Finger Counting Habits Research Articles

Cultural variability in finger representations / Variabilidad cultural en las representaciones con dedos

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.

Do numbers make us handy? Behavioral and electrophysiological evidence for number-hand congruency effect

Finger counting facilitates numerical representations and mathematical processing. The current study investigated the association between finger counting habits and number processing by employing behavioral and electrophysiological measures. We explored whether small and large numerical primes influence the recognition of embodied target hand stimuli. Twenty-four right-handed participants that were grouped into right-starters (n = 13) and left-starters (n = 11) for finger counting performed a hand recognition task that consisted of numerical magnitudes as prime and hand recognition as targets. Based on the finger counting habits, congruent (i.e., left-starters: small number/left hand or large number/right hand; right-starters: small number/right hand or large number/left hand) and incongruent (i.e., left-starters: large number/left hand or small number/right hand; right-starters: large number/right hand or small number/left hand) conditions were presented to the participants. The participants were required to indicate whether the targets were left or right hand by simply pressing the left or the right key, respectively. Results indicated faster reaction times (RTs) for congruent as opposed to incongruent trials for all participants. The mean amplitude of the centro-parietal P300 component was significantly increased for the incongruent compared to congruent condition, indicating increased mental effort. Also, analysis of the latency of the P300 in terms of congruency effect in all participants revealed significant results. These combined results provide behavioral and electrophysiological evidence indicating the embodied nature of numbers. The results are interpreted in light of the general findings related to the P300 component. This research supports the association of number-hand representations and corroborates the idea of embodied numerosity.

No fingers, no SNARC? Neither the finger counting starting hand, nor its stability robustly affect the SNARC effect

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.

Tactile Enumeration and Embodied Numerosity Among the Deaf.

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.

The Implicit Contribution of Fine Motor Skills to Mathematical Insight in Early Childhood.

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.

Registered Replication Report on Fischer, Castel, Dodd, and Pratt (2003)

The attentional spatial-numerical association of response codes (Att-SNARC) effect (Fischer, Castel, Dodd, & Pratt, 2003)—the finding that participants are quicker to detect left-side targets when the targets are preceded by small numbers and quicker to detect right-side targets when they are preceded by large numbers—has been used as evidence for embodied number representations and to support strong claims about the link between number and space (e.g., a mental number line). We attempted to replicate Experiment 2 of Fischer et al. by collecting data from 1,105 participants at 17 labs. Across all 1,105 participants and four interstimulus-interval conditions, the proportion of times the effect we observed was positive (i.e., directionally consistent with the original effect) was .50. Further, the effects we observed both within and across labs were minuscule and incompatible with those observed by Fischer et al. Given this, we conclude that we failed to replicate the effect reported by Fischer et al. In addition, our analysis of several participant-level moderators (finger-counting habits, reading and writing direction, handedness, and mathematics fluency and mathematics anxiety) revealed no substantial moderating effects. Our results indicate that the Att-SNARC effect cannot be used as evidence to support strong claims about the link between number and space.

Exploring the interactions among SNARC effect, finger counting direction and embodied cognition.

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.

Embodied numerical representations and their association with multi-digit arithmetic performance.

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.

ERP differences in processing canonical and noncanonical finger-numeral configurations

Finger-numeral configurations are used to represent numerosities, to count, and to do arithmetic across cultures. Previous research has distinguished between two forms of finger-numeral configurations; finger montring and finger counting. Montring refers to how people raise their fingers to show numerosities to others and usually serves a communicative function. Finger counting is used both for counting and arithmetic, and has a self-directed, facilitative function. In this study we compared the ERP markers for recognition of montring, counting, and noncanonical finger-numeral configurations with adult participants to explore differences in early perceptual and later semantic processing. Montring configurations were recognized faster and more accurately compared to counting and noncanonical. Recognition of montring configurations drew larger attentional resources, marked by higher positivity in the P1/N1 range, and montring and counting showed similar patterns of semantic processing, marked by higher positivity in the P3 range compared to noncanonical, possibly due to strategy differences (memory recall vs. counting). We also found some ERP evidence for participants’ finger counting habits affecting their processing of counting configurations. Overall, the results show differences in perceptual and semantic processes involved in extracting numerical information across the three finger-numeral configurations.

Cardinal and ordinal aspects of finger-counting habits predict different individual differences in embodied numerosity

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.

You can count on your fingers: The role of fingers in early mathematical development

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.

Stimulating numbers: signatures of finger counting in numerosity processing.

Finger counting is one of the first steps in the development of mature number concepts. With a one-to-one correspondence of fingers to numbers in Western finger counting, fingers hold two numerical meanings: one is based on the number of fingers raised and the second is based on their ordinal position within the habitual finger counting sequence. This study investigated how these two numerical meanings of fingers are intertwined with numerical cognition in adults. Participants received tactile stimulation on their fingertips of one hand and named either the number of fingers stimulated (2, 3, or 4 fingers; Experiment 1) or the number of stimulations on one fingertip (2, 3, or 4 stimulations; Experiment 2). Responses were faster and more accurate when the set of stimulated fingers corresponded to finger counting habits (Experiment 1) and when the number of stimulations matched the ordinal position of the stimulated finger (Experiment 2). These results show that tactile numerosity perception is affected by individual finger counting habits and that those habits give numerical meaning to single fingers.

Cross-cultural and intra-cultural differences in finger-counting habits and number magnitude processing: Embodied numerosity in Canadian and Chinese university students

Recent work in numerical cognition has shown-that number magnitude is not entirely abstract, and at least partly rooted in embodied and situated experiences, including finger-counting. The current study extends previous cross-cultural research to address within-culture individual differences in finger counting habits. Results indicated that Canadian participants demonstrated an additional cognitive load when comparing numbers that require more than one hand to represent, and this pattern of performance is further modulated by whether they typically start counting on their left hand or their right hand. Chinese students typically count on only one hand and so show no such effect, except for an increase in errors, similar to that seen in Canadians, for those whom self-identify as predominantly two-hand counters. Results suggest that the impact of finger counting habits extend beyond cultural experience and concord in predictable ways with differences in number magnitude processing for specific number-digits. We conclude that symbolic number magnitude processing is partially rooted in learned finger-counting habits, consistent with a motor simulation account of embodied numeracy and that argument is supported by both cross-cultural and within-culture differences in finger-counting habits.

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.

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

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

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

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

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

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

Related but not the same: Ordinality, cardinality and 1-to-1 correspondence in finger-based numerical representations

Finger-based numerical representations have gained increasing research interest. However, their description and assessment often refer to different numerical principles of ordinality, cardinality and 1-to-1 correspondence. Our aim was to investigate similarities and differences between these principles in finger-based numerical representations. Sixty-eight healthy adults performed ordinal finger counting, cardinal finger montring (showing the number of gestures) and finger-to-number mapping with twisted arms and fingers. We found that counting gestures and montring postures were identical for Number 10 but differed to varying degrees for other numbers. Interestingly, there was no systematic relation between finger-to-number mapping and ordinal finger counting habits. These data question the assumption of a unitary embodied finger-based numerical representation, but suggest that different finger-based representations co-exist and can be recruited flexibly depending on the numerical aspects to be conveyed.

Do not count on me to imagine how I act: behavior contradicts questionnaire responses in the assessment of finger counting habits

The directionality of finger counting (i.e., from left to right or right to left) is supposed to compete with the orientation of the mental number line in determining number mental representations. Indeed, Western individuals who count on their fingers from right to left present a weaker SNARC effect than do individuals for whom the directionality of counting is the same as the mental number line. Observations of natural behavior should be the preferred methodology for classifying individuals according to their counting habits. Yet, to perform such classification, researchers usually rely on questionnaires or reports of imagined behaviors. However, we show in a series of three experiments that, on average, 26% of a sample of adults reported the opposite behavior from the one they actually implemented spontaneously when tested with an original ecological task. In a fourth experiment, this new task proved reliable, using a test-retest method. These results suggest that future studies about counting habits could benefit from the use of more ecological and functional tasks, rather than depending on noncontextualized questionnaires.

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

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