60 children were selected and divided into the following three groups: typically developing children (TD; n = 29), children with mathematical difficulties only (MD only; n = 21), and children with mathematical and reading difficulties (MD+RD; n = 10). Children were tested with a numerical Eriksen task that was built to assess SNARC, numerical distance, and flanker (first and second order congruency) effects. Children with MD only showed stronger SNARC and second order congruency effects than did TD children, whereas the numerical distance effects were similar across the three groups. Finally, the first order congruency effect was associated with reading difficulties. These results showed that children with mathematical difficulties with or without reading difficulties were globally more impaired when spatial incompatibilities were presented.

Finger counting habit and spatial-numerical association in children and adults

Sensory-motor experiences are known to build up concrete and abstract concepts during the lifespan. The present study aimed to test how finger counting habits (right-hand vs. left-hand starters) could influence the spatial-numerical representation in number-to-position (explicit) and digit-string bisection (implicit) tasks. The subjects were Italian primary school children (N=184, from the first to the fifth year) and adults (N=42). No general preference for right- or left-starting in the finger counting was found. In the explicit task, right- or left-starting did not affect performance. In the implicit task, the right-hand starters shifted from the left to the right space when bisecting small and large numbers respectively, while the left-hand starters shifted from the right to the left space with higher leftward bias for large numbers. The finger configuration in Italian children and adults influences the spatial-numerical representation, but only when implicit number processing is required by the task.

What Is the Role of Manual Preference in Hand-Digit Mapping During Finger Counting? A Study in a Large Sample of Right- and Left-Handers

The goal of the present study was to test whether there is a relationship between manual preference and hand-digit mapping in 369 French adults with similar numbers of right- and left-handers. Manual laterality was evaluated with the finger tapping test to evaluate hand motor asymmetry, and the Edinburgh handedness inventory was used to assess manual preference strength (MPS) and direction. Participants were asked to spontaneously "count on their fingers from 1 to 10" without indications concerning the hand(s) to be used. The results indicated that both MPS and hand motor asymmetry affect the hand-starting preference for counting. Left-handers with a strong left-hand preference (sLH) or left-hand motor asymmetry largely started to count with their left hand (left-starter), while right-handers with a strong right-hand preference (sRH) or right-hand motor asymmetry largely started to count with their right hand (right-starter). Notably, individuals with weak MPS did not show a hand-starting preference. These findings demonstrated that manual laterality contributes to finger counting directionality. Lastly, the results showed a higher proportion of sLH left-starter individuals compared with sRH right-starters, indicating an asymmetric bias of MPS on hand-starting preference. We hypothesize that the higher proportion of sLH left-starters could be explained by the congruence between left-to-right hand-digit mapping and left-to-right mental number line representation that has been largely reported in the literature. Taken together, these results indicate that finger-counting habits integrate biological and cultural information.

Finger Counting and (2D:4D) Digit Ratio in Spatial-Numerical Association

It is reported that a canonical and cultural finger counting habit influences the spatial-numerical association. The digit ratio (the ratio between the lengths of the index and ring fingers as a putative indicator of prenatal androgen exposure) also plays an effect on space-number representation, reflecting a stronger left-to-right number representation in people with a short index finger and longer ring finger (i.e., 2D:4D ratio). It is unknown whether the finger counting habit and digit ratio have an effect on spatial-numerical association independently from each other or whether they interact with each other. In Study 1, the digit ratio and finger counting mapping were recorded in right handers. The participants performed number-to-position, digit string bisection, and physical line bisection tasks. In the number-to-position task, a finger counting effect was found, as well as a significant interaction between factors. A digit ratio effect was observed in the digit string bisection task. In Study 2, digit ratio and finger counting mapping were recorded in right and left handers. The results showed that the finger counting habit influenced the spatial biases in both numerical tasks. A significant interaction between finger counting and digit ratio was found in both numerical tasks when only the left hand was considered. The results are discussed considering the embodied nature of the spatial-numerical association.

Mental representations of magnitude and order: a dissociation by sensorimotor learning

Numbers and spatially directed actions share cognitive representations. This assertion is derived from studies that have demonstrated that the processing of small- and large-magnitude numbers facilitates motor behaviors that are directed to the left and right, respectively. However, little is known about the role of sensorimotor learning for such number-action associations. In this study, we show that sensorimotor learning in a serial reaction-time task can modify the associations between number magnitudes and spatially directed movements. Experiments 1 and 3 revealed that this effect is present only for the learned sequence and does not transfer to a novel unpracticed sequence. Experiments 2 and 4 showed that the modification of stimulus-action associations by sensorimotor learning does not occur for other sets of ordered stimuli such as letters of the alphabet. These results strongly suggest that numbers and actions share a common magnitude representation that differs from the common order representation shared by letters and spatially directed actions. Only the magnitude representation, but not the order representation, can be modified episodically by sensorimotor learning.

Considering digits in a current model of numerical development

Numerical cognition has long been considered the perfect example of abstract information processing. Nevertheless, there is accumulating evidence in recent years suggesting that the representation of number magnitude may not be entirely abstract but may present a specific case of embodied cognition rooted in the sensory and bodily experiences of early finger counting and calculating. However, so far none of the existing models of numerical development considers the influence of finger-based representations. Therefore, we make first suggestions on (i) how finger-based representations may be integrated into a current model of numerical development; and (ii) how they might corroborate the acquisition of basic numerical competencies at different development levels.

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.

Further evidence for a spatial-numerical association in children before formal schooling

Given the robust finding that number and space are associated systematically at least in school children and adults, it has been concluded that this association might be based on the frequent practice of reading or writing skills, which are usually consolidated by formal schooling. However, first studies contradict this assumption demonstrating that associations of "small" magnitudes with left space and of "large" magnitudes with right space exist already in preschoolers. The present study used a non-symbolic magnitude comparison task to examine whether kindergartners who have not yet been formally instructed in reading and writing show a SNARC effect, that is, whether they would respond more rapidly with the right hand to larger numbers and with the left hand to smaller numbers. This assumption was confirmed by the data. In view of further evidence for an association between number and space that evolves before children are proficient in reading and writing, the role of potential alternative culture-specific, individual, and universal foundations of this association is emphasized and discussed.

Development of spatial preferences for counting and picture naming

The direction of object enumeration reflects children's enculturation but previous work on the development of such spatial preferences has been inconsistent. Therefore, we documented directional preferences in finger counting, object counting, and picture naming for children (4 groups from 3 to 6 years, N = 104) and adults (N = 56). We found a right-side preference for finger counting in 3- to 6-year-olds and a left-side preference for counting objects and naming pictures by 6 years of age. Children were consistent in their special preferences when comparing object counting and picture naming, but not in other task pairings. Finally, spatial preferences were not related to cardinality comprehension. These results, together with other recent work, suggest a gradual development of spatial-numerical associations from early non-directional mappings into culturally constrained directional mappings.

Tactile enumeration of small quantities using one hand

Our study explores various aspects of enumerating small quantities in the tactile modality. Fingertips of one hand were stimulated by a vibro-tactile apparatus (for 100/800 ms). Between 1 and 5 stimuli were presented to the right or the left hand and applied to neighboring (e.g., thumb-index-middle) or non-neighboring (e.g., thumb-middle-pinkie) fingers. The results showed a moderate increase in RT up to 4 stimuli and then a decrease for 5 stimuli. Right hand stimulation evoked more accurate performance than left hand stimulation only under short exposures (100 ms). Importantly, when the stimuli were presented to neighboring fingers, the accuracy rate was higher and the RT was faster than when presented to non-neighboring fingers. We discuss the results and suggest that when the stimuli are presented to one hand the subitizing range is 4 rather than 3. Furthermore, the right hand advantage and the efficiency for neighboring fingers are further support for the association between number and spatial arrangement of the fingers.

Making fingers and words count in a cognitive robot

Evidence from developmental as well as neuroscientific studies suggest that finger counting activity plays an important role in the acquisition of numerical skills in children. It has been claimed that this skill helps in building motor-based representations of number that continue to influence number processing well into adulthood, facilitating the emergence of number concepts from sensorimotor experience through a bottom-up process. The act of counting also involves the acquisition and use of a verbal number system of which number words are the basic building blocks. Using a Cognitive Developmental Robotics paradigm we present results of a modeling experiment on whether finger counting and the association of number words (or tags) to fingers, could serve to bootstrap the representation of number in a cognitive robot, enabling it to perform basic numerical operations such as addition. The cognitive architecture of the robot is based on artificial neural networks, which enable the robot to learn both sensorimotor skills (finger counting) and linguistic skills (using number words). The results obtained in our experiments show that learning the number words in sequence along with finger configurations helps the fast building of the initial representation of number in the robot. Number knowledge, is instead, not as efficiently developed when number words are learned out of sequence without finger counting. Furthermore, the internal representations of the finger configurations themselves, developed by the robot as a result of the experiments, sustain the execution of basic arithmetic operations, something consistent with evidence coming from developmental research with children. The model and experiments demonstrate the importance of sensorimotor skill learning in robots for the acquisition of abstract knowledge such as numbers.

Aspects of situated cognition in embodied numerosity: the case of finger counting

Numerical cognitions such as spatial-numerical associations have been observed to be influenced by grounded, embodied and situated factors. For the case of finger counting, grounded and embodied influences have been reported. However, situated influences, e.g., that reported counting habits change with perception and action within a given situation, have not been systematically examined. To pursue the issue of situatedness of reported finger-counting habits, 458 participants were tested in three separate groups: (1) spontaneous condition: counting with both hands available, (2) perceptual condition: counting with horizontal (left-to-right) perceptual arrangement of fingers (3) perceptual and proprioceptive condition: counting with horizontal (left-to-right) perceptual arrangement of fingers and with busy dominant hand. Report of typical counting habits differed strongly between the three conditions. 28 % reported to start counting with the left hand in the spontaneous counting condition (1), 54 % in the perceptual condition (2) and 62 % in the perceptual and proprioceptive condition (3). Additionally, all participants in the spontaneous counting group showed a symmetry-based counting pattern (with the thumb as number 6), while in the two other groups, a considerable number of participants exhibited a spatially continuous counting pattern (with the pinkie as number 6). Taken together, the study shows that reported finger-counting habits depend on the perceptual and proprioceptive situation and thus are strongly influenced by situated cognition. We suggest that this account reconciles apparently contradictory previous findings of different counting preferences regarding the starting hand in different examination situations.

Fine-grained semantic categorization across the abstract and concrete domains

A consolidated approach to the study of the mental representation of word meanings has consisted in contrasting different domains of knowledge, broadly reflecting the abstract-concrete dichotomy. More fine-grained semantic distinctions have emerged in neuropsychological and cognitive neuroscience work, reflecting semantic category specificity, but almost exclusively within the concrete domain. Theoretical advances, particularly within the area of embodied cognition, have more recently put forward the idea that distributed neural representations tied to the kinds of experience maintained with the concepts' referents might distinguish conceptual meanings with a high degree of specificity, including those within the abstract domain. Here we report the results of two psycholinguistic rating studies incorporating such theoretical advances with two main objectives: first, to provide empirical evidence of fine-grained distinctions within both the abstract and the concrete semantic domains with respect to relevant psycholinguistic dimensions; second, to develop a carefully controlled linguistic stimulus set that may be used for auditory as well as visual neuroimaging studies focusing on the parametrization of the semantic space beyond the abstract-concrete dichotomy. Ninety-six participants rated a set of 210 sentences across pre-selected concrete (mouth, hand, or leg action-related) and abstract (mental state-, emotion-, mathematics-related) categories, with respect either to different semantic domain-related scales (rating study 1), or to concreteness, familiarity, and context availability (rating study 2). Inferential statistics and correspondence analyses highlighted distinguishing semantic and psycholinguistic traits for each of the pre-selected categories, indicating that a simple abstract-concrete dichotomy is not sufficient to account for the entire semantic variability within either domains.

Finding the spatial-numerical association of response codes (SNARC) in signed numbers: notational effects in accessing number representation

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