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Variability in finger counting systems, illustrated for number eight signs [(E) downloaded from Marmasse et al, 2000].
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Like number words and written numerals, fingers can be used to represent numbers. In fact, due to their ubiquitous availability, agility, and discrete quantity, they are considered the most natural tool for counting, which renders them attractive for theories of embodied (numerical) cognition (Andres et al., 2008; Di Luca and Pesenti, 2011). As the...
Citations
... In Belgium, for example, the typical finger-counting procedure involves raising the fingers of one hand, from the thumb to the little finger, to count from 1 to 5, and raising the fingers of the other hand in the exact same order to count from 6 to 10. By associating each raised finger with a specific number word, finger-counting supports the segmentation of the counting sequence (Bender & Beller, 2011) and thus help children to understand the oneto-one correspondence and stable order principles (Brissiaud, 2003;Fayol & Seron, 2005). As the number of fingers raised directly represents the number of counted elements, finger-counting moreover prompts the understanding of the cardinality principle (level II; Neveu et al., 2023). ...
Finger-counting plays a crucial role in grounding and establishing mathematics, one of the most abstract domains of human cognition. While the combination of visual and proprioceptive information enables the coordination of finger movements, it was recently suggested that the emergence of finger-counting primarily relies on visual cues. In this study, we aimed to directly test this assumption by examining whether explicit finger-counting training (through tactile stimulation) may assist visually impaired children in overcoming their difficulties in learning mathematics. Two visually impaired participants (2 boys of 8.5 and 7.5 years) were therefore trained to use their fingers to calculate. Their pre- and post-training performance were compared to two control groups of sighted children who underwent either the same finger counting training (8 boys, 10 girls, Mage = 5.9 years; 10 kindergarteners and eight 1st graders) or another control vocabulary training (10 boys, 8 girls, Mage = 5.9 years; 11 kindergarteners and seven 1st graders). Results demonstrated that sighted children’s arithmetic performance improved much more after the finger training than after the vocabulary training. Importantly, the positive impact of the finger training was also observed in both visually impaired participants (for addition and subtraction in one child; only for addition in the other child). These results are discussed in relation to the sensory compensation hypothesis and emphasize the importance of early and appropriate instruction of finger-based representations in both sighted and visually impaired children.
... Current literature provides a relatively broad account of finger counting and montring routines in several countries and cultures (e.g. Bender & Beller, 2011. Even when considering simple, one-dimensional systems, where numbers are linked to fingers based on one-to-one correspondence (see Bender & Beller, 2011, for a classification of other body part counting systems; Bender & Beller, 2012), there is still some space for variation in finger counting: (a) whether the palm is turned toward oneself or toward others, (b) whether the fingers are extended or bent, (c) whether the starting hand is right or left, (d) whether the switch between hands is based on anatomical symmetry or spatial continuation, (e) which finger starts the sequence. ...
... Bender & Beller, 2011. Even when considering simple, one-dimensional systems, where numbers are linked to fingers based on one-to-one correspondence (see Bender & Beller, 2011, for a classification of other body part counting systems; Bender & Beller, 2012), there is still some space for variation in finger counting: (a) whether the palm is turned toward oneself or toward others, (b) whether the fingers are extended or bent, (c) whether the starting hand is right or left, (d) whether the switch between hands is based on anatomical symmetry or spatial continuation, (e) which finger starts the sequence. In all these areas, variation has been observed both between and within cultures. ...
... We learned that finger counting is indeed widespread. However, their finger counting routines do not go beyond the simple one-to-one correspondence (i.e., can be classified as a simple, one-dimensional system; Bender & Beller, 2011). Tsimane' language is using a base-10 system, where the structure of multi-digit numbers can be considered transparent and reflects the place-value structure. ...
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. Tsi-mane' 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.
... Lists occur in spoken, written, and signed modalities, as well as in co-speech gestures. In the latter case, it is common to observe that hearing gesturers use hands and fingers for enumeration (Bender & Beller, 2011, 2012Fischer et al., 2012). Such finger counting has been attested among hearing gesturers for centuries (Bulwer, 1644). ...
This paper examines how signers make lists. One way is to use the fingers on the signer’s nondominant hand to enumerate items on a list. The signer points to these list-fingers with the dominant hand. Previous analyses considered lists to be nondominant, one-handed signs, and thus were called list buoys because the nondominant hand often remains in place during the production of the list. The pointing hand was largely ignored as a nonlinguistic gesture. We take a constructional approach based on Cognitive Grammar. In our approach, we analyze lists as a type of pointing construction consisting of two meaningful components: a pointing device (the pointing hand) used to direct attention; and a Place, also consisting of form and a meaning. Using data from Brazilian Sign Language (Libras) and Finland–Swedish Sign Language (FinSSL), we examine the semantic role of each component, showing how the nondominant list-fingers identify and track discourse referents, and how the pointing hand is used to create higher-order entities by grouping list-fingers. We also examine the integration of list constructions and their components with other conventional constructions.
... Of course, this is nothing more than a superficial analogy. The numerical meaning attached to fingers is culturally encoded and in strikingly diverse ways [136]. In modern human languages, the length of the code word of a number j is approximately proportional to log j (for large j), and the modern numeration system results from a long and complicated development. ...
Over the last 40–50 years, ethology has become increasingly quantitative and computational. However, when analysing animal behavioural sequences, researchers often need help finding an adequate model to assess certain characteristics of these sequences while using a relatively small number of parameters. In this review, I demonstrate that the information theory approaches based on Shannon entropy and Kolmogorov complexity can furnish effective tools to analyse and compare animal natural behaviours. In addition to a comparative analysis of stereotypic behavioural sequences, information theory can provide ideas for particular experiments on sophisticated animal communications. In particular, it has made it possible to discover the existence of a developed symbolic “language” in leader-scouting ant species based on the ability of these ants to transfer abstract information about remote events.
... Indigenous adults' representation of exact cardinal values are limited to the number words that they can recite (Pitt et al., 2022). This limitation is even true for the Oksapmin numeration system, which represents cardinalities up to 27 using one-to-one correspondence with body parts in a stable sequence (Bender & Beller, 2011;Saxe, 1981). Moreover, even literate adults in a modern society find it difficult to produce exact numerical quantities based on one-to-one correspondence when counting is made unavailable by a concurrent verbal shadowing task (Frank et al., 2012). ...
... A seminal work by Zhang and Norman (1995), which is further extended by others (Bender et al., 2015;Bender & Beller, 2011Schlimm, 2018), provides an in-depth theoretical analysis about how combinatorial rules of numerals affect the way humans think about number. According to these authors, our understanding of number and ability to solve numerical tasks comes from the integration of distributed numerical information represented externally as numerals and internally in memory. ...
Predominant psychological theories of number acquisition posit that children acquire natural number concepts as they acquire the successor principle, or the knowledge that every natural number is succeeded by another natural number that is exactly-one more than it. However, exactly how children acquire the successor principle remains largely unexplained. Recently developed ideas within this family of theories posit that an abstract recursive successor function is acquired from the recursive structure of number words; however, the types of recursion underlying the successor function and number words are distinctively different (one is a self-referential function and the other is a self-embedded structure), making it difficult to theorize how one type triggers the acquisition of another. Moreover, our analysis of the literature questions if the knowledge about the successor principle is even empirically measurable. Here, we argue that number acquisition is a process of understanding a generative rule that governs the system of natural numbers and point out that the successor principle is not the only generative rule that governs the natural number system. We propose an alternative hypothesis that generative number concepts emerge from children's realization about how the combinatorial rules of numerals allow arithmetic (specifically additive and multiplicative) representations of quantity. Importantly, under addition and multiplication—which are historically rooted in concatenation and grouping of physical objects—natural numbers are mathematically closed. As a corollary, the system of infinitely generative natural numbers is conceptualized. This new theoretical framework allows the construction of novel empirical questions and testable hypotheses based on the formalized rules of numerical syntax and numeration systems, and therefore opens a new avenue for studying later stages of children's acquisition of number concepts.
... Even though the use of fingers for counting is quite widespread, there are considerable differences in how the finger counting routine looks like. Even when we consider simple, onedimensional systems, where numbers are linked to fingers based on one-to-one correspondence (see Bender & Beller, 2011, for a classification of other body part counting systems; 2012), there is still quite some space for variation in finger counting: (a) whether the palm is turned toward oneself or toward others, (b) whether the fingers are extended or bent, (c) whether the starting hand is right or left, (d) whether the switch between hands is based on anatomical symmetry or spatial continuation. To this list one can add another point on (e) which finger starts the sequence. ...
... To start, what seems clear from multiple studies conducted across different cultures and countries is that fingers are used for counting (Bender & Beller, 2011. It also seems that they do play a functional role for numerical cognition (e.g., Andres & Pesenti, 2015). ...
Despite variety of cultures, our shared biology and the universality of finger counting suggests that numbers are embodied. Another lines of research show that numerical cognition might be bound to what our bodies are able to do. 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 indiginous people living in the Bolivian Amazon rainforest, depending on handedness, education level, and exposure to mainstream, industrialised 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 might affect cross-cultural and within-cultural variation in finger counting.
... Accordingly, it is very likely that the dots in the present study were discriminated at an earlier stage of information processing than the fingers, thus creating a more direct access to the corresponding numbers. As previously mentioned, being able to pronounce the number corresponding to a specific finger configuration depends on participants' culturally embedded knowledge of how finger configurations are encoded and used to express quantities (Bender & Beller, 2011). This culturally dependent knowledge might, therefore, be subsumed by higher cognitive processes associated with conceptual representation (Di Luca et al., 2010). ...
Fingers can express quantities and thus contribute to the acquisition and manipulation of numbers as well as the development of arithmetical skills. As embodied entities, the processing of finger numerical configurations should, therefore, be facilitated when they match shared cultural representations and are presented close to the body. To investigate these issues, the present study investigated whether canonical finger configurations are processed faster than noncanonical configurations or spatially matched dot configurations, taking into account their location in the peripersonal or the extrapersonal space. Analysis of verbal responses to the enumeration of small and large numerosities showed that participants (N = 30) processed small numerosities faster than large ones and dots faster than finger configurations despite visuo-spatial matching. Canonical configurations were also processed faster than noncanonical configurations but for finger numerical stimuli only. Furthermore, the difference in response time between dots and fingers processing was greater when the stimuli were located in the peripersonal space than in the extrapersonal space. As a whole, the data suggest that, due to their motor nature, finger numerical configurations are not processed as simple visual stimuli but in relation to corporal and cultural counting habits, in agreement with the embodied framework of numerical cognition.
... In fact, the use of finger-counting for arithmetic calculations may indicate that mental processes are not developed enough to function without external/concrete support. This, however, does not mean that it is not worth getting the support of finger-counting strategies (Bender & Beller, 2011). On the contrary, it might be a sign that affective and cognitive factors, which form the basis of students' finger-counting needs, should be identified to perform long-term alternative educational interventions or to encourage students to use different finger-counting strategies. ...
The aim of this study is to determine preschool, special education, elementary school teacher and mathematics teachers' views of finger-counting in mathematics teaching. The study was conducted with case study design. The sample of the study consisted of 34 teachers. Data were collected using an 8-item written form, and content analysis was performed. The findings of the study indicate that most participants use fingers as manipulatives in the teaching of numbers and counting but use them very little when teaching the four operations. Most
... Frente a la pregunta de composición aditiva de colecciones invisibles, NA no utiliza la estrategia más avanzada de cálculo mental. Sin embargo, utiliza una estrategia sofisticada de cuantificación usando sus dedos como herramienta natural (Bender & Beller, 2011;Geary et al, 2004). Frente a la meta de unir colecciones, NA activa los principios de conteo y usa la secuencia numérica verbal convencional como recursos cognitivos para contar uno a uno con levantamiento de dedos cada colección visible por aparte, y después contar uno a uno con levantamiento de dedos uniendo las dos colecciones invisibles en una sola. ...
... Según perspectivas de cognición corporeizada, NA capitaliza recursos de conteo adquiridos con elementos perceptuales de colecciones visibles utilizadas previamente en continuos conteos, para activar representaciones enactivas de cada uno de los objetos cuantificables corporeizados (Bender & Beller, 2011), simultáneamente con una representación enactiva de repetibilidad. Esto permite el uso recurrente de conteos con levantamiento de dedos mostrando que las colecciones de ítems para contar están embebidas en sus manos y en sus dedos (Bender & Beller, 2011), y que su conocimiento es distribuido entre la tarea, sus representaciones mentales y su cuerpo (Malafouris, 2013). ...
... Según perspectivas de cognición corporeizada, NA capitaliza recursos de conteo adquiridos con elementos perceptuales de colecciones visibles utilizadas previamente en continuos conteos, para activar representaciones enactivas de cada uno de los objetos cuantificables corporeizados (Bender & Beller, 2011), simultáneamente con una representación enactiva de repetibilidad. Esto permite el uso recurrente de conteos con levantamiento de dedos mostrando que las colecciones de ítems para contar están embebidas en sus manos y en sus dedos (Bender & Beller, 2011), y que su conocimiento es distribuido entre la tarea, sus representaciones mentales y su cuerpo (Malafouris, 2013). Los conteos de dedos evidencian que NA naturalmente encuentra estrategias que facilitan el aprendizaje y disminuyen la carga de la memoria de trabajo, y que su cognición está encarnada en su cuerpo. ...
El objetivo del estudio es describir e ilustrar el Análisis Cognitivo de Tareas (ACT) como un método que agrupa variadas técnicas de análisis cualitativo de datos para caracterizar la actividad cognitiva subyacente al desempeño de individuos cuando resuelven una tarea, así como la tarea misma. El abordaje metodológico incluyó inicialmente una revisión documental de modelos reconocidos de ACT desde enfoques de la psicología y la educación. Estos modelos han sido utilizados para analizar procesos cognitivos, de pensamiento y de toma de decisiones en situaciones de resolución de problemas. Se realizó una adaptación y aplicación del ACT para analizar tareas en psicología y educación, específicamente en la evaluación de habilidades matemáticas tempranas en ambientes de aprendizaje escolar. Los resultados ilustran tres niveles metodológicos del ACT: a) análisis de la estructura de la tarea, b) análisis de la exigencia cognitiva en niveles potenciales de desempeño y, c) análisis de desempeños a profundidad. Se concluye que la adaptación realizada hace el método ACT accesible a psicólogos y educadores en escenarios de evaluación educativa.
... Hand is the first counting and calculating machine of all ages (Ifrah, 1985). Fingers are considered the most natural tool for counting due to being universally accessible, nimble, and having a discrete quantity (Andres et al., 2008;Di Luca & Pesenti, 2011;Bender & Beller, 2011). At a very early age, children discover their fingers are useful for representing numbers and counting (Butterworth, 1999). ...
Fingers are universal tools used for different forms of fundamental numerical processing. Children across cultures use their hands and fingers to count and do arithmetic. Research shows that finger representations and finger-based strategies play an integral role in the learning and understanding of arithmetic. Sustained difficulties in mathematics lead to math anxiety. Math anxiety cause to impared working memory and finally impared working memory increase the need of concrete materials, such as fingers, for counting. The current study will explain finger-counting habits of students with dyscalculia through the perspective of cognitive neuroscience and psychology.
