Number as a cognitive technology: Evidence from Pirahã language and cognition

Time Tools

Many core human activities require an understanding of time. To coordinate rituals, plan harvests and hunts, recall histories, keep appointments, and follow recipes, we need to grapple with invisible temporal structures like durations, sequences, and cycles. No other species seems to do this. But it is not a capacity we humans have because we developed special neural equipment over biological evolution. We have it because we developed concepts, practices, and artifacts to help us-in short, because we developed time tools. The overarching function of such tools is that they render time more concrete: they identify structure in the flow of experience and make that structure available to the senses. By concretizing time in this way, these tools serve a range of practical purposes, from tallying and measuring, to coordinating and predicting, to remembering and reasoning. Beyond their practical utility, time tools have further consequences, too: they reverberate through cognition and culture, and ultimately reshape our understanding of what time is.

Sources of variation in preschoolers' relational reasoning: The interaction between language use and working memory

Previous research has suggested the importance of relational language and working memory in children's relational reasoning. The tendency to use language (e.g., using more relational than object-focused language, prioritizing focal objects over background in linguistic descriptions) could reflect children's biases toward the relational versus object-based solutions in a relational match-to-sample (RMTS) task. In the lack of any apparent object match as a foil option, object-focused children might rely on other cognitive mechanisms (i.e., working memory) to choose a relational match in the RMTS task. The current study examined the interactive roles of language- and working memory-related sources of variation in Turkish-learning preschoolers' relational reasoning. We collected data from 4- and 5-year-olds (N = 41) via Zoom in the RMTS task, a scene description task, and a backward word span task. Generalized binomial mixed effects models revealed that children who used more relational language and background-focused scene descriptions performed worse in the relational reasoning task. Furthermore, children with less frequent relational language use and focal object descriptions of the scenes benefited more from working memory to succeed in the relational reasoning task. These results suggest additional working memory demands for object-focused children to choose relational matches in the RMTS task, highlighting the importance of examining the interactive effects of different cognitive mechanisms on relational reasoning.

What the Science of Learning Teaches Us About Arithmetic Fluency

High-quality mathematics education not only improves life outcomes for individuals but also drives innovation and progress across society. But what exactly constitutes high-quality mathematics education? In this article, we contribute to this discussion by focusing on arithmetic fluency. The debate over how best to teach arithmetic has been long and fierce. Should we emphasize memorization techniques such as flashcards and timed drills or promote "thinking strategies" via play and authentic problem solving? Too often, recommendations for a "balanced" approach lack the depth and specificity needed to effectively guide educators or inform public understanding. Here, we draw on developmental cognitive science, particularly Sfard's process-object duality and Karmiloff-Smith's implicit-explicit knowledge continuum, to present memorization and thinking strategies not as opposing methods but as complementary forces. This framework enables us to offer specific recommendations for fostering arithmetic fluency based on the science of learning. We define arithmetic fluency, provide evidence on its importance, describe the cognitive structures and processes supporting it, and share evidence-based guidance for promoting it. Our recommendations include progress monitoring for early numeracy, providing explicit instruction to teach important strategies and concepts, implementing well-structured retrieval practice, introducing time-limited practice only after students demonstrate accuracy, and allocating sufficient time for discussion and cognitive reflection. By blending theory, evidence, and practical advice, we equip educators and policymakers with the knowledge needed to ensure all children have access to the opportunities needed to achieve arithmetic fluency.

The calculating brain

The human brain possesses neural networks and mechanisms enabling the representation of numbers, basic arithmetic operations, and mathematical reasoning. Without the ability to represent numerical quantity and perform calculations, our scientifically and technically advanced culture would not exist. However, the origins of numerical abilities are grounded in an intuitive understanding of quantity deeply rooted in biology. Nevertheless, more advanced symbolic arithmetic skills require a cultural background with formal mathematical education. In the past two decades, cognitive neuroscience has seen significant progress in understanding the workings of the calculating brain through various methods and model systems. This review begins by exploring the mental and neuronal representations of nonsymbolic numerical quantity and then progresses to symbolic representations acquired in childhood. During arithmetic operations (addition, subtraction, multiplication, and division), these representations are processed and transformed according to arithmetic rules and principles, leveraging different mental strategies and types of arithmetic knowledge that can be dissociated in the brain. Although it was once believed that number processing and calculation originated from the language faculty, it is now evident that mathematical and linguistic abilities are primarily processed independently in the brain. Understanding how the healthy brain processes numerical information is crucial for gaining insights into debilitating numerical disorders, including acquired conditions like acalculia and learning-related calculation disorders such as developmental dyscalculia.

Dedicated comparatives aid comparisons of magnitude: a study with Pitjantjatjara-English bilinguals

When expressing comparisons of magnitude, Pitjantjatjara, a language indigenous to the land now known as Australia, employs contextually driven comparators (e.g., Anyupa is tall. Uma is short) rather than a dedicated morphological or syntactic comparative construction (e.g., Anyupa is taller than Uma). Pitjantjatjara also has a small number of lexicalized numerals, employing 'one', 'two', 'three', then 'many'. It is hypothesized that having dedicated comparatives in language and elaborated number systems aid comparisons of magnitudes. Fluent Pitjantjatjara-English bilinguals participated in tasks assessing their accuracy and reaction times when comparing two types of magnitude: numerosity (quantities of dots), and extent (line lengths). They repeated the comparisons in both languages on different days, allowing for the effect of language being spoken on responses to be assessed. No differences were found for numerosity; however, participants were less accurate when making comparisons of extent using Pitjantjatjara. Accuracy when using Pitjantjatjara decreased as the magnitude of the comparison increased and as differences between the comparators decreased. This result suggests a potential influence of linguistic comparison strategy on comparison behavior.

Recruitment of magnitude representations to understand graded words

Language understanding and mathematics understanding are two fundamental forms of human thinking. Prior research has largely focused on the question of how language shapes mathematical thinking. The current study considers the converse question. Specifically, it investigates whether the magnitude representations that are thought to anchor understanding of number are also recruited to understand the meanings of graded words. These are words that come in scales (e.g., Anger) whose members can be ordered by the degree to which they possess the defining property (e.g., calm, annoyed, angry, furious). Experiment 1 uses the comparison paradigm to find evidence that the distance, ratio, and boundary effects that are taken as evidence of the recruitment of magnitude representations extend from numbers to words. Experiment 2 uses a similarity rating paradigm and multi-dimensional scaling to find converging evidence for these effects in graded word understanding. Experiment 3 evaluates an alternative hypothesis - that these effects for graded words simply reflect the statistical structure of the linguistic environment - by using machine learning models of distributional word semantics: LSA, word2vec, GloVe, counterfitted word vectors, BERT, RoBERTa, and GPT-2. These models fail to show the full pattern of effects observed of humans in Experiment 2, suggesting that more is needed than mere statistics. This research paves the way for further investigations of the role of magnitude representations in sentence and text comprehension, and of the question of whether language understanding and number understanding draw on shared or independent magnitude representations. It also informs the role of machine learning models in cognitive psychology research.

Language is primarily a tool for communication rather than thought

Language is a defining characteristic of our species, but the function, or functions, that it serves has been debated for centuries. Here we bring recent evidence from neuroscience and allied disciplines to argue that in modern humans, language is a tool for communication, contrary to a prominent view that we use language for thinking. We begin by introducing the brain network that supports linguistic ability in humans. We then review evidence for a double dissociation between language and thought, and discuss several properties of language that suggest that it is optimized for communication. We conclude that although the emergence of language has unquestionably transformed human culture, language does not appear to be a prerequisite for complex thought, including symbolic thought. Instead, language is a powerful tool for the transmission of cultural knowledge; it plausibly co-evolved with our thinking and reasoning capacities, and only reflects, rather than gives rise to, the signature sophistication of human cognition.

The language network as a natural kind within the broader landscape of the human brain

Language behaviour is complex, but neuroscientific evidence disentangles it into distinct components supported by dedicated brain areas or networks. In this Review, we describe the 'core' language network, which includes left-hemisphere frontal and temporal areas, and show that it is strongly interconnected, independent of input and output modalities, causally important for language and language-selective. We discuss evidence that this language network plausibly stores language knowledge and supports core linguistic computations related to accessing words and constructions from memory and combining them to interpret (decode) or generate (encode) linguistic messages. We emphasize that the language network works closely with, but is distinct from, both lower-level - perceptual and motor - mechanisms and higher-level systems of knowledge and reasoning. The perceptual and motor mechanisms process linguistic signals, but, in contrast to the language network, are sensitive only to these signals' surface properties, not their meanings; the systems of knowledge and reasoning (such as the system that supports social reasoning) are sometimes engaged during language use but are not language-selective. This Review lays a foundation both for in-depth investigations of these different components of the language processing pipeline and for probing inter-component interactions.

Nameability supports rule-based category learning in children and adults

The present study tested the hypothesis that verbal labels support category induction by providing compact hypotheses. Ninety-seven 4- to 6-year-old children (M = 63.2 months; 46 female, 51 male; 77% White, 8% more than one race, 4% Asian, and 3% Black; tested 2018) and 90 adults (M = 20.1 years; 70 female, 20 male) in the Midwestern United States learned novel categories with features that were easy (e.g., "red") or difficult (e.g., "mauve") to name. Adults (d = 1.06) and-to a lesser extent-children (d = 0.57; final training block) learned categories composed of more nameable features better. Children's knowledge of difficult-to-name color words predicted their learning for categories with difficult-to-name features. Rule-based category learning may be supported by the emerging ability to form verbal hypotheses.

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.

Local similarity and global variability characterize the semantic space of human languages

How does meaning vary across the world's languages? Scholars recognize the existence of substantial variability within specific domains, ranging from nature and color to kinship. The emergence of large language models enables a systems-level approach that directly characterizes this variability through comparison of word organization across semantic domains. Here, we show that meanings across languages manifest lower variability within semantic domains and greater variability between them, using models trained on both 1) large corpora of native language text comprising Wikipedia articles in 35 languages and also 2) Test of English as a Foreign Language (TOEFL) essays written by 38,500 speakers from the same native languages, which cluster into semantic domains. Concrete meanings vary less across languages than abstract meanings, but all vary with geographical, environmental, and cultural distance. By simultaneously examining local similarity and global difference, we harmonize these findings and provide a description of general principles that govern variability in semantic space across languages. In this way, the structure of a speaker's semantic space influences the comparisons cognitively salient to them, as shaped by their native language, and suggests that even successful bilingual communicators likely think with "semantic accents" driven by associations from their native language while writing English. These findings have dramatic implications for language education, cross-cultural communication, and literal translations, which are impossible not because the objects of reference are uncertain, but because associations, metaphors, and narratives interlink meanings in different, predictable ways from one language to another.

Characterizing exact arithmetic abilities before formal schooling

Children appear to have some arithmetic abilities before formal instruction in school, but the extent of these abilities as well as the mechanisms underlying them are poorly understood. Over two studies, an initial exploratory study of preschool children in the U.S. (N = 207; Age = 2.89-4.30 years) and a pre-registered replication of preschool children in Italy (N = 130; Age = 3-6.33 years), we documented some basic behavioral signatures of exact arithmetic using a non-symbolic subtraction task. Furthermore, we investigated the underlying mechanisms by analyzing the relationship between individual differences in exact subtraction and assessments of other numerical and non-numerical abilities. Across both studies, children performed above chance on the exact non-symbolic arithmetic task, generally showing better performance on problems involving smaller quantities compared to those involving larger quantities. Furthermore, individual differences in non-verbal approximate numerical abilities and exact cardinal number knowledge were related to different aspects of subtraction performance. Specifically, non-verbal approximate numerical abilities were related to subtraction performance in older but not younger children. Across both studies we found evidence that cardinal number knowledge was related to performance on subtraction problems where the answer was zero (i.e., subtractive negation problems). Moreover, subtractive negation problems were only solved above chance by children who had a basic understanding of cardinality. Together these finding suggest that core non-verbal numerical abilities, as well as emerging knowledge of symbolic numbers provide a basis for some, albeit limited, exact arithmetic abilities before formal schooling.

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.

Directionality in the interrelations between approximate number, verbal number, and mathematics in preschool-aged children

A fundamental question in numerical development concerns the directional relation between an early-emerging non-verbal approximate number system (ANS) and culturally acquired verbal number and mathematics knowledge. Using path models on longitudinal data collected in preschool children (M_age  = 3.86 years; N = 216; 99 males; 80.8% White; 10.8% Multiracial, 3.8% Latino; 1.9% Black; collected 2013-2017) over 1 year, this study showed that earlier verbal number knowledge was associated with later ANS precision (average β = .32), even after controlling for baseline differences in numerical, general cognitive, and language abilities. In contrast, earlier ANS precision was not associated with later verbal number knowledge (β = -.07) or mathematics abilities (average β = .10). These results suggest that learning about verbal numbers is associated with a sharpening of pre-existing non-verbal numerical abilities.

The plural counts: Inconsistent grammatical number hinders numerical development in preschoolers - A cross-linguistic study

The role of grammar in numerical development, and particularly the role of grammatical number inflection, has already been well-documented in toddlerhood. It is unclear, however, whether the influence of grammatical language structure further extends to more complex later stages of numerical development. Here, we addressed this question by exploiting differences between Polish, which has a complex grammatical number paradigm, leading to a partially inconsistent mapping between numerical quantities and grammatical number, and German, which has a comparatively easy verbal paradigm: 151 Polish-speaking and 123 German-speaking kindergarten children were tested using a symbolic numerical comparison task. Additionally, counting skills (Give-a-Number and count-list), and mapping between non-symbolic (dot sets) and symbolic representations of numbers, as well as working memory (Corsi blocks and Digit span) were assessed. Based on the Give-a-Number and mapping tasks, the children were divided into subset-knowers, CP-knowers-non-mappers, and CP-knowers-mappers. Linguistic background was related to performance in several ways: Polish-speaking children expectedly progressed to the CP-knowers stage later than German children, despite comparable non-numerical capabilities, and even after this stage was achieved, they fared worse in the numerical comparison task. There were also meaningful differences in spatial-numerical mapping between the Polish and German groups. Our findings are in line with the theory that grammatical number paradigms influence. the development of representations and processing of numbers, not only at the stage of acquiring the meaning of the first number-words but at later stages as well, when dealing with symbolic numbers.

Embodiment and repeated exposure do not suffice for abstract concepts acquisition: evidence from tonal music cognition

Research on abstract concepts (AC) suggests that while some AC are enacted indirectly and occasionally, others are largely grounded in our sensory-motor and affective experience, and the opportunities to enact them are countless, which would allow us to acquire them without supervision. From this, the following question arises: do embodiment and repeated exposure suffice to dispense with supervision in abstract concepts acquisition (ACA)? In the present study, this question was addressed in the context of tonal music cognition, which demands a high level of abstraction, and via musical materials that participants had frequently heard and sung. Specifically, highly trained, moderately trained, and untrained participants (24 each) were given 12 well-known melodic fragments ending on tones instantiating 6 different scale degrees (2 times each) and asked to group (round 1) or pair (round 2) those fragments whose last tone conveyed the same (or a similar enough) level of stability or rest. If embodiment and repeated exposure suffice for ACA, then one would expect a scale degree-based grouping strategy regardless of participants' training level. Results showed that only highly trained participants systematically grouped stimuli ending on the same scale degree, particularly in round 2; moderately trained participants' performance was mixed, and tonality's influence on untrained participants was negligible. Further, moderately trained and untrained participants performed inconsistently, discarding in round 2 almost all of the pairs formed in round 1. These findings are integrated with previous findings on the effect of language, affect, and category type on conceptualization to account for why and when ACA requires supervision.

Language as a mechanism for reasoning about possibilities

The ability to entertain and reflect on possibilities is a crucial component of human reasoning. However, the origin of this reasoning-whether it is language-based or not-is highly debated. We contribute to this debate by investigating the relation between language and thought in the domain of possibility from a developmental perspective. Our investigation focuses on disjunctive syllogism, a specific type of possibility reasoning that has been explored extensively in the developmental literature and has clear linguistic correlates. Seeking links between conceptual and linguistic representations, we review evidence on how children reason by the disjunctive syllogism and how they acquire logical and modal language. We sketch a proposal for how language and thought interact during development. This article is part of the theme issue 'Thinking about possibilities: mechanisms, ontogeny, functions and phylogeny'.

Aprendizaje del conteo y los números naturales en preescolar: una revisión sistemática de la literatura

Aprender a contar cantidades discretas de forma exacta constituye uno de los primeros hitos del desarrollo del conocimiento matemático infantil. En los últimos años, ha habido un extenso debate en torno a cómo ocurre este proceso de aprendizaje en preescolar. La actual investigación tuvo como objetivo conocer las temáticas y preguntas de investigación generales desarrolladas en los últimos cinco años en cuanto al aprendizaje del conteo y los números naturales en preescolar. Para ello, se realizó una revisión sistemática en la que se hizo una indagación en las bases de datos ScienceDirect, EBSCO, Web of Science, SpringerLink, JSTOR y Sage. Se obtuvieron 98 artículos de investigación que fueron examinados mediante análisis de conglomerados y mapas jerárquicos a través de NVIVO 11.0.  Se encontraron cuatro núcleos temáticos (Ideas sobre los procesos cognitivos implicados en la comprensión del número, Representación de magnitudes numéricas, Intervenciones para favorecer el desarrollo de habilidades matemáticas y Aspectos estructurales del número), que muestran el panorama actual de investigación sobre aprendizaje del conteo. Los resultados de este estudio son importantes para delimitar posibles programas futuros de investigación, y pueden ser usados por docentes como insumo para enriquecer los ambientes de aprendizaje de sus aulas de clase.

Reduced choice-confidence in negative numerals

Negative numbers are central in math. However, they are abstract, hard to learn, and manipulated slower than positive numbers regardless of math ability. It suggests that confidence, namely the post-decision estimate of being correct, should be lower than positives. We asked participants to pick the larger single-digit numeral in a pair and collected their implicit confidence with button pressure (button pressure was validated with three empirical signatures of confidence). We also modeled their choices with a drift-diffusion decision model to compute the post-decision estimate of being correct. We found that participants had relatively low confidence with negative numerals. Given that participants compared with high accuracy the basic base-10 symbols (0–9), reduced confidence may be a general feature of manipulating abstract negative numerals as they produce more uncertainty than positive numerals per unit of time.

Verbal counting and the timing of number acquisition in an indigenous Amazonian group

Children in industrialized cultures typically succeed on Give-N, a test of counting ability, by age 4. On the other hand, counting appears to be learned much later in the Tsimane’, an indigenous group in the Bolivian Amazon. This study tests three hypotheses for what may cause this difference in timing: (a) Tsimane’ children may be shy in providing behavioral responses to number tasks, (b) Tsimane’ children may not memorize the verbal list of number words early in acquisition, and/or (c) home environments may not support mathematical learning in the same way as in US samples, leading Tsimane’ children to primarily acquire mathematics through formalized schooling. Our results suggest that most of our subjects are not inhibited by shyness in responding to experimental tasks. We also find that Tsimane’ children (N = 100, ages 4-11) learn the verbal list later than US children, but even upon acquiring this list, still take time to pass Give-N tasks. We find that performance in counting varies across tasks and is related to formal schooling. These results highlight the importance of formal education, including instruction in the count list, in learning the meanings of the number words.

When multiplying is meaningful in memory: Electrophysiological signature of the problem size effect in children

Children are less fluent at verifying the answers to larger single-digit arithmetic problems compared with smaller ones. This problem size effect may reflect the structure of memory for arithmetic facts. In the current study, typically developing third to fifth graders judged the correctness of single-digit multiplication problems, presented as a sequence of three digits, that were either small (e.g., 4 3 12 vs. 4 3 16) or large (e.g., 8 7 56 vs. 8 7 64). We measured the N400, an index of access to semantic memory, along with accuracy and response time. The N400 was modulated by problem size only for correct solutions, with larger amplitude for large problems than for small problems. This suggests that only solutions that exist in memory (i.e., correct solutions) reflect a modulation of semantic access likely based on the relative frequency of encountering small versus large problems. The absence of an N400 problem size effect for incorrect solutions suggests that the behavioral problem size effects were not due to differences in initial access to memory but instead were due to a later stage of cognitive processing that was reflected in a post-N400 main effect of problem size. A second post-N400 main effect of correctness at occipital electrodes resembles the beginning of an adult-like brain response observed in prior studies. In sum, event-related brain potentials revealed different cognitive processes for correct and incorrect solutions. These results allude to a gradual transition to an adult-like brain response, from verifying multiplication problems using semantic memory to doing so using more automatic categorization.

The development of early numeracy in deaf and hard of hearing children acquiring spoken language

Most deaf and hard-of-hearing (DHH) children are born to hearing parents and steered toward spoken rather than signed language, introducing a delay in language access. This study investigated the effects of this delay on number acquisition. DHH children (N = 44, mean_age  = 58 months, 21F, >50% White) and typically-hearing (TH) children (N = 79, mean_age  = 49 months, 51F, >50% White) were assessed on number and language in 2011-13. DHH children showed similar trajectories to TH children but delayed timing; a binary logistic regression showed that the odds of being a cardinal-principle (CP) knower were 17 times higher for TH children than DHH children, controlling for age (d = .69). Language fully mediated the association between deaf/hearing group and number knowledge, suggesting that language access sets the pace for number acquisition.

When eleven does not equal 11: Investigating exactness at a number's upper bound

The approximate number system (a) views number as an imprecise signal that (b) functions equivalently regardless of a number's initial presentation. These features do not readily account for exact readings when a task calls for them. While profiting from insights in areas neighboring the number cognition literature, we propose that linguistic-pragmatic and cultural pressures operate on a number's upper bound in order to provide exact readings. With respect to (a), Experimental Pragmatic findings indicate that numbers appear to be semantically lower-bounded (Eleven candidates are coming means at least eleven) but fluid at its upper-bound; exactly readings emerge as a consequence of an additional pragmatic process that solidifies the upper bound. With respect to (b), studies from cognitive anthropology underline how symbolic representations of number are distinct from written codes. Here, we investigate a novel hypothesis proposing that symbolic expressions of number (such as "11") explicitly provide exactly readings unlike verbal (oral and written) ones, which engender at least readings. We then employ a Numerical Magnitude Task (NMT), in which French-speaking participants determine whether a presented number is lesser or greater than a benchmark (12) in one of three presentation conditions: i) Symbolic/Hindu-Arabic (e.g. "11" via screen), ii) Oral (e.g. "/'on.zə/" via headphones), or; iii) spelled-out-in-Letters (e.g. "onze" via screen). Participants also carry out a Number Identification Task (NIT) so that each participant's recognition speed per number can be removed from their NMT times. We report that decision reaction times to "onze" take longer to process (and prompt more errors) than "treize" whereas "11" and "13" are comparable. One prediction was not supported: Decision times to the critical oral forms ("/'on.zə/" and "[tʁ̥ɛːzə̆]") were comparable, making these outcomes resonate with those in the Symbolic condition.

Exact Number Concepts Are Limited to the Verbal Count Range

Previous findings suggest that mentally representing exact numbers larger than four depends on a verbal count routine (e.g., "one, two, three . . ."). However, these findings are controversial because they rely on comparisons across radically different languages and cultures. We tested the role of language in number concepts within a single population-the Tsimane' of Bolivia-in which knowledge of number words varies across individual adults. We used a novel data-analysis model to quantify the point at which participants (N = 30) switched from exact to approximate number representations during a simple numerical matching task. The results show that these behavioral switch points were bounded by participants' verbal count ranges; their representations of exact cardinalities were limited to the number words they knew. Beyond that range, they resorted to numerical approximation. These results resolve competing accounts of previous findings and provide unambiguous evidence that large exact number concepts are enabled by language.

Superior verbal but not nonverbal memory in congenital blindness

Previous studies suggest that people who are congenitally blind outperform sighted people on some memory tasks. Whether blindness-associated memory advantages are specific to verbal materials or are also observed with nonverbal sounds has not been determined. Congenitally blind individuals (n = 20) and age and education matched blindfolded sighted controls (n = 22) performed a series of auditory memory tasks. These included: verbal forward and backward letter spans, a complex letter span with intervening equations, as well as two matched recognition tasks: one with verbal stimuli (i.e., letters) and one with nonverbal complex meaningless sounds. Replicating previously observed findings, blind participants outperformed sighted people on forward and backward letter span tasks. Blind participants also recalled more letters on the complex letter span task despite the interference of intervening equations. Critically, the same blind participants showed larger advantages on the verbal as compared to the nonverbal recognition task. These results suggest that blindness selectively enhances memory for verbal material. Possible explanations for blindness-related verbal memory advantages include blindness-induced memory practice and 'visual' cortex recruitment for verbal processing.

Children's attention to numerical quantities relates to verbal number knowledge: An introduction to the Build-A-Train task

Which dimension of a set of objects is more salient to young children: number or size? The 'Build-A-Train' task was developed and used to examine whether children spontaneously use a number or physical size approach on an un-cued matching task. In the Build-A-Train task, an experimenter assembles a train using one to five blocks of a particular length and asks the child to build the same train. The child's blocks differ in length from the experimenter's blocks, causing the child to build a train that matches based on either the number of blocks or length of the train, as it is not possible to match on both. One hundred and nineteen children between 2 years 2 months and 6 years 0 months of age (M = 4.05, SD = 0.84) completed the Build-A-Train task, and the Give-a-Number task, a classic task used to assess children's conceptual knowledge of verbal number words. Across train lengths and verbal number knowledge levels, children used a number approach more than a size approach on the Build-A-Train task. However, children were especially likely to use a number approach over a size approach when they knew the verbal number word that corresponded to the quantity of blocks in the train, particularly for quantities smaller than four. Therefore, children's attention to number relates to their knowledge of verbal number words. The Build-A-Train task and findings from the current study set a foundation for future longitudinal research to investigate the causal relationship between children's acquisition of symbolic mathematical concepts and attention to number.

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.

Testing the role of symbols in preschool numeracy: An experimental computer-based intervention study

Numeracy is of critical importance for scholastic success and modern-day living, but the precise mechanisms that drive its development are poorly understood. Here we used novel experimental training methods to begin to investigate the role of symbols in the development of numeracy in preschool-aged children. We assigned pre-school children in the U.S. and Italy (N = 215; Mean age = 49.15 months) to play one of five versions of a computer-based numerical comparison game for two weeks. The different versions of the game were equated on basic features of gameplay and demands but systematically varied in numerical content. Critically, some versions included non-symbolic numerical comparisons only, while others combined non-symbolic numerical comparison with symbolic aids of various types. Before and after training we assessed four components of early numeracy: counting proficiency, non-symbolic numerical comparison, one-to-one correspondence, and arithmetic set transformation. We found that overall children showed improvement in most of these components after completing these short trainings. However, children trained on numerical comparisons with symbolic aids made larger gains on assessments of one-to-one correspondence and arithmetic transformation compared to children whose training involved non-symbolic numerical comparison only. Further exploratory analyses suggested that, although there were no major differences between children trained with verbal symbols (e.g., verbal counting) and non-verbal visuo-spatial symbols (i.e., abacus counting), the gains in one-to-one correspondence may have been driven by abacus training, while the gains in non-verbal arithmetic transformations may have been driven by verbal training. These results provide initial evidence that the introduction of symbols may contribute to the emergence of numeracy by enhancing the capacity for thinking about exact equality and the numerical effects of set transformations. More broadly, this study provides an empirical basis to motivate further focused study of the processes by which children’s mastery of symbols influences children’s developing mastery of numeracy.

Nonhuman and Nonhuman-Human Communication: Some Issues and Questions

Deciphering nonhuman communication – particularly nonhuman vocal communication – has been a longstanding human quest. We are, for example, fascinated by the songs of birds and whales, the grunts of apes, the barks of dogs, and the croaks of frogs; we wonder about their potential meaning and their relationship to human language. Do these utterances express little more than emotional states, or do they convey actual bits and bytes of concrete information? Humans’ numerous attempts to decipher nonhuman systems have, however, progressed slowly. We still wonder why only a small number of species are capable of vocal learning, a trait that, because it allows for innovation and adaptation, would seem to be a prerequisite for most language-like abilities. Humans have also attempted to teach nonhumans elements of our system, using both vocal and nonvocal systems. The rationale for such training is that the extent of success in instilling symbolic reference provides some evidence for, at the very least, the cognitive underpinnings of parallels between human and nonhuman communication systems. However, separating acquisition of reference from simple object-label association is not a simple matter, as reference begins with such associations, and the point at which true reference emerges is not always obvious. I begin by discussing these points and questions, predominantly from the viewpoint of someone studying avian abilities. I end by examining the question posed by Premack: do nonhumans that have achieved some level of symbolic reference then process information differently from those that have not? I suggest the answer is likely “yes,” giving examples from my research on Grey parrots (Psittacus erithacus).

Psychology Within and Without the State

Psychological research in small-scale societies is crucial for what it stands to tell us about human psychological diversity. However, people in these communities, typically Indigenous communities in the global South, have been underrepresented and sometimes misrepresented in psychological research. Here I discuss the promises and pitfalls of psychological research in these communities, reviewing why they have been of interest to social scientists and how cross-cultural comparisons have been used to test psychological hypotheses. I consider factors that may be undertheorized in our research, such as political and economic marginalization, and how these might influence our data and conclusions. I argue that more just and accurate representation of people from small-scale communities around the world will provide us with a fuller picture of human psychological similarity and diversity, and it will help us to better understand how this diversity is shaped by historical and social processes. Expected final online publication date for the Annual Review of Psychology, Volume 73 is January 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Space in Hand and Mind: Gesture and Spatial Frames of Reference in Bilingual Mexico

Speakers of many languages prefer allocentric frames of reference (FoRs) when talking about small-scale space, using words like "east" or "downhill." Ethnographic work has suggested that this preference is also reflected in how such speakers gesture. Here, we investigate this possibility with a field experiment in Juchitán, Mexico. In Juchitán, a preferentially allocentric language (Isthmus Zapotec) coexists with a preferentially egocentric one (Spanish). Using a novel task, we elicited spontaneous co-speech gestures about small-scale motion events (e.g., toppling blocks) in Zapotec-dominant speakers and in balanced Zapotec-Spanish bilinguals. Consistent with prior claims, speakers' spontaneous gestures reliably reflected either an egocentric or allocentric FoR. The use of the egocentric FoR was predicted-not by speakers' dominant language or the language they used in the task-but by mastery of words for "right" and "left," as well as by properties of the event they were describing. Additionally, use of the egocentric FoR in gesture predicted its use in a separate nonlinguistic memory task, suggesting a cohesive cognitive style. Our results show that the use of spatial FoRs in gesture is pervasive, systematic, and shaped by several factors. Spatial gestures, like other forms of spatial conceptualization, are thus best understood within broader ecologies of communication and cognition.

Emergent Morphology in Child Homesign: Evidence from Number Language

Human languages, signed and spoken, can be characterized by the structural patterns they use to associate communicative forms with meanings. One such pattern is paradigmatic morphology, where complex words are built from the systematic use and re-use of sub-lexical units. Here, we provide evidence of emergent paradigmatic morphology akin to number inflection in a communication system developed without input from a conventional language, homesign. We study the communication systems of four deaf child homesigners (mean age 8;02). Although these idiosyncratic systems vary from one another, we nevertheless find that all four children use handshape and movement devices productively to express cardinal and non-cardinal number information, and that their number expressions are consistent in both form and meaning. Our study shows, for the first time, that all four homesigners not only incorporate number devices into representational devices used as predicates , but also into gestures functioning as nominals, including deictic gestures. In other words, the homesigners express number by systematically combining and re-combining additive markers for number (qua inflectional morphemes) with representational and deictic gestures (qua bases). The creation of new, complex forms with predictable meanings across gesture types and linguistic functions constitutes evidence for an inflectional morphological paradigm in homesign and expands our understanding of the structural patterns of language that are, and are not, dependent on linguistic input.

The Effect of Language-Specific Characteristics on English and Japanese Speakers' Ability to Recall Number Information

The current paper presents two experiments investigating the effect of presence versus absence of compulsory number marking in a native language on a speaker's ability to recall number information from photos. In Experiment 1, monolingual English and Japanese adults were shown a sequence of 110 photos after which they were asked questions about the photos. We found that the English participants showed a significantly higher accuracy rate for questions testing recall for number information when the correct answer was "2" (instead of "1") than Japanese participants. In Experiment 2, English and Japanese adults engaged in the same task as in Experiment 1 with an addition that explored reasons for the results found in Experiment 1. The results of Experiment 2 were in line with the results of Experiment 1, but also suggested that the results could not be attributed to differences in guessing patterns between the two groups or the type of linguistic constructions used in the test situations. The current study suggests that native language affects speakers' ability to recall number information from scenes and thus provides evidence for the Whorfian hypothesis.

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.

Deductive-reasoning brain networks: A coordinate-based meta-analysis of the neural signatures in deductive reasoning

OBJECTIVE

Deductive reasoning is a complex and poorly understood concept in the field of psychology. Many cognitive neuroscience studies have been published on deductive reasoning but have yielded inconsistent findings.

METHODS

In this study, we analyzed collected data from 38 articles using a recently proposed activation likelihood estimation (ALE) approach and used conjunction analysis to better determine the intersection of the results of meta-analyses.

RESULTS

First, the left hemispheres in the inferior parietal lobule (Brodmann area 40 [BA40]), middle frontal gyrus (BA6), medial frontal gyrus (BA8), inferior frontal gyrus (BA45/46), caudate, and insula (BA47) were revealed to be significant brain regions via simple-effect analysis (deductive reasoning versus baseline). Furthermore, IFG, insula, and cingulate (the key neural hubs of the cingulo-opercular network) were highlighted in overlapped functional connectivity maps.

CONCLUSION

The findings of the current study are consistent with the view that deductive reasoning requires a succession of stages, which included decoding of linguistic information, conversion and correction of rules, and transformation of inferential results into conclusive outputs, all of which are putatively processed via a distributed network of brain regions encompassing frontal/parietal cortices, as well as the caudate and other subcortical structures, which suggested that in the process of deductive reasoning, the coding and integration of premise information is indispensable, and it is also crucial to the execution and monitoring of the cognitive processing of reasoning.

Unraveling the contribution of left-right language on spatial perspective taking

We examine whether acquiring left/right language affects children's ability to take a non-egocentric left-right perspective. In Experiment 1, we tested 10-13 year-old Tseltal (Mayan) and Spanish-speaking children from the same community on a task that required they retrieve a coin they previously seen hidden in one of four boxes to the left/right/front/back of a toy sheep after the entire array was rotated out of view. Their performance on the left/right boxes correlated positively with their comprehension and use of left-right language. In Experiment 2, we found that training Tseltal-speaking children to apply left-right lexical labels to represent the location of the coin improved performance, but improvement was more robust among a second group of children trained to use gestures instead.

Absolute Numerosity Discrimination as a Case Study in Comparative Vertebrate Intelligence

The question of whether some non-human animal species are more intelligent than others is a reoccurring theme in comparative psychology. To convincingly address this question, exact comparability of behavioral methodology and data across species is required. The current article explores one of the rare cases in which three vertebrate species (humans, macaques, and crows) experienced identical experimental conditions during the investigation of a core cognitive capability – the abstract categorization of absolute numerical quantity. We found that not every vertebrate species studied in numerical cognition were able to flexibly discriminate absolute numerosity, which suggests qualitative differences in numerical intelligence are present between vertebrates. Additionally, systematic differences in numerosity judgment accuracy exist among those species that could master abstract and flexible judgments of absolute numerosity, thus arguing for quantitative differences between vertebrates. These results demonstrate that Macphail’s Null Hypotheses – which suggests that all non-human vertebrates are qualitatively and quantitatively of equal intelligence – is untenable.

Reduced neural selectivity for mental states in deaf children with delayed exposure to sign language

Language provides a rich source of information about other people's thoughts and feelings. Consequently, delayed access to language may influence conceptual development in Theory of Mind (ToM). We use functional magnetic resonance imaging and behavioral tasks to study ToM development in child (n = 33, 4-12 years old) and adult (n = 36) fluent signers of American Sign Language (ASL), and characterize neural ToM responses during ASL and movie-viewing tasks. Participants include deaf children whose first exposure to ASL was delayed up to 7 years (n = 12). Neural responses to ToM stories (specifically, selectivity of the right temporo-parietal junction) in these children resembles responses previously observed in young children, who have similar linguistic experience, rather than those in age-matched native-signing children, who have similar biological maturation. Early linguistic experience may facilitate ToM development, via the development of a selective brain region for ToM.

The Comparative Psychology of Intelligence: Some Thirty Years Later

After re-reading Macphail's (1987) essay "The Comparative Psychology of Intelligence" with all the associated commentaries, I was struck by how contemporary many of the arguments and counter-arguments still appear. Of course, we now know much more about the abilities of many more species (including their neurobiology) and fewer researchers currently favor explanations of behavior based solely on associative processes; however, the role of contextual variables in comparative psychology still remains cloudy. I discuss these issues briefly. Given my research interests involving the cognitive and communicative abilities of Grey parrots, the one aspect of the original article upon which I feel I can comment in depth involves Macphail's claims about the importance of language-and specifically syntax-in problem-solving and thus in placing humans above all other creatures. Granted, no other species has (or in my opinion is likely ever to acquire) everything that goes into what is considered "human language." Nevertheless, several other species have acquired symbolic representation, and considerable information now exists upon which to base an argument that such acquisition by itself enables more complex and "human-like" cognitive processes. Such processes may form the basis of the kind of intelligence that is measured-not surprisingly-with human-based tasks, including the use of such representations as a means to directly query non-human subjects in ways not unlike those used with young children.

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.

Language-specific numerical estimation in bilingual children

We tested 5- to 7-year-old bilingual learners of French and English (N = 91) to investigate how language-specific knowledge of verbal numerals affects numerical estimation. Participants made verbal estimates for rapidly presented random dot arrays in each of their two languages. Estimation accuracy differed across children's two languages, an effect that remained when controlling for children's familiarity with number words across their two languages. In addition, children's estimates were equivalently well ordered in their two languages, suggesting that differences in accuracy were due to how children represented the relative distance between number words in each language. Overall, these results suggest that bilingual children have different mappings between their verbal and nonverbal counting systems across their two languages and that those differences in mappings are likely driven by an asymmetry in their knowledge of the structure of the count list across their languages. Implications for bilingual math education are discussed.

Large as being on top of the world and small as hitting the roof: a common magnitude representation for the comparison of emotions and numbers

Previous work on the direct speed-intensity association (SIA) on comparative judgement tasks involved spatially distributed responses over spatially distributed stimuli with high motivational significance like facial expressions of emotions. This raises the possibility that the inferred stimulus-driven regulation of lateralized motor reactivity described by SIA, which was against the one expected on the basis of a valence-specific lateral bias, was entirely due to attentional capture from motivational significance (beyond numerical cognition). In order to establish the relevance of numerical cognition on the regulation of attentional capture we ran two complementary experiments. These involved the same direct comparison task on stimulus pairs that were fully comparable in terms of their analog representation of intensity but with different representational domain and motivational significance: symbolic magnitudes with low motivational significance in experiment 1 vs. emotions with rather high motivational significance in experiment 2. The results reveal a general SIA and point to a general mechanism regulating comparative judgements. This is based on the way spatial attention is captured toward locations that contain the stimulus which is closest in term of relative intensity to the extremal values of the series, regardless from its representational domain being it symbolic or emotional.

Using eye-tracking to understand relations between visual attention and language in children's spatial skills

Relations between children's spatial language and spatial skills raise questions regarding whether the effects are unique to language or reflect non-linguistic processes. Different paradigms provided mixed evidence: experimenter-provided language supports spatial performance more than visual cues; however, children's non-verbal attention predicts their spatial performance more than their language production. The current study used eye-tracking during spatial recall to compare effects of language versus visual cues. Four- to five-year-old children completed two tasks requiring memory for the location of a toy under one of four cups in an array of cups and landmarks after a 5 s delay and array rotation. Children first completed the baseline task with non-specific cues, followed by the cue-manipulation task with either language, visual, or non-specific cues provided by the experimenter. As in prior studies, language cues were most effective in facilitating recall. Children's visual attention was directed by both language and visual cues to support their recall. However, visual attention only partially mediated the effects of language: language supported recall above and beyond directing visual attention. These results indicate that visual attention supports spatial recall, but language has additional unique influences. This may result from language providing a more coherent or redundant code to visual information, or due to the pragmatic nature of language cueing relevance in ways visual cues do not. Additionally, differences across conditions may reflect more benefit from endogenous versus exogenous attentional control. Through using eye-tracking, this research provided new insights into processes by which language and visual attention influence children's spatial cognition.