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Finger representations are used to count or show quantities. How fingers are lifted to count and the type of representation that we use to communicate quantities have been the focus of studies that have aimed at providing evidence of dominant patterns across cultures. In the current study, we go beyond those studies and investigate intracultural variability. Specifically, whether finger counting habits and finger montring patterns are similar in children and adults. To this aim, a total of 3,210 Spaniard participants took part in this study (637 children and 2,573 adults). All of them were assessed regarding handedness, the way in which they counted with their fingers from 1 to 10 (finger counting) and how they show quantities with their fingers (finger montring). The results showed certain consistency; however, there was substantial variability within each group. Findings are interpreted within the context of current theories reinforcing the relevance of finger patterns to support the understanding of the meaning of numbers. [ABSTRACT FROM AUTHOR]

The article presents a novel approach to counting letters in spanish words or phrases using the fingers of the right hand. An algebraic model based on matrices represents the counting process, ensuring that each finger and letter are associated. It is demonstrated that the count is repeated once or five times, leaving no fingers or letters unassociated. Letter matrices are introduced as a representation associated with counting, forming a monoid structure. This study delves into the counting of letters and its relationship with matrices, with implications in linguistics, cryptography, and computer science. [ABSTRACT FROM AUTHOR]

Teachers' beliefs and attitudes are known to guide the type of activities they implement in their classrooms. A traditional conception that finger counting is merely a back-up when children fail to use more sophisticated and efficient strategies could therefore prevent teachers from encouraging children's use of fingers in arithmetic tasks. However, the potential benefit of finger counting for young learners has been recently documented and setting aside its practice within classrooms may hinder children's mathematical skill development. It is therefore important to establish whether there is a discrepancy between teacher's beliefs regarding finger counting and the latest discoveries in this field of research. To this aim, we interrogated 413 teachers from preschool to Grade 5. We found that, despite being generally positive towards finger counting, teachers think that finger counting is typical of children who present math difficulties or lack of confidence, even during the first years of learning. These results are discussed considering what is known and what remains to be determined in the current scientific literature.

Finger-based representation of numbers is a high-level cognitive strategy to assist numerical and arithmetic processing in children and adults. It is unclear whether this paradigm builds on simple perceptual features or comprises several attributes through embodiment. Here we describe the development and initial testing of an experimental setup to study embodiment during a finger-based numerical task using Virtual Reality (VR) and a low-cost tactile stimulator that is easy to build. Using VR allows us to create new ways to study finger-based numerical representation using a virtual hand that can be manipulated in ways our hand cannot, such as decoupling tactile and visual stimuli. The goal is to present a new methodology that can allow researchers to study embodiment through this new approach, maybe shedding new light on the cognitive strategy behind the finger-based representation of numbers. In this case, a critical methodological requirement is delivering precisely targeted sensory stimuli to specific effectors while simultaneously recording their behavior and engaging the participant in a simulated experience. We tested the device's capability by stimulating users in different experimental configurations. Results indicate that our device delivers reliable tactile stimulation to all fingers of a participant's hand without losing motion tracking quality during an ongoing task. This is reflected by an accuracy of over 95% in participants detecting stimulation of a single finger or multiple fingers in sequential stimulation as indicated by experiments with sixteen participants. We discuss possible application scenarios, explain how to apply our methodology to study the embodiment of finger-based numerical representations and other high-level cognitive functions, and discuss potential further developments of the device based on the data obtained in our testing. [ABSTRACT FROM AUTHOR]

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.

Finger-based representation of numbers is a high-level cognitive strategy to assist numerical and arithmetic processing in children and adults. It is unclear whether this paradigm builds on simple perceptual features or comprises several attributes through embodiment. Here we describe the development and initial testing of an experimental setup to study embodiment during a finger-based numerical task using Virtual Reality (VR) and a low-cost tactile stimulator that is easy to build. Using VR allows us to create new ways to study finger-based numerical representation using a virtual hand that can be manipulated in ways our hand cannot, such as decoupling tactile and visual stimuli. The goal is to present a new methodology that can allow researchers to study embodiment through this new approach, maybe shedding new light on the cognitive strategy behind the finger-based representation of numbers. In this case, a critical methodological requirement is delivering precisely targeted sensory stimuli to specific effectors while simultaneously recording their behavior and engaging the participant in a simulated experience. We tested the device’s capability by stimulating users in different experimental configurations. Results indicate that our device delivers reliable tactile stimulation to all fingers of a participant’s hand without losing motion tracking quality during an ongoing task. This is reflected by an accuracy of over 95% in participants detecting stimulation of a single finger or multiple fingers in sequential stimulation as indicated by experiments with sixteen participants. We discuss possible application scenarios, explain how to apply our methodology to study the embodiment of finger-based numerical representations and other high-level cognitive functions, and discuss potential further developments of the device based on the data obtained in our testing.

• This study tests a prediction of embodied cognition theory. • It asks whether childhood sensory-motor habits shape cognitive representations of number in adulthood. • A high-powered cross-cultural comparison between European and Chinese adults measures comprehension of two number notations: finger postures and Arabic symbols. • Clear differences were found for finger postures but these did not modulate number symbol processing. • Results are discussed in terms of notation-specific 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. [ABSTRACT FROM AUTHOR]

The Spatial-Numerical Association of Response Codes (SNARC) effect (i.e., faster left/right sided responses to small/large magnitude numbers, respectively) is considered to be strong evidence for the link between numbers and space. Studies have shown considerable variation in this effect. Among the factors determining individual differences in the SNARC effect is the hand an individual uses to start the finger counting sequence. Left-starters show a stronger and less variable SNARC effect than right-starters. This observation has been used as an argument for the embodied nature of the SNARC effect. For this to be the case, one must assume that the finger counting sequence (especially the starting hand) is stable over time. Subsequent studies challenged the view that the SNARC differs depending on the finger counting starting hand. At the same time, it has been pointed out that the temporal stability of the finger counting starting hand should not be taken for granted. Thus, in this preregistered study, we aimed to replicate the difference in the SNARC between left- and right-starters and explore the relationship between the self-reported temporal stability of the finger counting starting hand and the SNARC effect. In line with the embodied cognition account, left-starters who declare more temporarily stable finger counting habits should reveal a stronger SNARC effect. Results of the preregistered analysis did not show the difference between left- and right-starters. However, further exploratory analysis provided weak evidence that this might be the case. Lastly, we found no evidence for the relationship between finger counting starting hand stability and the SNARC effect. Overall, these results challenge the view on the embodied nature of the SNARC effect.

• Finger use in kindergarteners is associated with knowledge of the counting principles. • Still, some finger users do not know the counting principles, but perform badly in the addition task. • Knowledge of the counting principles does not naturally prompt finger use. • Finger use does not seem to have a specific role in the development of counting principles. It has been established that young children who use their fingers to solve arithmetic problems outperform those who do not. However, it remains unclear whether finger counting itself enhances arithmetic performance or if children with already advanced numerical abilities are more inclined to use this strategy. In the current study, to shed light on this matter, we observed the behavior of 189 4- and 5-year-old children in an addition task and a task assessing their knowledge of the three "how-to-count" principles (i.e., stable order, one-to-one correspondence, and cardinality principles). Of these children, 169 were reassessed 1 year later (the second testing point). At the first testing point, our results revealed that finger users better know the counting principles than non-finger users. Nevertheless, some children use their fingers without knowing the principles, but in this case they present low performance in the addition task. Moreover, we found that knowing the counting principles does not naturally prompt finger use. Finally, we did not find evidence supporting the idea that finger use has a specific role in the development of counting principles, which questions the idea that finger counting has a functional role in the construction of the number concept. All in all, our results tend to show that children need to know the counting principles to be efficient finger users. Therefore, finger counting seems to be a useful tool when used by children who already possess advanced numerical knowledge. [ABSTRACT FROM AUTHOR]

• Ninety-three 4-to-5-year-old Vietnamese children were included in this study. • They belonged to families with relatively high SES and presented high numerical skills. • They used both their fingers and manipulatives to solve arithmetic problems. • Their performance was not higher when they used their fingers than manipulatives. Recent empirical investigations have revealed that finger counting is a strategy associated with good arithmetic performance in young children. Fingers could have a special status during development because they operate as external support that provide sensory-motor and kinesthetic affordances in addition to visual input. However, it was unknown whether fingers are more helpful than manipulatives such as tokens during arithmetic problem solving. To address this question, we conducted a study with 93 Vietnamese children (48 girls) aged 4 and 5 years (mean = 58 months, range = 47–63) with high arithmetic and counting skills from families with relatively high socioeconomic status. Their behaviors were observed as they solved addition problems with manipulatives at their disposal. We found that children spontaneously used both manipulatives and fingers to solve the problems. Crucially, their performance was not higher when fingers rather than manipulatives were used (i.e., 70% vs. 81% correct answers, respectively). Therefore, at the beginning of learning, it is possible that, at least for children with high numerical skills, fingers are not the only gateway to efficient arithmetic development and manipulatives might also lead to proficient arithmetic. [ABSTRACT FROM AUTHOR]

Developmental dyscalculia (DD) is a developmental disorder characterized by arithmetic difficulties. Recently, it has been suggested that the neural networks supporting procedure-based calculation (e.g., in subtraction) and left-hemispheric verbal arithmetic fact retrieval (e.g., in multiplication) are partially distinct. Here we compared the neurofunctional correlates of subtraction and multiplication in a 19-year-old student (RM) with DD to 18 age-matched controls. Behaviorally, RM performed significantly worse than controls in multiplication, while subtraction was unaffected. Neurofunctional differences were most pronounced regarding multiplication: RM showed significantly stronger activation than controls not only in left angular gyrus but also in a fronto-parietal network (including left intraparietal sulcus and inferior frontal gyrus) typically activated during procedure-based calculation. Region-of-interest analyses indicated group differences in multiplication only, which, however, did not survive correction for multiple comparisons. Our results are consistent with dissociable and processing-specific, but not operation-specific neurofunctional networks. Procedure-based calculation is not only associated with subtraction but also with (untrained) multiplication facts. Only after rote learning, facts can be retrieved quasi automatically from memory. We suggest that this learning process and the associated shift in activation patterns has not fully occurred in RM, as reflected in her need to resort to procedure-based strategies to solve multiplication facts. [ABSTRACT FROM AUTHOR]

Most children use their fingers when learning to count and calculate. These sensorimotor experiences were argued to underlie reported behavioral associations of finger gnosis and counting with mathematical skills. On the neural level, associations were assumed to originate from overlapping neural representations of fingers and numbers. This study explored whether finger-based training in children would lead to specific neural activation in the sensorimotor cortex, associated with finger movements, as well as the parietal cortex, associated with number processing, during mental arithmetic. Following finger-based training during the first year of school, trained children showed finger-related arithmetic effects accompanied by activation in the sensorimotor cortex potentially associated with implicit finger movements. This indicates embodied finger-based numerical representations after training. Results for differences in neural activation between trained children and a control group in the IPS were less conclusive. This study provides the first evidence for training-induced sensorimotor plasticity in brain development potentially driven by the explicit use of fingers for initial arithmetic, supporting an embodied perspective on the representation of numbers. [ABSTRACT FROM AUTHOR]

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.

Recent evidence suggests that using finger-based strategies is beneficial for the acquisition of basic numerical skills. There are basically two finger-based strategies to be distinguished: (a) finger counting (i.e., extending single fingers successively) and (b) finger number gesturing (i.e., extending fingers simultaneously to represent magnitudes). In this study, we investigated both spontaneous and prompted finger counting and finger number gesturing as well as their contribution to basic numerical skills in 3- to 5-year-olds (N = 156). Results revealed that only 6% of children spontaneously used their fingers for counting when asked to name a specific number of animals, whereas 59% applied finger number gesturing to show their age. This indicates that the spontaneous use of finger-based strategies depends heavily on the specific context. Moreover, children performed significantly better in prompted finger counting than in finger number gesturing, suggesting that both strategies build on each other. Finally, both prompted finger counting and finger number gesturing significantly and individually predicted counting, cardinal number knowledge, and basic arithmetic. These results indicate that finger counting and finger number gesturing follow and positively relate to numerical development. [ABSTRACT FROM AUTHOR]

Previous research has established that finger counting in arithmetic positively correlates with accuracy in 5 ½ to 8-year-old children. Whether this relation also exists in younger children was unknown until the present study in which 172 children aged 4 ½ years (M = 56 months) were followed over one year across 3 sessions spaced 6 months apart. Initially, we observed 31 children who calculated on their fingers to solve addition problems, they were 43 at session 2 and 66 at session 3. Even though a minority of children used their fingers at each session, establishing their developmental pathways in the use of finger counting revealed that more than a half of them had used their fingers at least in one of the three sessions (87 children out of 172). Using this strategy proved highly advantageous because, at each session, finger users were more accurate than non-finger users, which reproduces the observations made in older children. Moreover, when children did not use their fingers, they were always more accurate if they had used their fingers in a previous session than if they had not. Children were also more likely to present accuracy improvement between two sessions when finger counting was observed for the first time or was repeatedly observed across sessions than when it had never been observed or was not observed in the prior session. Finally, children who never used their fingers across the three sessions corresponded to children with the lowest performance in addition and the lowest intellectual capacities. These results show that finger counting not only improves addition performance but also maximizes young children's chances to develop good addition skills. • Four-year-old children who use their fingers to solve additions outperform those who do not. • Children who never use their fingers until kindergarten have the worst addition performance. • Abandoning the finger strategy at this young age always leads to a decrease in performance. • Non-finger users have lower intellectual abilities than finger users. • Then, using finger counting between preschool and kindergarten is the strategy optimizing addition performance. [ABSTRACT FROM AUTHOR]

Numerical cognition is a fundamental component of human intelligence that has not been fully understood yet. Indeed, it is a subject of research in many disciplines, e.g., neuroscience, education, cognitive and developmental psychology, philosophy of mathematics, linguistics. In Artificial Intelligence, aspects of numerical cognition have been modelled through neural networks to replicate and analytically study children behaviours. However, artificial models need to incorporate realistic sensory-motor information from the body to fully mimic the children's learning behaviours, e.g., the use of fingers to learn and manipulate numbers. To this end, this article presents a database of images, focused on number representation with fingers using both human and robot hands, which can constitute the base for building new realistic models of numerical cognition in humanoid robots, enabling a grounded learning approach in developmental autonomous agents. The article provides a benchmark analysis of the datasets in the database that are used to train, validate, and test five state-of-the art deep neural networks, which are compared for classification accuracy together with an analysis of the computational requirements of each network. The discussion highlights the trade-off between speed and precision in the detection, which is required for realistic applications in robotics.

The study has two objectives: (1) to introduce grip force recording as a new technique for studying embodied numerical processing; and (2) to demonstrate how three competing accounts of numerical magnitude representation can be tested by using this new technique: the Mental Number Line (MNL), A Theory of Magnitude (ATOM) and Embodied Cognition (finger counting-based) account. While 26 healthy adults processed visually presented single digits in a go/no-go n-back paradigm, their passive holding forces for two small sensors were recorded in both hands. Spontaneous and unconscious grip force changes related to number magnitude occurred in the left hand already 100–140 ms after stimulus presentation and continued systematically. Our results support a two-step model of number processing where an initial stage is related to the automatic activation of all stimulus properties whereas a later stage consists of deeper conscious processing of the stimulus. This interpretation generalizes previous work with linguistic stimuli and elaborates the timeline of embodied cognition. We hope that the use of grip force recording will advance the field of numerical cognition research.

Developmental dyscalculia (DD) is a developmental disorder characterized by arithmetic difficulties. Recently, it has been suggested that the neural networks supporting procedure-based calculation (e.g., in subtraction) and left-hemispheric verbal arithmetic fact retrieval (e.g., in multiplication) are partially distinct. Here we compared the neurofunctional correlates of subtraction and multiplication in a 19-year-old student (RM) with DD to 18 age-matched controls. Behaviorally, RM performed significantly worse than controls in multiplication, while subtraction was unaffected. Neurofunctional differences were most pronounced regarding multiplication: RM showed significantly stronger activation than controls not only in left angular gyrus but also in a fronto-parietal network (including left intraparietal sulcus and inferior frontal gyrus) typically activated during procedure-based calculation. Region-of-interest analyses indicated group differences in multiplication only, which, however, did not survive correction for multiple comparisons. Our results are consistent with dissociable and processing-specific, but not operation-specific neurofunctional networks. Procedure-based calculation is not only associated with subtraction but also with (untrained) multiplication facts. Only after rote learning, facts can be retrieved quasi automatically from memory. We suggest that this learning process and the associated shift in activation patterns has not fully occurred in RM, as reflected in her need to resort to procedure-based strategies to solve multiplication facts.

Most children use their fingers when learning to count and calculate. These sensorimotor experiences were argued to underlie reported behavioral associations of finger gnosis and counting with mathematical skills. On the neural level, associations were assumed to originate from overlapping neural representations of fingers and numbers. This study explored whether finger-based training in children would lead to specific neural activation in the sensorimotor cortex, associated with finger movements, as well as the parietal cortex, associated with number processing, during mental arithmetic. Following finger-based training during the first year of school, trained children showed finger-related arithmetic effects accompanied by activation in the sensorimotor cortex potentially associated with implicit finger movements. This indicates embodied finger-based numerical representations after training. Results for differences in neural activation between trained children and a control group in the IPS were less conclusive. This study provides the first evidence for training-induced sensorimotor plasticity in brain development potentially driven by the explicit use of fingers for initial arithmetic, supporting an embodied perspective on the representation of numbers.

Numerical cognition is a fundamental component of human intelligence that has not been fully understood yet. Indeed, it is a subject of research in many disciplines, e.g., neuroscience, education, cognitive and developmental psychology, philosophy of mathematics, linguistics. In Artificial Intelligence, aspects of numerical cognition have been modelled through neural networks to replicate and analytically study children behaviours. However, artificial models need to incorporate realistic sensory-motor information from the body to fully mimic the children's learning behaviours, e.g., the use of fingers to learn and manipulate numbers. To this end, this article presents a database of images, focused on number representation with fingers using both human and robot hands, which can constitute the base for building new realistic models of numerical cognition in humanoid robots, enabling a grounded learning approach in developmental autonomous agents. The article provides a benchmark analysis of the datasets in the database that are used to train, validate, and test five state-of-the art deep neural networks, which are compared for classification accuracy together with an analysis of the computational requirements of each network. The discussion highlights the trade-off between speed and precision in the detection, which is required for realistic applications in robotics. [ABSTRACT FROM AUTHOR]

The study has two objectives: (1) to introduce grip force recording as a new technique for studying embodied numerical processing; and (2) to demonstrate how three competing accounts of numerical magnitude representation can be tested by using this new technique: the Mental Number Line (MNL), A Theory of Magnitude (ATOM) and Embodied Cognition (finger counting-based) account. While 26 healthy adults processed visually presented single digits in a go/no-go n-back paradigm, their passive holding forces for two small sensors were recorded in both hands. Spontaneous and unconscious grip force changes related to number magnitude occurred in the left hand already 100–140 ms after stimulus presentation and continued systematically. Our results support a two-step model of number processing where an initial stage is related to the automatic activation of all stimulus properties whereas a later stage consists of deeper conscious processing of the stimulus. This interpretation generalizes previous work with linguistic stimuli and elaborates the timeline of embodied cognition. We hope that the use of grip force recording will advance the field of numerical cognition research. [ABSTRACT FROM AUTHOR]

Understanding number magnitude is an important prerequisite for children’s mathematical development. One early experience that contributes to this understanding is the common practice of finger counting. Recent research suggested that through repeated finger counting, children internalize their fingers as representations of number magnitude. Furthermore, finger counting habits have been proposed to predict concurrent and future mathematical performance. However, little is known about how finger-based number representations are formed and by which processes they could influence mathematical development. Regarding the emergence of finger-based number representations, it is likely that they result from repeated practice of finger counting. Accordingly, children need sufficient fine motor skills (FMS) to successfully count on their fingers. However, the role that different types of FMS (such as dexterity and graphomotor skills) might play in the development of finger-based number representations is still unknown. In the current study, we investigated (a) whether children’s FMS (dexterity and graphomotor skills) are associated with their emerging finger-based number representations (ordinal and cardinal), (b) whether FMS explain variance in children’s finger-based number representations beyond the influence of general cognitive skills, and (c) whether the association between FMS and numerical skills is mediated by finger-based representations. We tested associations between preschool children’s (N = 80) FMS (dexterity and graphomotor skills), finger-based number representations, and numerical skills. Furthermore, visuo-spatial working memory and nonverbal intelligence were controlled for. Dexterity was related to children’s finger-based number representations as well as numerical skills after controlling for chronological age, but not after also controlling for cognitive skills. Moreover, the relationship between dexterity and numerical skills was mediated by finger-based number representations. No such associations were observed for graphomotor skills. These results suggest that dexterity plays a role in children’s development of finger-based number representations, which in turn contribute to their numerical skills. Possible explanations are discussed.

The well-documented association between fingers and numbers is not only based on the observation that most children use their fingers for counting and initial calculation, but also on extensive behavioral and neuro-functional evidence. In this article, we critically review developmental studies evaluating the association between finger sensorimotor skills (i.e., finger gnosis and fine motor skills) and numerical abilities. In sum, reviewed studies were found to provide evidential value and indicated that both finger gnosis and fine motor skills predict measures of counting, number system knowledge, number magnitude processing, and calculation ability. Therefore, specific and unique contributions of both finger gnosis and fine motor skills to the development of numerical skills seem to be substantiated. Through critical consideration of the reviewed evidence, we suggest that the association of finger gnosis and fine motor skills with numerical abilities may emerge from a combination of functional and redeployment mechanisms, in which the early use of finger-based numerical strategies during childhood might be the developmental process by which number representations become intertwined with the finger sensorimotor system, which carries an innate predisposition for said association to unfold. Further research is nonetheless necessary to clarify the causal mechanisms underlying this association.

The Spatial Numerical Association of Response Code (SNARC) is the preferential association between smaller/larger magnitudes and left/right side, respectively. Some evidence suggest a link between SNARC and a left-to-right finger counting habit. We asked 268 participants to show how they use the hands to count from 1 to 10. By means of this ecological task, 80% of the sample use first the right hand (to count from 1 to 5) and the majority of them use a palm-up posture. In Experiment 2 (N = 46) right-starters were asked to categorize 1-to-5 magnitudes as even or odd, using the left and right hand. Stimuli were presented both as Arabic numbers and by means of left and right hand photographs in palm-up and palm-down posture. Results confirmed the expected SNARC effect in the Arabic condition. With hand images we found that right hand responses were better for larger than for smaller magnitudes (SNARC, mainly for left hand palm-up stimuli), showing that the SNARC can be generalized to different codes. Finally, the interactions between magnitudes and left/right hand images in palm-up and palm-down posture suggest that embodied cognition can influence numerical processing.

The hand with which one starts to count has been shown repeatedly to influence numerical performance. However, methods vary greatly in how researchers determine starting hand. As such, it is impossible to say whether starting hand reflects one construct that is being differently measured, or if these methods reflect different constructs. To investigate these possibilities, we employed a binary magnitude comparison task known to elicit spatial-numerical biases and embodied number magnitude effects, as well as both cardinal and ordinal assessments of starting hand. In addition to this, we further examined whether being made aware of one’s finger-counting habits prior to the numerical task (through a finger-counting inventory) may alter performance during a spatial-numerical reaction-time task. Ordinal and cardinal starting hand classifications disagreed significantly in their classification of left vs. right-starters and predicted different aspects of numerical performance, which further interacted with procedure-order. The pattern of results suggest that 1) ordinal and cardinal aspects of finger-counting are dissociable and predict differing aspects of embodied numerosity, and 2) that assessing finger counting habits before performing a numerical task may affect performance on that task. Therefore, these methodological variations have important theoretical ramifications and need to be reported in greater detail in future work.

Even though mathematics is considered one of the most abstract domains of human cognition, recent work on embodiment of mathematics has shown that we make sense of mathematical concepts by using insights and skills acquired through bodily activity. Fingers play a significant role in many of these bodily interactions. Finger-based interactions provide the preliminary access to foundational mathematical constructs, such as one-to-one correspondence and whole-part relations in early development. In addition, children across cultures use their fingers to count and do simple arithmetic. There is also some evidence for an association between children’s ability to individuate fingers (finger gnosis) and mathematics ability. Paralleling these behavioral findings, there is accumulating evidence for overlapping neural correlates and functional associations between fingers and number processing. In this paper, we synthesize mathematics education and neurocognitive research on the relevance of fingers for early mathematics development. We delve into issues such as how the early multimodal (tactile, motor, visuospatial) experiences with fingers might be the gateway for later numerical skills, how finger gnosis, finger counting habits, and numerical abilities are associated at the behavioral and neural levels, and implications for mathematics education. We argue that, taken together, the two bodies of research can better inform how different finger skills support the development of numerical competencies, and we provide a road map for future interdisciplinary research that can yield to development of diagnostic tools and interventions for preschool and primary grade classrooms.

What constitutes effective teaching of arithmetical skills in early school years is still uncertain. Finger use could play a crucial role in this acquisition, but some children do not use them spontaneously and studies would be necessary to know if it is possible to teach them. This research assesses the impact of a teacher-implemented intervention program to teach 5-year- to 6-year-old children to use their fingers in numerical tasks. Participants were 36 kindergarten pupils (16 girls, 20 boys; mean age 5 years, 5 months) from two classrooms. The research compares a program in which motor training and explicit teaching of finger use are promoted to represent numbers and to act on them, with a "business as usual" contrast group. Children were tested before and after the intervention with problem-solving. After the experimental training program, finger counting appears to be a good strategy because its frequency is positively linked to the scores in the problem-solving tasks. We showed a greater improvement in problem-solving following the finger use intervention, compared to the contrast group. Our results support the explicit teaching of finger use to build numerical representation and enhance the calculation skills of kindergarten students (age 5) in French schools. [ABSTRACT FROM AUTHOR]

Representations of the fingers are embodied in our cognition and influence performance in enumeration tasks. Among deaf signers, the fingers also serve as a tool for communication in sign language. Previous studies in normal hearing (NH) participants showed effects of embodiment (i.e., embodied numerosity) on tactile enumeration using the fingers of one hand. In this research, we examined the influence of extensive visuo‐manual use on tactile enumeration among the deaf. We carried out four enumeration task experiments, using 1–5 stimuli, on a profoundly deaf group (n = 16) and a matching NH group (n = 15): (a) tactile enumeration using one hand, (b) tactile enumeration using two hands, (c) visual enumeration of finger signs, and (d) visual enumeration of dots. In the tactile tasks, we found salient embodied effects in the deaf group compared to the NH group. In the visual enumeration of finger signs task, we controlled the meanings of the stimuli presentation type (e.g., finger‐counting habit, fingerspelled letters, both or neither). Interestingly, when comparing fingerspelled letters to neutrals (i.e., not letters or numerical finger‐counting signs), an inhibition pattern was observed among the deaf. The findings uncover the influence of rich visuo‐manual experiences and language on embodied representations. In addition, we propose that these influences can partially account for the lag in mathematical competencies in the deaf compared to NH peers. Lastly, we further discuss how our findings support a contemporary model for mental numerical representations and finger‐counting habits. [ABSTRACT FROM AUTHOR]

Understanding number magnitude is an important prerequisite for children's mathematical development. One early experience that contributes to this understanding is the common practice of finger counting. Recent research suggested that through repeated finger counting, children internalize their fingers as representations of number magnitude. Furthermore, finger counting habits have been proposed to predict concurrent and future mathematical performance. However, little is known about how finger-based number representations are formed and by which processes they could influence mathematical development. Regarding the emergence of finger-based number representations, it is likely that they result from repeated practice of finger counting. Accordingly, children need sufficient fine motor skills (FMS) to successfully count on their fingers. However, the role that different types of FMS (such as dexterity and graphomotor skills) might play in the development of finger-based number representations is still unknown. In the current study, we investigated (a) whether children's FMS (dexterity and graphomotor skills) are associated with their emerging finger-based number representations (ordinal and cardinal), (b) whether FMS explain variance in children's finger-based number representations beyond the influence of general cognitive skills, and (c) whether the association between FMS and numerical skills is mediated by finger-based representations. We tested associations between preschool children's (N = 80) FMS (dexterity and graphomotor skills), finger-based number representations, and numerical skills. Furthermore, visuo-spatial working memory and nonverbal intelligence were controlled for. Dexterity was related to children's finger-based number representations as well as numerical skills after controlling for chronological age, but not after also controlling for cognitive skills. Moreover, the relationship between dexterity and numerical skills was mediated by finger-based number representations. No such associations were observed for graphomotor skills. These results suggest that dexterity plays a role in children's development of finger-based number representations, which in turn contribute to their numerical skills. Possible explanations are discussed. [ABSTRACT FROM AUTHOR]

The well-documented association between fingers and numbers is not only based on the observation that most children use their fingers for counting and initial calculation, but also on extensive behavioral and neuro-functional evidence. In this article, we critically review developmental studies evaluating the association between finger sensorimotor skills (i.e., finger gnosis and fine motor skills) and numerical abilities. In sum, reviewed studies were found to provide evidential value and indicated that both finger gnosis and fine motor skills predict measures of counting, number system knowledge, number magnitude processing, and calculation ability. Therefore, specific and unique contributions of both finger gnosis and fine motor skills to the development of numerical skills seem to be substantiated. Through critical consideration of the reviewed evidence, we suggest that the association of finger gnosis and fine motor skills with numerical abilities may emerge from a combination of functional and redeployment mechanisms, in which the early use of finger-based numerical strategies during childhood might be the developmental process by which number representations become intertwined with the finger sensorimotor system, which carries an innate predisposition for said association to unfold. Further research is nonetheless necessary to clarify the causal mechanisms underlying this association. [ABSTRACT FROM AUTHOR]

The Spatial Numerical Association of Response Code (SNARC) is the preferential association between smaller/larger magnitudes and left/right side, respectively. Some evidence suggest a link between SNARC and a left-to-right finger counting habit. We asked 268 participants to show how they use the hands to count from 1 to 10. By means of this ecological task, 80% of the sample use first the right hand (to count from 1 to 5) and the majority of them use a palm-up posture. In Experiment 2 (N D46) right-starters were asked to categorize 1-to-5 magnitudes as even or odd, using the left and right hand. Stimuli were presented both as Arabic numbers and by means of left and right hand photographs in palm-up and palm-down posture. Results confirmed the expected SNARC effect in the Arabic condition. With hand images we found that right hand responses were better for larger than for smaller magnitudes (SNARC, mainly for left hand palm-up stimuli), showing that the SNARC can be generalized to different codes. Finally, the interactions between magnitudes and left/right hand images in palm-up and palm-down posture suggest that embodied cognition can influence numerical processing. [ABSTRACT FROM AUTHOR]

There is a well-documented association between fingers and numbers, which was claimed to stem from the use of finger-based strategies for counting and calculating during childhood. Recently, it has been argued that this may lead to a concomitant activation of finger-based alongside other numerical representations when encountering single-digit numbers. Indeed, the occurrence of such a co-activation is supported by observed influences of finger counting habits on different numerical tasks, including single-digit arithmetic problem solving. In this study, we pursued the question whether the influence of finger-based representations on arithmetic generalizes to multi-digit arithmetic by investigating the association between the recognition of canonical and non-canonical finger patterns and multi-digit arithmetic in adults. Results indicated that canonical finger-based numerical representations were significantly associated with addition performance only, whereas non-canonical finger-based representations were associated significantly with all four arithmetic operations. We argue that, because non-canonical patterns do not benefit from the iconicity of canonical patterns, their magnitude may need to be constructed through magnitude manipulation which may in turn increase associations with mental arithmetic. In sum, our findings provide converging evidence for a functional association between finger-based representations and arithmetic performance. [ABSTRACT FROM AUTHOR]

Background. Embodied finger counting has been shown to have cross-cultural differences in previous studies (Lindemann, Alipour, & Fisher, 2011; Soto & Lalain, 2008). However, their results were contradictory in reference to Western populations with regard to the hand preferred: The first study showed that in Western countries — Europe and the United States — participants preferred to start with the left hand (whereas in the Middle East — Iran — they used the right hand); the second study showed that participants in France preferred the right hand. Objective. Our study aimed to observe these differences in two countries, Spain (Western Europe) and Russia (Eastern Europe part), although taking into account the variety of cultural or ethnic groups who live there. Design. The observational/descriptive study, together with correlational analysis of the finger-counting pattern (from 1 to 10) used by children aged 10 to 12 who had not been taught to use their fingers for counting, considered factors of cultural origin and hand dominance. The possible effects of this action on cognition — in our case, math achievement — were considered also. Results and conclusion. The differences in the frequency of the finger-counting patterns might suggest cultural-individual differences in performance; however, the correlational analysis did not reveal that these differences were statistically significant, either for gender or for mark in math. However, hand dominance was a significant predictor of the preferred hand with which to start counting.

• We examined visual and tactile enumeration among adults with developmental dyscalculia (DD) and matched controls. • DD participants were less accurate than controls in canonical arrangements of 5–9 dots and in random arrangements of 5 dots. • DD participants were less accurate in tactile enumeration, most profoundly in neighboring finger-counting arrangements. • We showed a modal-independent pattern recognition deficit in those with DD. • We emphasized the role of fingers in ordinal and cardinal representation of numbers. Developmental dyscalculia (DD) is characterized by lower numerical and finger-related skills. Studies of enumeration among those DD that suggested core deficiency in pattern recognition, working memory or/and attention were mostly carried out in the visual modality. In our study, we examined visual (dots) enumeration of 1–10 stimuli and tactile (vibration) enumeration of 1–10 fingers among DD and matched-control adults. We used 800-ms stimuli exposure time of either random/non-neighboring or canonical/neighboring stimuli arrangements (visual/tactile). Compared to controls, those with DD responded faster in visual random enumeration and did not differ in reaction time (RT) of canonical stimuli arrangements. However, while the control group had near perfect accuracy in random stimuli arrangements of up to five stimuli, DD participants performed accurately for only up to four stimuli, and they were less accurate in the canonical stimuli arrangements in the counting range. In the tactile task, DD participants showed less accurate tactile enumeration only for neighboring arrangements, more profoundly for finger counting (FC) patterns. The longer exposure time in the visual task enabled us to explore pattern recognition effects when working memory and attention loads were low. We discuss possible modal-independent deficits in pattern recognition and working memory on enumeration performance among those with DD and the unique role of fingers in ordinal and cardinal representation of numbers. [ABSTRACT FROM AUTHOR]

By recovering the history of simple finger counting techniques and their relevance to a wide range of enumerative and calculative technologies, this article argues that human fingers have long shaped the digital, and more importantly, that the digital has long shaped the fingers. The interfaces of calculating machines from the Roman abacus to the touchscreen calculators mathematize the body in very specific and consistent ways, such that the fingers have come to connote human reason just as fluids such as tears have come to connote human feeling. This embodied digitality naturalizes and humanizes the digital in ways that we have too often taken for granted. Digital calculating machines are not just utilitarian instruments under human control, but engines of hominization that, across much of the world today, define what it means to be human. [ABSTRACT FROM AUTHOR]

Teachers' beliefs and attitudes are known to guide the type of activities they implement in their classrooms. A traditional conception that finger counting is merely a back-up when children fail to use more sophisticated and efficient strategies could therefore prevent teachers from encouraging children's use of fingers in arithmetic tasks. However, the potential benefit of finger counting for young learners has been recently documented and setting aside its practice within classrooms may hinder children's mathematical skill development. It is therefore important to establish whether there is a discrepancy between teacher's beliefs regarding finger counting and the latest discoveries in this field of research. To this aim, we interrogated 413 teachers from preschool to Grade 5. We found that, despite being generally positive towards finger counting, teachers think that finger counting is typical of children who present math difficulties or lack of confidence, even during the first years of learning. These results are discussed considering what is known and what remains to be determined in the current scientific literature. [ABSTRACT FROM AUTHOR]

The first steps in numerical cognition are usually done in conjunction with fingers. Following the assumption that abstract concepts stay associated with the sensory-motor information that was present during their acquisition and consolidation, mental number representations should always be associated with the respective finger counting components. We tested whether finger movements that imply finger counting actually prime the corresponding number concepts in adults. All participants counted number 1 with their thumb and incremented sequentially to number 5 with their pinky. In the experiment, participants sequentially and repeatedly pressed five buttons from thumb to pinky. Each button press triggered the visual presentation of a random number between 1 and 5 that had to be named aloud, resulting in 20% counting-congruent and 80% counting-incongruent finger-number mappings. Average naming latencies were significantly shorter for congruent than incongruent finger-number combinations. Furthermore, there was a distance effect where primes partly co-activated numerically close target numbers and with decreasing priming for more distant prime-target pairs. Overall, these results provide further evidence that number representations are strongly associated with finger counting experience, making fingers an effective tool for number comprehension.

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 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The diversion of a driver’s attention from driving can be catastrophic. Given that conventional button- and touch-based interfaces may distract the driver, developing novel distraction-free interfaces for the various devices present in cars has becomes necessary. Hand gesture recognition may provide an alternative interface inside cars. Given that cars are the targeted application area, we determined the optimal location for the radar sensor, so that the signal reflected from the driver’s hand during gesturing is unaffected by interference from the motion of the driver’s body or other motions within the car. We implemented a Convolutional Neural Network-based technique to recognize the finger-counting-based hand gestures using an Impulse Radio (IR) radar sensor. The accuracy of the proposed method was sufficiently high for real-world applications.

This paper proposes a finger counting algorithm for a hand with stuck fingers. The proposed algorithm is based on the fact that straight line type shadows are inevitably generated between fingers. It divides the hand region into the thumb region and the four fingers region for effective shadow detection, and generates an edge image in each region. Projection curves are generated by appling a line detection and a projection technique to each edge image, and the peaks of the curves are detected as candidates for finger shadows. And then peaks due to finger shadows are extracted from them and counted. In the finger counting experiment on hand images expressing various shapes with stuck fingers, the counting success rate is from 83.3% to 100% according to the number of fingers, and 93.1% on the whole. It also shows that if hand images are generated under controlled conditions, the failure cases can be sufficiently improved. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 might 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.