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*Correspondence:

This article was submitted to Frontiers in Cognition, a specialty of Frontiers in Psychology.

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Representing numerosities with finger configurations offers children the opportunity to learn and internalize fundamental properties of natural numbers through sensory–motor interactions with the world. Recent findings show that even educated adults use their fingers as a visuo-motor support to process, represent, and communicate numerosities. Indeed, using fingers to represent numerosities prototypically has been shown to give the corresponding finger configurations a special status in long-term memory: these configurations are recognized and processed faster than other finger configurations, providing a direct access to number magnitude, what other finger configurations do less efficiently. This occurs for configurations stemming from finger counting (i.e., the way the fingers are raised to count for oneself; for example, thumb, index, and middle fingers for numerosity {

Children from many human cultures use finger-counting strategies to enumerate sets of objects and use their fingers when solving mathematical tasks. They “visually” represent numerosities by raising the same number of fingers as the number of items counted and, by doing this, they get a finger configuration preserving the cardinality of the set. Using finger counting is the first or second most frequent strategy observed in preschoolers during counting and arithmetical tasks (Fuson,

This influence of fingers on the acquisition of numbers and numerical concepts is also indicated by several historical and linguistic facts. Indeed, “handling” numerosities not only improved human mathematical competencies (Butterworth,

Besides these developmental and cultural pieces of evidence, recent findings in adults show that finger counting shapes number processing and calculation throughout life, and that finger numeral representations do not disappear when symbolic numerical representations develop. On the contrary, their critical impact is still observed in educated adults.

Firstly, finger-counting strategies influence the way numerical information is projected onto physical space and induces compatibility effects, at least at the level of motor outputs. For example, personal finger-counting habits were found to actively interact with Arabic digit processing during a number-to-finger mapping task. When asked to identify Arabic digits by pressing a key with 1 of their 10 fingers, participants produced faster responses when the mapping between the Arabic digits and the fingers matched their own finger-counting habits than with other mappings (Di Luca et al.,

Next, finger numeral representations exert their influence even when no motor outputs are required. For example, just like children (Noël,

Finally, finger numeral representations also have an impact on arithmetic. In a recent study (Badets et al.,

Given these findings in children and adults, finger numeral representations (whether they come from finger counting, finger montring, or other personal ways of using fingers to represent numerosities) certainly qualify as another type of numerical representation worthy of being considered by current cognitive number-processing architectures – perhaps as a fourth type of representation if they were to be integrated into Dehaene's (

We believe and argue that finger numeral representations are more than just another way of mentally representing numerosities. Firstly, they possess almost all the properties presented separately by the other representations (i.e., visual, verbal, and analog). Although they are optimal only for small numerosities and they are not linked to a written notation, they possess simultaneously iconic (i.e., features shared with the referent), symbolic (i.e., conventional meaning shared with other individuals), computational (i.e., used to support calculation procedures), and communicative (i.e., used to communicate numerosities through gestures with other individuals whatever their language) properties. Secondly, and most importantly, all these properties rely on perceptual and sensory–motor processes that provide a non-arbitrary link between the symbols (here, finger configurations) and reality (here, numerosity), and that can be spontaneously self-experienced by every human child and adult. In contrast, other representations only possess some of these properties and they cannot be inferred and acquired without external influence. Visual and verbal representations serve a communicative purpose because they are shared among individuals, but they possess no numerical meaning and very little can be inferred from them by the cognitive system as they stand for symbolic notations (respectively, verbal and Arabic numerals) composed of totally arbitrary symbols. For example, “6” and “six” can unambiguously be communicated and understood, but no numerical meaning can be inferred from either their physical traits, or their mental representation. An analog number line can easily represent continuous and large numerical quantities and their ratio, but it cannot easily serve the purpose of accurate communication. Moreover, except in very few people who explicitly develop a spatio-linear representation of numbers (Galton,

Recent findings show that finger numeral representations possess many characteristics of the other numerical representations postulated in classical cognitive number architectures. Among others, they, like other symbolic notations, are shared by individuals of the same cultural group, they can be used to communicate numerosities and to calculate, they possess iconic properties preserving cardinality, and place-coding properties. Most importantly, they have specific sensory–motor properties preserving numerical properties and allowing mathematical principles to be inferred and experienced. Thus, they are not just a way of mentally representing (in the sense of “standing for”) numerosities as other representations do; they represent and, at the same time, can help to build or, at least, improve the concept of number. We do not intend to claim that finger numeral representations replace all other representations, or that without finger-counting activities, human beings could not develop an accurate concept of number. But finger-counting/montring activities, especially if practiced at an early age, can contribute to a fast and deep understanding of number concepts, which has an impact during the entire cycle of life by providing the sensory–motor roots onto which the number concept grows.

Samuel Di Luca is a post-doctoral researcher and Mauro Pesenti a research associate at the National Fund for Scientific Research (Belgium).