Fingers as a tool for counting - naturally fixed or culturally flexible?

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.

Finger use mirroring young children's ways of experiencing numbers

Children who encounter questions about quantities or numbers are observed to use their fingers in different ways to aid their problem solving. This study aimed to contribute to the area of finger counting research with an inquiry of what children's finger use tells us about their knowledge of numbers. A basic argument is that it is not sufficient to observe the actual use of fingers; there is a need for interpretations of what the finger use means to the children, taking the children's perspective as the outset. This was done by analyzing 4- and 5-year-olds' finger use through the lens of phenomenography and variation theory of learning to describe the qualitatively different ways in which children use fingers as an expression of their ways of experiencing the meanings of numbers. Five categories of finger use that show a variety in the meanings the fingers represent emerged: Fingers represent individual items, quantities, countables, number relations, and number structure. The results show that children's finger use may give access to their ways of understanding numbers; some ways of using fingers indicate expressions of more or less advanced meanings of numbers. A conclusion from the results is that to develop number knowledge and skills, children are aided by learning to see and use their fingers as representing composed units. Some children need the structural support of fingers to solve number problems, and fingers should be used to explore number structures rather than used as countables.

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.

Creating ad hoc graphical representations of number

The ability to communicate about exact number is critical to many modern human practices spanning science, industry, and politics. Although some early numeral systems used 1-to-1 correspondence (e.g., 'IIII' to represent 4), most systems provide compact representations via more arbitrary conventions (e.g., '7' and 'VII'). When people are unable to rely on conventional numerals, however, what strategies do they initially use to communicate number? Across three experiments, participants used pictures to communicate about visual arrays of objects containing 1-16 items, either by producing freehand drawings or combining sets of visual tokens. We analyzed how the pictures they produced varied as a function of communicative need (Experiment 1), spatial regularities in the arrays (Experiment 2), and visual properties of tokens (Experiment 3). In Experiment 1, we found that participants often expressed number in the form of 1-to-1 representations, but sometimes also exploited the configuration of sets. In Experiment 2, this strategy of using configural cues was exaggerated when sets were especially large, and when the cues were predictably correlated with number. Finally, in Experiment 3, participants readily adopted salient numerical features of objects (e.g., four-leaf clover) and generally combined them in a cumulative-additive manner. Taken together, these findings corroborate historical evidence that humans exploit correlates of number in the external environment - such as shape, configural cues, or 1-to-1 correspondence - as the basis for innovating more abstract number representations.

Cultural similarities and specificities of finger counting and montring: Evidence from Amazon Tsimane' people

Numerical cognition might be embodied, that is, grounded in bodily actions. This claim is supported by the observation that, potentially due to our shared biology, finger counting is prevalent among a variety of cultures. Differences in finger counting are apparent even within Western cultures. Relatively few indigenous cultures have been systematically analyzed in terms of traditional finger counting and montring (i.e., communicating numbers with fingers) routines. Even fewer studies used the same protocols across cultures, allowing for a systematic comparison of indigenous and Western finger counting routines. We analyze the finger counting and montring routines of Tsimane' (N = 121), an indigenous people living in the Bolivian Amazon rainforest, depending on handedness, education level, and exposure to mainstream, industrialized Bolivian culture. Tsimane' routines are compared with those of German and British participants. Tsimane' reveal a greater variation in finger counting and montring routines, which seems to be modified by their education level. We outline a framework on how different factors such as handedness and reading direction might affect cross-cultural and within-cultural variation in finger counting.

Information Theory Opens New Dimensions in Experimental Studies of Animal Behaviour and Communication

Over the last 40–50 years, ethology has become increasingly quantitative and computational. However, when analysing animal behavioural sequences, researchers often need help finding an adequate model to assess certain characteristics of these sequences while using a relatively small number of parameters. In this review, I demonstrate that the information theory approaches based on Shannon entropy and Kolmogorov complexity can furnish effective tools to analyse and compare animal natural behaviours. In addition to a comparative analysis of stereotypic behavioural sequences, information theory can provide ideas for particular experiments on sophisticated animal communications. In particular, it has made it possible to discover the existence of a developed symbolic “language” in leader-scouting ant species based on the ability of these ants to transfer abstract information about remote events.

Finger-Counting and Numerical Structure

Number systems differ cross-culturally in characteristics like how high counting extends and which number is used as a productive base. Some of this variability can be linked to the way the hand is used in counting. The linkage shows that devices like the hand used as external representations of number have the potential to influence numerical structure and organization, as well as aspects of numerical language. These matters suggest that cross-cultural variability may be, at least in part, a matter of whether devices are used in counting, which ones are used, and how they are used.

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 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.

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.

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.

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.

Mangarevan invention of binary steps for easier calculation

When Leibniz demonstrated the advantages of the binary system for computations as early as 1703, he laid the foundation for computing machines. However, is a binary system also suitable for human cognition? One of two number systems traditionally used on Mangareva, a small island in French Polynesia, had three binary steps superposed onto a decimal structure. Here, we show how this system functions, how it facilitated arithmetic, and why it is unique. The Mangarevan invention of binary steps, centuries before their formal description by Leibniz, attests to the advancements possible in numeracy even in the absence of notation and thereby highlights the role of culture for the evolution of and diversity in numerical cognition.

Learning and development of embodied numerosity

Recent empirical evidence indicates that seemingly abstract numerical cognitions are rooted in sensory and bodily experiences. In particular in finger counting finger-based representations reflect a specific case of embodied cognition, we termed embodied numerosity. Furthermore, we suggest that finger-based representations should be considered a distinct representation of number (magnitude) and argue that this representation is activated automatically whenever we encounter a number. We discuss in what way such a theoretical framework can account for the associations of fingers and numbers observed so far. In the final part, we evaluate whether the concept of embodied numerosity should be generalized beyond finger-based representations with particular focus on whether bodily-sensory experiences (such as moving the whole body along the mental number line) may corroborate numerical capabilities. In a series of intervention studies, we consistently observed more pronounced training effects for our embodied numerosity trainings for different age groups, different digital media, different number ranges, and different control conditions. Taken together, we conclude that embodied representations of number (magnitude) exist, are not limited to finger-based representations, and influence number processing in a systematic and functional way that can be used to foster the efficiency of numerical trainings.

Cognition is … Fundamentally Cultural

A prevailing concept of cognition in psychology is inspired by the computer metaphor. Its focus on mental states that are generated and altered by information input, processing, storage and transmission invites a disregard for the cultural dimension of cognition, based on three (implicit) assumptions: cognition is internal, processing can be distinguished from content, and processing is independent of cultural background. Arguing against each of these assumptions, we point out how culture may affect cognitive processes in various ways, drawing on instances from numerical cognition, ethnobiological reasoning, and theory of mind. Given the pervasive cultural modulation of cognition—on all of Marr’s levels of description—we conclude that cognition is indeed fundamentally cultural, and that consideration of its cultural dimension is essential for a comprehensive understanding.

Multimodal semantic quantity representations: further evidence from korean sign language

Korean deaf signers performed a number comparison task on pairs of Arabic digits. In their response times profiles, the expected magnitude effect was systematically modified by properties of number signs in Korean sign language in a culture-specific way (not observed in hearing and deaf Germans or hearing Chinese). We conclude that finger-based quantity representations are automatically activated even in simple tasks with symbolic input although this may be irrelevant and even detrimental for task performance. These finger-based numerical representations are accessed in addition to another, more basic quantity system which is evidenced by the magnitude effect. In sum, these results are inconsistent with models assuming only one single amodal representation of numerical quantity.

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

The spontaneous use of finger counting has been for long recognized as critical to the acquisition of number skills. Recently, the great interest on space–number associations shifted attention to the practice of finger counting itself, and specifically, to its spatial components. Besides general cross-cultural differences in mapping numbers onto fingers, contrasting results have been reported with regard to the directional features of this mapping. The key issue we address is to what extent directionality is culturally mediated, i.e., linked to the conventional reading–writing system direction, and/or biologically determined, i.e., linked to hand dominance. Although the preferred starting-hand for counting seems to depend on the surveyed population, even within the same population high inter-individual variability minimizes the role of cultural factors. Even if so far largely overlooked, handedness represents a sound candidate for shaping finger counting direction. Here we discuss adults and developmental evidence in support of this view and we reconsider the plausibility of multiple and coexistent number–space mapping in physical and representational space.