Nature and culture of finger counting: diversity and representational effects of an embodied cognitive tool

A five-finger mnemonic for teaching schoolchildren the theoretical components of adult basic life support: a modified reactive Delphi-guided development and memorability pilot test with schoolchildren

BACKGROUND

A mnemonic is a cognitive aid frequently used in health-related education. The main goal of this study was to develop and test a 5-finger mnemonic for teaching schoolchildren the theoretical aspects of adult Basic Life Support (BLS) steps, a process rarely described in the context of instructing laypersons.

METHODS

Experts from the European Resuscitation Council's Basic Life Support Science and Education Committee (ERC BLS SEC), specializing in teaching adult BLS, participated in the first phase of the pilot study. This phase employed the modified reactive Delphi to develop a 5-finger mnemonic for teaching schoolchildren the theoretical aspects of adult BLS steps, in accordance with the 2021 ERC BLS guidelines. The mnemonic underwent revision rounds based on expert suggestions and was evaluated using a 9-point Likert scale. The process was repeated until there was unanimous approval. In the second phase, a pilot test was conducted with schoolchildren at a summer camp to assess their recall of the 5-finger mnemonic. Following their training in adult BLS steps utilizing the 5-finger mnemonic, schoolchildren were tasked with arranging cards depicting images from the mnemonic both before and after the training.

RESULTS

From March to October 2022, a four-round modified reactive Delphi engaged four experts from the ERC BLS SEC. Initial expert consensus was moderate, 6.0 (IQR = 4.5-7.5, min = 1, max = 9), on a scale 1 ("totally disagree") to 9 ("totally agree"). The experts consensus improved over subsequent rounds, resulting in two final versions of the 5-finger mnemonic. Both versions concentrate on the comprehensive adult BLS, differing only in their approach to cardiopulmonary resuscitation (CPR): one employs a method of 30 chest compressions followed by two rescue breaths, while the other utilizes compression-only CPR. In August 2023, a recall pilot test involved mostly female schoolchildren (12/13, 92.3%). Pre-training, no cards with 5-finger mnemonic content were arranged correctly, but post-training, progress improvement was observed, especially in older schoolchildren (Z = -2.727, p = 0.006).

CONCLUSIONS

The pilot study highlights the potential of using tailored educational tools, such as mnemonics, to teach important lifesaving skills to different age groups. This suggests that the 5-finger mnemonic effectively improved schoolchildren's understanding of the theoretical aspects of adult BLS steps.

A global cross-cultural analysis of string figures reveals evidence of deep transmission and innovation

Few cultural practices beyond language are as widespread as string figure games. Their global distribution and potential to yield insights into cultural transmission and cognition have long been noted. Yet, it remains unknown how or when this behaviour originated and to what extent shared motifs are signals of repeated innovations or deep cultural transmission. Here, we combined a global cross-cultural inventory of string figures with a novel methodology based on knot theory, which enables the unequivocal numerical coding of string figures. We performed a computational analysis of a sample of 826 figures from 92 societies around the world. Across these societies, we found 83 recurring string figure designs, some of which are regionally restricted while others display a global distribution. The cognitively opaque nature of string figure designs and their clear geographic distribution reveal processes of cultural transmission, innovation, and convergent evolution. Most strikingly, the global distribution of some figures raises the possibility of shared ancient origins.

Measuring Beyond the Standard: Informal Measurement Systems as Cognitive Technologies

This paper explores the role of measurement as a cognitive technology across human history, emphasizing the coexistence of formal and informal measurement systems. While standardized systems dominate contemporary culture and are well documented across large-scale societies of the past, this manuscript highlights the less explored domain of informal measurement practices that have been integral to daily life from the past to the present. Through the examination of body-based measurement systems and proportional heuristics, we demonstrate how these informal strategies were not merely precursors to formal standards but essential adaptive tools for solving everyday problems. Often, these informal solutions come with practical advantages. This manuscript calls for a broader recognition of their significance in cultural and technological evolution.

Age-related changes in how 5- to 8-year-old children use and execute finger-based strategies in arithmetic

To determine how young children use and execute finger-based strategies, 5- to 8-year-olds were asked to solve simple addition problems under a choice condition (i.e., they could choose finger-based or non-finger strategies on each problem) and under two no-choice conditions (one in which they needed to use finger-based strategies on all problems and one in which they could not use finger-based strategies). Results showed that children (a) used both finger-based and non-finger strategies to solve simple addition problems in all age groups, (b) used fingers less and less often as they grew older, especially while solving smaller problems, (c) calibrated their use of finger-based strategies to both problem features and strategy performance, and (d) improved efficiency of both finger-based and non-finger strategy execution. Moreover, (e) strategy performance was the best predictor of strategy selection in all age groups, and (f) when they had the possibility to use fingers, children of all age groups obtained better performance relative to when they could not use fingers, especially on larger problems.

The efficacy of manipulatives versus fingers in supporting young children's addition skills

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.

Finger counting to relieve working memory in children with developmental coordination disorder: Insights from behavioral and three-dimensional motion analyses

A limited number of studies have attempted to understand how motor deficits affect numerical abilities in children with developmental coordination disorder (DCD). The purpose of this study was to explore the functionality of finger-counting (FC) in children with DCD. The participants, 15 children with DCD and 15 typically developing (TD) children matched on school level and fluid reasoning abilities, were asked to use FC to solve an ordinal task with high working memory (WM) load. Behavioral measures supplemented with biomechanical measures, from three-dimensional motion analysis synchronized to a voice recording were used to assess children's performance and FC functionality (total duration, inter-finger [IF] transition, IF variance, finger/voice synchronization, and automatization of FC movements). Children with DCD were less accurate than TD children in using FC to solve ordinal problems with high WM load. This group difference could not be accounted for by poor FC skills given that FC movement turned out to be as functional in children with DCD as in their TD peers. When added to the model as a covariate, WM captured a greater proportion of intergroup variability than manual dexterity, further suggesting that their difficulties would be better accounted for by limited WM resources than by fine motor skills.

Finger counting, finger number gesturing, and basic numerical skills: A cross-sectional study in 3- to 5-year-olds

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.

What Makes Us Smart?

How did humans become clever enough to live in nearly every major ecosystem on earth, create vaccines against deadly plagues, explore the oceans depths, and routinely traverse the globe at 30,000 feet in aluminum tubes while nibbling on roasted almonds? Drawing on recent developments in our understanding of human evolution, we consider what makes us distinctively smarter than other animals. Contrary to conventional wisdom, human brilliance emerges not from our innate brainpower or raw computational capacities, but from the sharing of information in communities and networks over generations. We review how larger, more diverse, and more optimally interconnected networks of minds give rise to faster innovation and how the cognitive products of this cumulative cultural evolutionary process feedback to make us individually "smarter"-in the sense of being better at meeting the challenges and problems posed by our societies and socioecologies. Here, we consider not only how cultural evolution supplies us with "thinking tools" (like counting systems and fractions) but also how it has shaped our ontologies (e.g., do germs and witches exist?) and epistemologies, including our notions of what constitutes a "good reason" or "good evidence" (e.g., are dreams a source of evidence?). Building on this, we consider how cultural evolution has organized and distributed cultural knowledge and cognitive tasks among subpopulations, effectively shifting both thinking and production to the level of the community, population, or network, resulting in collective information processing and group decisions. Cultural evolution can turn mindless mobs into wise crowds by facilitating and constraining cognition through a wide variety of epistemic institutions-political, legal, and scientific. These institutions process information and aid better decision-making by suppressing or encouraging the use of different cultural epistemologies and ontologies.

Creating ad hoc graphical representations of number

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

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

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

Understanding the complexities of mathematical cognition: A multi-level framework

Mathematics skills are associated with future employment, well-being, and quality of life. However, many adults and children fail to learn the mathematics skills they require. To improve this situation, we need to have a better understanding of the processes of learning and performing mathematics. Over the past two decades, there has been a substantial growth in psychological research focusing on mathematics. However, to make further progress, we need to pay greater attention to the nature of, and multiple elements involved in, mathematical cognition. Mathematics is not a single construct; rather, overall mathematics achievement is comprised of proficiency with specific components of mathematics (e.g., number fact knowledge, algebraic thinking), which in turn recruit basic mathematical processes (e.g., magnitude comparison, pattern recognition). General cognitive skills and different learning experiences influence the development of each component of mathematics as well as the links between them. Here, I propose and provide evidence for a framework that structures how these components of mathematics fit together. This framework allows us to make sense of the proliferation of empirical findings concerning influences on mathematical cognition and can guide the questions we ask, identifying where we are missing both research evidence and models of specific mechanisms.

Multimodality matters in numerical communication

Modern society depends on numerical information, which must be communicated accurately and effectively. Numerical communication is accomplished in different modalities-speech, writing, sign, gesture, graphs, and in naturally occurring settings it almost always involves more than one modality at once. Yet the modalities of numerical communication are often studied in isolation. Here we argue that, to understand and improve numerical communication, we must take seriously this multimodality. We first discuss each modality on its own terms, identifying their commonalities and differences. We then argue that numerical communication is shaped critically by interactions among modalities. We boil down these interactions to four types: one modality can amplify the message of another; it can direct attention to content from another modality (e.g., using a gesture to guide attention to a relevant aspect of a graph); it can explain another modality (e.g., verbally explaining the meaning of an axis in a graph); and it can reinterpret a modality (e.g., framing an upwards-oriented trend as a bad outcome). We conclude by discussing how a focus on multimodality raises entirely new research questions about numerical communication.

Embodying measurement

Measuring with body parts is a handy and persistent cross-cultural phenomenon.

A sensorimotor perspective on numerical cognition

Numbers are present in every part of modern society and the human capacity to use numbers is unparalleled in other species. Understanding the mental and neural representations supporting this capacity is of central interest to cognitive psychology, neuroscience, and education. Embodied numerical cognition theory suggests that beyond the seemingly abstract symbols used to refer to numbers, their underlying meaning is deeply grounded in sensorimotor experiences, and that our specific understanding of numerical information is shaped by actions related to our fingers, egocentric space, and experiences with magnitudes in everyday life. We propose a sensorimotor perspective on numerical cognition in which number comprehension and numerical proficiency emerge from grounding three distinct numerical core concepts: magnitude, ordinality, and cardinality.

Evaluation des bénéfices d’un dispositif d’entraînement à l’usage des doigts en mathématiques

Numerous studies have shown a significant positive relationship between the mental representation of hands in young children and their calculation performance. The literature indicates that certain components of manual motor skills may be critical to the quality of this relationship. The main objective of this study is to measure the benefit of an explicit training and teaching device for finger use in mathematics by measuring the initial motor imitation abilities of young children. A protocol of pretest, training, and post-test type was proposed to 101 children with an average age of 5 years and 3 months. Measurements focused on manual motor skills and arithmetical skills. The 12-week classroom-based device was designed to develop manual motor skills and explicitly teach finger use in mathematics. The results indicate that significant progress was made in arithmetic for the students who benefited from the training. Interestingly this progress is modulated by the children’s initial motor imitation skills. This contribution opens up new research and application perspectives on the relationships between mental motor imagery, fine motor skills, and arithmetic ability.

The Tools of Enculturation

We propose an account of cognitive tools that takes into account the process of enculturation by which tools are integrated into our cognitive systems. Drawing on work in cultural evolution and developmental psychology, we argue that cognitive tools are complex entities consisting of physical objects, representational systems, and cognitive practices for the physical manipulation of the tool. We use an extensive case study of spatial navigation to demonstrate the core claims. The account we provide is contrasted with conceptions of cognitive tools that simplify cognition, in particular that they offload cognitive work, or that the tools themselves are temporary developmental scaffolds or props. Enculturation results in transformed cognitive systems, and we can now think and act in new ways with cognitive tools.

Pedagogical Ecology for an Alternative Sustainability: With Insights from Francis of Assisi and Contemporary Life Sciences

Sustainability is a widely discussed issue nowadays. The “human factor” appears to be the key to a suitable theory of sustainable development and, even more, to understanding the real scope of the issue at stake. We begin by highlighting that the issue of sustainability and the related ecological crisis ultimately stem from the fundamental view of the human–environment relationships. We tackle such a fundamental view from two apparently distant but converging perspectives: the one of Francis of Assisi (the patron saint of ecologists) and the one of contemporary advancements in evolutionary biology known as the “extended evolutionary theory” (EES). This will allow us to highlight how current life sciences ground a strong form of organism–environment complementarity—a core point for any allegedly comprehensive approach to sustainability and ecology. After that, we focus on recent developments in cultural evolution studies that see culture both as the driving force of (recent) human evolution and as the general context where the human–environment relationships take place and develop. Therefore, we argue that the environment exerts a powerful pedagogical influence on the human being and on humanity as a whole. We conclude by proposing a pedagogical criterion for ecology and sustainable development, according to which the modifications caused by the human being to the environment must be assessed (also) for their pedagogical import.

Counting and the ontogenetic origins of exact equality

Humans are unique in their capacity to both represent number exactly and to express these representations symbolically. This correlation has prompted debate regarding whether symbolic number systems are necessary to represent large exact number. Previous work addressing this question in innumerate adults and semi-numerate children has been limited by conflicting results and differing methodologies, and has not yielded a clear answer. We address this debate by adapting methods used with innumerate populations (a "set-matching" task) for 3- to 5-year-old US children at varying stages of symbolic number acquisition. In five studies we find that children's ability to match sets exactly is related not simply to knowing the meanings of a few number words, but also to understanding how counting is used to generate sets (i.e., the cardinal principle). However, while children were more likely to match sets after acquiring the cardinal principle, they nevertheless demonstrated failures, compatible with the hypothesis that the ability to reason about exact equality emerges sometime later. These findings provide important data on the origin of exact number concepts, and point to knowledge of a counting system, rather than number language in general, as a key ingredient in the ability to reason about large exact number.

Finger-Counting and Numerical Structure

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

An immersive first-person navigation task for abstract knowledge acquisition

Advances in virtual reality (VR) technology have greatly benefited spatial navigation research. By presenting space in a controlled manner, changing aspects of the environment one at a time or manipulating the gain from different sensory inputs, the mechanisms underlying spatial behaviour can be investigated. In parallel, a growing body of evidence suggests that the processes involved in spatial navigation extend to non-spatial domains. Here, we leverage VR technology advances to test whether participants can navigate abstract knowledge. We designed a two-dimensional quantity space-presented using a head-mounted display-to test if participants can navigate abstract knowledge using a first-person perspective navigation paradigm. To investigate the effect of physical movement, we divided participants into two groups: one walking and rotating on a motion platform, the other group using a gamepad to move through the abstract space. We found that both groups learned to navigate using a first-person perspective and formed accurate representations of the abstract space. Interestingly, navigation in the quantity space resembled behavioural patterns observed in navigation studies using environments with natural visuospatial cues. Notably, both groups demonstrated similar patterns of learning. Taken together, these results imply that both self-movement and remote exploration can be used to learn the relational mapping between abstract stimuli.

Numeral Systems Across Languages Support Efficient Communication: From Approximate Numerosity to Recursion

Languages differ qualitatively in their numeral systems. At one extreme, some languages have a small set of number terms, which denote approximate or inexact numerosities; at the other extreme, many languages have forms for exact numerosities over a very large range, through a recursively defined counting system. Why do numeral systems vary as they do? Here, we use computational analyses to explore the numeral systems of 30 languages that span this spectrum. We find that these numeral systems all reflect a functional need for efficient communication, mirroring existing arguments in other semantic domains such as color, kinship, and space. Our findings suggest that cross-language variation in numeral systems may be understood in terms of a shared functional need to communicate precisely while using minimal cognitive resources.

Metaphor and the Philosophical Implications of Embodied Mathematics

Embodied approaches to cognition see abstract thought and language as grounded in interactions between mind, body, and world. A particularly important challenge for embodied approaches to cognition is mathematics, perhaps the most abstract domain of human knowledge. Conceptual metaphor theory, a branch of cognitive linguistics, describes how abstract mathematical concepts are grounded in concrete physical representations. In this paper, we consider the implications of this research for the metaphysics and epistemology of mathematics. In the case of metaphysics, we argue that embodied mathematics is neutral in the sense of being compatible with all existing accounts of what mathematical entities really are. However, embodied mathematics may be able to revive an older position known as psychologism and overcome the difficulties it faces. In the case of epistemology, we argue that the evidence collected in the embodied mathematics literature is inconclusive: It does not show that abstract mathematical thinking is constituted by metaphor; it may simply show that abstract thinking is facilitated by metaphor. Our arguments suggest that closer interaction between the philosophy and cognitive science of mathematics could yield a more precise, empirically informed account of what mathematics is and how we come to have knowledge of it.

Processing of numerical representation of fingers depends on their location in space

Fingers can express quantities and thus contribute to the acquisition and manipulation of numbers as well as the development of arithmetical skills. As embodied entities, the processing of finger numerical configurations should, therefore, be facilitated when they match shared cultural representations and are presented close to the body. To investigate these issues, the present study investigated whether canonical finger configurations are processed faster than noncanonical configurations or spatially matched dot configurations, taking into account their location in the peripersonal or the extrapersonal space. Analysis of verbal responses to the enumeration of small and large numerosities showed that participants (N = 30) processed small numerosities faster than large ones and dots faster than finger configurations despite visuo-spatial matching. Canonical configurations were also processed faster than noncanonical configurations but for finger numerical stimuli only. Furthermore, the difference in response time between dots and fingers processing was greater when the stimuli were located in the peripersonal space than in the extrapersonal space. As a whole, the data suggest that, due to their motor nature, finger numerical configurations are not processed as simple visual stimuli but in relation to corporal and cultural counting habits, in agreement with the embodied framework of numerical cognition.

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.

Putting a Finger on Numerical Development - Reviewing the Contributions of Kindergarten Finger Gnosis and Fine Motor Skills to Numerical Abilities

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 Challenge of Modeling the Acquisition of Mathematical Concepts

As a full-blown research topic, numerical cognition is investigated by a variety of disciplines including cognitive science, developmental and educational psychology, linguistics, anthropology and, more recently, biology and neuroscience. However, despite the great progress achieved by such a broad and diversified scientific inquiry, we are still lacking a comprehensive theory that could explain how numerical concepts are learned by the human brain. In this perspective, I argue that computer simulation should have a primary role in filling this gap because it allows identifying the finer-grained computational mechanisms underlying complex behavior and cognition. Modeling efforts will be most effective if carried out at cross-disciplinary intersections, as attested by the recent success in simulating human cognition using techniques developed in the fields of artificial intelligence and machine learning. In this respect, deep learning models have provided valuable insights into our most basic quantification abilities, showing how numerosity perception could emerge in multi-layered neural networks that learn the statistical structure of their visual environment. Nevertheless, this modeling approach has not yet scaled to more sophisticated cognitive skills that are foundational to higher-level mathematical thinking, such as those involving the use of symbolic numbers and arithmetic principles. I will discuss promising directions to push deep learning into this uncharted territory. If successful, such endeavor would allow simulating the acquisition of numerical concepts in its full complexity, guiding empirical investigation on the richest soil and possibly offering far-reaching implications for educational practice.

What Early Sapiens Cognition Can Teach Us: Untangling Cultural Influences on Human Cognition Across Time

Evidence of cultural influences on cognition is accumulating, but untangling these cultural influences from one another or from non-cultural influences has remained a challenging task. As between-group differences are neither a sufficient nor a necessary indicator of cultural impact, cross-cultural comparisons in isolation are unable to furnish any cogent conclusions. This shortfall can be compensated by taking a diachronic perspective that focuses on the role of culture for the emergence and evolution of our cognitive abilities. Three strategies for reconstructing early human cognition are presented: the chaîne opératoire approach and its extension to brain-imaging studies, large-scale extrapolations, and phylogenetic comparative methods. While these strategies are reliant on our understanding of present-day cognition, they conversely also have the potential to advance this understanding in fundamental ways.

Writing in the air: Facilitative effects of finger writing in older adults

Kūsho, which refers to a behavior in which one moves the index finger as a substitute for a pen in the air or on a surface, mostly used when trying to recall the shape of a written character or the spelling of a word, has been known to facilitate cognitive task performance among kanji writing-system users. This study investigates whether the facilitative effect of kūsho, the existence of which has been exclusively confirmed in younger adults, is present in old age. Moreover, to further understand the interaction between finger movement and cognitive processing, we analyzed the correlation between the kūsho effect and factors such as age, mini-mental state examination (MMSE) score, and number of years of education. The kūsho effect was assessed by a task where participants mentally assembled a set of kanji subparts to form an actual character. The results showed a significant facilitative effect of kūsho and a strong negative correlation between kūsho effect and education. This study confirms the benefits of finger movement for solving cognitive tasks involving visual processing of written language among older adults and suggests the kūsho effect may be mediated by education.

Investigating the respective contribution of sensory modalities and spatial disposition in numerical training

Recent studies have suggested that multisensory redundancy may improve cognitive learning. According to this view, information simultaneously available across two or more modalities is highly salient and, therefore, may be learned and remembered better than the same information presented to only one modality. In the current study, we wanted to evaluate whether training arithmetic with a multisensory intervention could induce larger learning improvements than a visual intervention alone. Moreover, because a left-to-right-oriented mental number line was for a long time considered as a core feature of numerical representation, we also wanted to compare left-to-right-organized and randomly organized arithmetic training. Therefore, five training programs were created and called (a) multisensory linear, (b) multisensory random, (c) visual linear, (d) visual random, and (e) control. A total of 85 preschoolers were randomly assigned to one of these five training conditions. Whereas children were trained to solve simple addition and subtraction operations in the first four training conditions, story understanding was the focus of the control training. Several numerical tasks (arithmetic, number-to-position, number comparison, counting, and subitizing) were used as pre- and post-test measures. Although the effect of spatial disposition was not significant, results demonstrated that the multisensory training condition led to a significantly larger performance improvement than the visual training and control conditions. This result was specific to the trained ability (arithmetic) and is discussed in light of the multisensory redundancy hypothesis.

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.

The Enculturated Move From Proto-Arithmetic to Arithmetic

The basic human ability to treat quantitative information can be divided into two parts. With proto-arithmetical ability, based on the core cognitive abilities for subitizing and estimation, numerosities can be treated in a limited and/or approximate manner. With arithmetical ability, numerosities are processed (counted, operated on) systematically in a discrete, linear, and unbounded manner. In this paper, I study the theory of enculturation as presented by Menary (2015) as a possible explanation of how we make the move from the proto-arithmetical ability to arithmetic proper. I argue that enculturation based on neural reuse provides a theoretically sound and fruitful framework for explaining this development. However, I show that a comprehensive explanation must be based on valid theoretical distinctions and involve several stages in the development of arithmetical knowledge. I provide an account that meets these challenges and thus leads to a better understanding of the subject of enculturation.

The career of measurement

Units as they exist today are highly abstract. Meters, miles, and other modern measures have no obvious basis in tangible phenomena and can be applied broadly across domains. Historical examples suggest, however, that units have not always been so abstract. Here, we examine this issue systematically. We begin by analyzing linear measures in the Oxford English Dictionary (OED) and in an ethnographic database that spans 114 cultures (HRAF). Our survey of both datasets shows, first, that early length units have mostly come from concrete sources-body parts, artifacts, events, and other tangible phenomena-and, second, that they have often been tied to particular contexts. Measurement units have thus undergone a shift from highly concrete to highly abstract. How did this shift happen? Drawing on historical surveys and case studies-as well as data from the OED and HRAF-we next propose a reconstruction of how abstract units might have evolved gradually through a series of overlapping stages. We also consider the cognitive processes that underpin this evolution-in particular, comparison. Finally, we discuss the cognitive origins of units. Units are not only slow to emerge historically, they are also slow to be acquired developmentally, and mastering them appears to have cognitive consequences. Taken together, these observations suggest that units are not inevitable intuitions, but are best thought of as culturally evolved cognitive tools. By analyzing the career of measurement in detail, we illustrate how such tools-abstract as they are today-can arise from concrete, often bodily origins.

Number gestures predict learning of number words

When asked to explain their solutions to a problem, children often gesture and, at times, these gestures convey information that is different from the information conveyed in speech. Children who produce these gesture-speech "mismatches" on a particular task have been found to profit from instruction on that task. We have recently found that some children produce gesture-speech mismatches when identifying numbers at the cusp of their knowledge, for example, a child incorrectly labels a set of two objects with the word "three" and simultaneously holds up two fingers. These mismatches differ from previously studied mismatches (where the information conveyed in gesture has the potential to be integrated with the information conveyed in speech) in that the gestured response contradicts the spoken response. Here, we ask whether these contradictory number mismatches predict which learners will profit from number-word instruction. We used the Give-a-Number task to measure number knowledge in 47 children (Mage  = 4.1 years, SD = 0.58), and used the What's on this Card task to assess whether children produced gesture-speech mismatches above their knower level. Children who were early in their number learning trajectories ("one-knowers" and "two-knowers") were then randomly assigned, within knower level, to one of two training conditions: a Counting condition in which children practiced counting objects; or an Enriched Number Talk condition containing counting, labeling set sizes, spatial alignment of neighboring sets, and comparison of these sets. Controlling for counting ability, we found that children were more likely to learn the meaning of new number words in the Enriched Number Talk condition than in the Counting condition, but only if they had produced gesture-speech mismatches at pretest. The findings suggest that numerical gesture-speech mismatches are a reliable signal that a child is ready to profit from rich number instruction and provide evidence, for the first time, that cardinal number gestures have a role to play in number-learning.

Scanning of speechless comics changes spatial biases in mental model construction

The mental representation of both time and number shows lateral spatial biases, which can be affected by habitual reading and writing direction. However, this effect is in place before children begin to read. One potential early cause is the experiences of looking at picture books together with a carer, as those images also follow the directionality of the script. What is the underlying mechanism for this effect? In the present study, we test the possibility that such experiences induce spatial biases in mental model construction, a mechanism which is a good candidate to induce the biases observed with numbers and times. We presented a speechless comic in either standard (left-to-right) or mirror-reversed (right-to-left) form to adult Spanish participants. We then asked them to draw the scene depicted by sentences like 'the square is between the cross and the circle'. The position of the lateral objects in these drawings reveals the spatial biases at work when building mental models in working memory. Under conditions of highly consistent directionality, the mirror comic changed pre-existing lateral biases. Processes of mental model construction in working memory stand as a potential mechanism for the generation of spatial biases for time and number.This article is part of the theme issue 'Varieties of abstract concepts: development, use and representation in the brain'.

Variability in the Alignment of Number and Space Across Languages and Tasks

While the domains of space and number appear to be linked in human brains and minds, their conceptualization still differs across languages and cultures. For instance, frames of reference for spatial descriptions vary according to task, context, and cultural background, and the features of the mental number line depend on formal education and writing direction. To shed more light on the influence of culture/language and task on such conceptualizations, we conducted a large-scale survey with speakers of five languages that differ in writing systems, preferences for spatial and temporal representations, and/or composition of number words. Here, we report data obtained from tasks on ordered arrangements, including numbers, letters, and written text. Comparing these data across tasks, domains, and languages indicates that, even within a single domain, representations may differ depending on task characteristics, and that the degree of cross-domain alignment varies with domains and culture.

Cognitive Development Is a Reconstruction Process that May Follow Different Pathways: The Case of Number

Some cognitive functions shared by humans and certain animals were acquired early in the course of phylogeny and, in humans, are operational in their primitive form shortly after birth. This is the case for the quantification of discrete objects. The further phylogenetic evolution of the human brain allows such functions to be reconstructed in a much more sophisticated way during child development. Certain functional characteristics of the brain (plasticity, multiple cognitive processes involved in the same response, interactions, and substitution relationships between those processes) provide degrees of freedom that open up the possibility of different pathways of reconstruction. The within- and between-individual variability of these developmental pathways offers an original window on the dynamics of development. Here, I will illustrate this theoretical approach to cognitive development-which can be called "reconstructivist" and "pluralistic"-using children's construction of number as an example.

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.

Current Perspectives on Cognitive Diversity

To what extent is cognition influenced by a person’s cultural background? This question has remained controversial in large fields of the cognitive sciences, including cognitive psychology, and is also underexplored in anthropology. In this perspective article, findings from a recent wave of cross-cultural studies will be outlined with respect to three aspects of cognition: perception and categorization, number representation and counting, and explanatory frameworks and beliefs. Identifying similarities and differences between these domains allows for general conclusions regarding cognitive diversity and helps to highlight the importance of culturally shaped content for a comprehensive understanding of cognition.

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.