Prefrontal cortex and the evolution of symbolic reference

(Dis)similarities between non-symbolic and symbolic number representations: Insights from vector space models

Empirical evidence in support of a shared system for non-symbolic and symbolic number processing has been inconclusive. The current study aims to address this question in a novel way, specifically by testing whether the efficient coding principle based on co-occurrence of number symbols in natural language holds for both non-symbolic and symbolic number processing. The efficient coding principle postulates that perception is optimized when stimuli frequently co-occur in a natural environment. We hypothesized that both numerical ratios and co-occurrence frequencies of symbolic numbers would significantly influence participants' performance on a non-symbolic and symbolic number comparison task. To test this hypothesis, we employed latent semantic analysis on a TASA corpus to quantify number co-occurrence in natural language and calculate language similarity estimates. We engaged 73 native English speakers (mean age = 19.36, standard deviation = 1.83) with normal or corrected vision and no learning disorders in a number comparison task involving non-symbolic (dot arrays) and symbolic stimuli (Arabic numerals and English number words). Results showed that numerical ratios significantly predicted participants' performances across all number formats (ps < 0.001). Language similarity estimates derived from everyday language also predicted performance on the non-symbolic task and the symbolic task involving number words (ps < 0.007). Our results highlight the complex nature of numerical processing, pointing to the co-occurrence of number symbols in natural language as an auxiliary factor in understanding the shared characteristics between non-symbolic and symbolic number representations. Given that our study focused on a limited number range (5 to 16) and a specific task type, future studies should explore a wider range of tasks and numbers to further test the role of the efficient coding principle in number processing.

Regionally specific cortical lateralization of abstract and concrete verb processing: Magnetic mismatch negativity study

The neural underpinnings of processing concrete and abstract semantics remain poorly understood. Previous fMRI studies have shown that multimodal and amodal neural networks respond differentially to different semantic types; importantly, abstract semantics activates more left-lateralized networks, as opposed to more bilateral activity for concrete words. Due to the lack of temporal resolution, these fMRI results do not allow to easily separate language- and task-specific brain responses and to disentangle early processing stages from later post-comprehension phenomena. To tackle this, we used magnetoencephalography (MEG), a time-resolved neuroimaging technique, in combination with a task-free oddball mismatch negativity (MMN) paradigm, an established approach to tracking early automatic activation of word-specific memory traces in the brain. We recorded the magnetic MMN responses in 30 healthy adults to auditorily presented abstract and concrete action verbs to assess lateralization of word-specific lexico-semantic processing in a set of neocortical areas. We found that MMN responses to these stimuli showed different lateralization patterns of activity in the upper limb motor area (BA4) and parts of Broca's area (BA45/BA47) within ∼100-350 ms after the word disambiguation point. Importantly, the greater leftward response lateralization for abstract semantics was due to the lesser involvement of the right-hemispheric homologues, not increased left-hemispheric activity. These findings suggest differential region-specific involvement of bilateral sensorimotor systems already in the early automatic stages of processing abstract and concrete action semantics.

Feasibility of Virtual Shopping Budget-Management Training on Executive Functions in Healthy Young Adults: A Pilot Study

To date, budget management in virtual shopping training has not been given much importance. The main objective of this study was to investigate the effects of virtual shopping budget-management training on executive functions and brain activation. Sixteen participants were randomly assigned to the experimental group that received virtual shopping budget-management training or the waitlist control group for a total of 16 sessions. To examine the effects of virtual shopping budget-management training on brain activation, HbO2 was measured in the prefrontal cortex via functional near-infrared spectroscopy (fNIRS) during the Trail Making Test Part B (TMT-B) and Stroop test. Mann-Whitney and Wilcoxon signed-rank tests were used to compare outcomes between and within the two groups. The virtual shopping budget-management training showed no significant difference in all outcomes between both groups (p > 0.05). No significant differences were observed in HbO2 levels during both TMT-B (p > 0.05) and the Stroop test (p > 0.05). However, in the pre-post comparisons, there was a significant difference in the TMT-B (p < 0.05) and Stroop test (p < 0.05) in the experimental group. In this study, although we did not find a distinct advantage in training, it confirmed its potential for clinical benefits in healthy young adults through training.

Association neurons in the crow telencephalon link visual signs to numerical values

Many animals can associate signs with numerical values and use these signs in a goal-directed way during task performance. However, the neuronal basis of this semantic association has only rarely been investigated, and so far only in primates. How mechanisms of number associations are implemented in the distinctly evolved brains of other animal taxa such as birds is currently unknown. Here, we explored this semantic number-sign mapping by recording single-neuron activity in the crows' nidopallium caudolaterale (NCL), a brain structure critically involved in avian numerical cognition. Crows were trained to associate visual shapes with varying numbers of items in a number production task. The responses of many NCL neurons during stimulus presentation reflected the numerical values associated with visual shapes in a behaviorally relevant way. Consistent with the crow's better behavioral performance with signs, neuronal representations of numerical values extracted from shapes were more selective compared to those from dot arrays. The existence of number association neurons in crows points to a phylogenetic preadaptation of the brains of cognitively advanced vertebrates to link visual shapes with numerical meaning.

The two-network framework of number processing: a step towards a better understanding of the neural origins of developmental dyscalculia

Developmental dyscalculia is a specific learning disorder that persists over lifetime and can have an enormous impact on personal, health-related, and professional aspects of life. Despite its central importance, the origin both at the cognitive and neural level is not yet well understood. Several classification schemas of dyscalculia have been proposed, sometimes together with an associated deficit at the neural level. However, these explanations are (a) not providing an exhaustive framework that is at levels with the observed complexity of developmental dyscalculia at the behavioral level and (b) are largely mono-causal approaches focusing on gray matter deficits. We suggest that number processing is instead the result of context-dependent interaction of two anatomically largely separate, distributed but overlapping networks that function/cooperate in a closely integrated fashion. The proposed two-network framework (TNF) is the result of a series of studies in adults on the neural correlates underlying magnitude processing and arithmetic fact retrieval, which comprised neurofunctional imaging of various numerical tasks, the application of probabilistic fiber tracking to obtain well-defined connections, and the validation and modification of these results using disconnectome mapping in acute stroke patients. Emerged from data in adults, it represents the endpoint of the acquisition and use of mathematical competencies in adults. Yet, we argue that its main characteristics should already emerge earlier during development. Based on this TNF, we develop a classification schema of phenomenological subtypes and their underlying neural origin that we evaluate against existing propositions and the available empirical data.

Fronto-Cerebellar Neurometabolite Alterations After Methylphenidate in Children and Adolescents With ADHD: A Proton Magnetic Resonance Spectroscopy Study

OBJECTIVE

The fronto-cerebellar circuit is involved in ADHD pathophysiology. Methylphenidate, as a first-line medication for ADHD, affects different brain regions, however, its effect on the fronto-cerebellar circuit is not investigated sufficiently. We aimed to investigate the effect of 8-week treatment with methylphenidate on neurometabolite ratios in the fronto-cerebellar circuit in ADHD participants using magnetic resonance spectroscopy (MRS).

METHODS

Fifteen drug-naïve ADHD children and adolescents were enrolled in the present study. Two single-voxel MR spectra were acquired from the right dorsolateral prefrontal cortex (DLPFC) and left Crus 1, before and after the medication. Also, neuropsychological and behavioral assessments were administered.

RESULTS

After medication, the glutamate/creatine in the DLPFC and the choline/creatine in the Crus 1 decreased in the ADHD participants.

CONCLUSION

These findings propose that methylphenidate-induced metabolite changes in the fronto-cerebellar circuit could be associated with improvement in cognitive/behavioral characteristics in ADHD. Also, results highlighted cerebellar engagement in ADHD pathophysiology.

A-B-3-Associations and dissociations of reading and arithmetic: Is domain-specific prediction outdated?

Reading and arithmetic are core domains of academic achievement with marked impact on career opportunities and socioeconomic status. While associations between reading and arithmetic are well established, evidence on underlying mechanisms is inconclusive. The main goal of this study was to reevaluate the domain-specificity of established predictors and to enhance our understanding of the (co-)development of reading and arithmetic. In a sample of 885 German-speaking children, standard domain-specific predictors of reading and arithmetic were assessed before and/or at the onset of formal schooling. Reading and arithmetic skills were measured at the beginning and end of second grade. Latent variables were extracted for all relevant constructs: Grapheme-phoneme processing (phonological awareness, letter identification), RAN (RAN-objects, RAN-digits), number system knowledge (number identification, successor knowledge), and magnitude processing (non-symbolic and symbolic magnitude comparison), as well as the criterion measures reading and arithmetic. Four structural equation models tested distinct research questions. Grapheme-phoneme processing was a specific predictor of reading, and magnitude processing explained variance specific to arithmetic. RAN explained variance in both domains, and it explained variance in reading even after controlling for arithmetic. RAN and number system knowledge further explained variance in skills shared between reading and arithmetic. Reading and arithmetic entail domain-specific cognitive components, and they both require tight networks of visual, verbal, and semantic information, as reflected by RAN. This perspective provides a useful background to explain associations and dissociations between reading and arithmetic performance.

Recursive sequence generation in crows

Recursion, the process of embedding structures within similar structures, is often considered a foundation of symbolic competence and a uniquely human capability. To understand its evolution, we can study the recursive aptitudes of nonhuman animals. We adopted the behavioral protocol of a recent study demonstrating that humans and nonhuman primates grasp recursion. We presented sequences of bracket pair stimuli (e.g., [ ] and { }) to crows who were instructed to peck at training lists. They were then tested on their ability to transfer center-embedded structure to never-before-seen pairings of brackets. We reveal that crows have recursive capacities; they perform on par with children and even outperform macaques. The crows continued to produce recursive sequences after extending to longer and thus deeper embeddings. These results demonstrate that recursive capabilities are not limited to the primate genealogy and may have occurred separately from or before human symbolic competence in different animal taxa.

Symbols and mental programs: a hypothesis about human singularity

Natural language is often seen as the single factor that explains the cognitive singularity of the human species. Instead, we propose that humans possess multiple internal languages of thought, akin to computer languages, which encode and compress structures in various domains (mathematics, music, shape…). These languages rely on cortical circuits distinct from classical language areas. Each is characterized by: (i) the discretization of a domain using a small set of symbols, and (ii) their recursive composition into mental programs that encode nested repetitions with variations. In various tasks of elementary shape or sequence perception, minimum description length in the proposed languages captures human behavior and brain activity, whereas non-human primate data are captured by simpler nonsymbolic models. Our research argues in favor of discrete symbolic models of human thought.

A Theoretical Framework for Human and Nonhuman Vocal Interaction

Vocal communication is a critical feature of social interaction across species; however, the relation between such behavior in humans and nonhumans remains unclear. To enable comparative investigation of this topic, we review the literature pertinent to interactive language use and identify the superset of cognitive operations involved in generating communicative action. We posit these functions comprise three intersecting multistep pathways: (a) the Content Pathway, which selects the movements constituting a response; (b) the Timing Pathway, which temporally structures responses; and (c) the Affect Pathway, which modulates response parameters according to internal state. These processing streams form the basis of the Convergent Pathways for Interaction framework, which provides a conceptual model for investigating the cognitive and neural computations underlying vocal communication across species.

Neurobiology of early life adversity: A systematic review of meta-analyses towards an integrative account of its neurobiological trajectories to mental disorders

Adverse childhood experiences (ACEs) may leave long-lasting neurobiological scars, increasing the risk of developing mental disorders in later life. However, no review has comprehensively integrated existing evidence across the fields: hypothalamic-pituitary-adrenal axis, immune/inflammatory system, neuroimaging, and genetics/epigenetics. We thus systematically reviewed previous meta-analyses towards an integrative account of ACE-related neurobiological alterations. Following Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guideline, a total of 27 meta-analyses until October 2021 were identified. This review found that individuals with ACEs possess blunted cortisol response to psychosocial stressors, low-grade inflammation evinced by increased C-reactive protein levels, exaggerated amygdalar response to emotionally negative information, and diminished hippocampal gray matter volume. Importantly, these alterations were consistently observed in those with and without psychiatric diagnosis. These findings were integrated and discussed in a schematic model of ACE-related neurobiological alterations. Future longitudinal research based on multidisciplinary approach is imperative for ACE-related mental disorders' prevention and treatment.

The neural basis of number word processing in children and adults

The ability to map number words to their corresponding quantity representations is a gatekeeper for children's future math success (Spaepen et al., 2018). Without number word knowledge at school entry, children are at greater risk for developing math learning difficulties (Chu et al., 2019). In the present study, we used functional magnetic resonance imaging (fMRI) to examine the neural basis for processing the meaning of spoken number words and its developmental trajectory in 4- to 10-year-old children, and in adults. In a number word-quantity mapping paradigm, participants listened to number words while simultaneously viewing quantities that were congruent or incongruent to the number word they heard. Whole brain analyses revealed that adults showed a neural congruity effect with greater neural activation for incongruent relative to congruent trials in anterior cingulate cortex (ACC) and left intraparietal sulcus (LIPS). In contrast, children did not show a significant neural congruity effect. However, a region of interest analysis in the child sample demonstrated age-related increases in the neural congruity effect, specifically in the LIPS. The positive correlation between neural congruity in LIPS and age was stronger in children who were already attending school, suggesting that developmental changes in LIPS function are experience-dependent.

The Brain and the New Foundations of Mathematics

Many concepts in mathematics are not fully defined, and their properties are implicit, which leads to paradoxes. New foundations of mathematics were formulated based on the concept of innate programs of behavior and thinking. The basic axiom of mathematics is proposed, according to which any mathematical object has a physical carrier. This carrier can store and process only a finite amount of information. As a result of the D-procedure (encoding of any mathematical objects and operations on them in the form of qubits), a mathematical object is digitized. As a consequence, the basis of mathematics is the interaction of brain qubits, which can only implement arithmetic operations on numbers. A proof in mathematics is an algorithm for finding the correct statement from a list of already-existing statements. Some mathematical paradoxes (e.g., Banach–Tarski and Russell) and Smale’s 18th problem are solved by means of the D-procedure. The axiom of choice is a consequence of the equivalence of physical states, the choice among which can be made randomly. The proposed mathematics is constructive in the sense that any mathematical object exists if it is physically realized. The consistency of mathematics is due to directed evolution, which results in effective structures. Computing with qubits is based on the nontrivial quantum effects of biologically important molecules in neurons and the brain.

Do Bats Have the Necessary Prerequisites for Symbolic Communication?

Training animals such as apes, gray parrots, or dolphins that communicate via arbitrary symbols with humans has revealed astonishing mental capacities that may have otherwise gone unnoticed. Albeit bats have not yet been trained to communicate via symbols with humans, we are convinced that some species, especially captive Pteropodid bats ("flying foxes"), show the potential to master this cognitive task. Here, we briefly review what is known about bats' cognitive skills that constitute relevant prerequisites for symbolic communication with humans. We focus on social learning in general, trainability by humans, associative learning from humans, imitation, vocal production learning and usage learning, and social knowledge. Moreover, we highlight potential training paradigms that could be used to elicit simple "symbolic" bat-human communication, i.e., training bats to select arbitrary symbols on a touchscreen to elicit a desired behavior of the human caregiver. Touchscreen-proficient bats could participate in cognition research, e.g., to study their numerical competence or categorical perception, to further elucidate how nonhuman animals learn and perceive the world.

Functional connectivity of the dorsolateral prefrontal cortex contributes to different components of executive functions

OBJECTIVE

The dorsolateral prefrontal cortex (DLPFC) orchestrates other brain regions and plays a vital role for "the most uniquely human" executive functions (EFs), which are divided into distinct components. Components of EFs have been localized to different brain regions and at the same time the DLPFC was found to be involved in a majority of EF components. The possible mechanism of the DLPFC's contribution to EF components might be found in DLPFC functional connectivity (FC): this FC of the DLPFC with other brain regions contributes to different EF components.

METHOD

To explore the DLPFC FC contribution to different EFs, we used an integrative approach involving analysis of fMRI and neuropsychological assessment of EFs. Fifty healthy adults (27 females and 23 males, mean age 34.5 ± 16.6 years) underwent neuropsychological assessment of EFs as well as task-based and resting-state fMRI. Task-based fMRI was applied as a functional localizer for individually defined DLPFC ROIs that were further used for the FC seed-based correlation analysis of the resting-state data. Then we looked for associations between individual scores of different EF components and the whole-brain resting-state FC of the DLPFC.

RESULTS

Resting-state correlates of DLPFC FC were revealed for three out of the seven EF components derived from an extensive neuropsychological assessment: inhibition, switching, and the verbal EF component.

CONCLUSIONS

Our study is the first to reveal the contribution of the DLPFC FC to several distinct EF components. The obtained results give insight into the brain mechanisms of EFs.

Symbolic labeling in 5-month-old human infants

Humans' ability to create and manipulate symbolic structures far exceeds that of other animals. We hypothesized that this ability rests on an early capacity to use arbitrary signs to represent any mental representation, even as abstract as an algebraic rule. In three experiments, we collected high-density EEG recordings while 150 5-month-old infants were presented with speech triplets characterized by their abstract syllabic structure-the location of syllable repetition-which predicted a following arbitrary label (e.g., ABA words were followed by a fish picture, AAB words by a lion). After a brief learning phase, EEG responses to novel words revealed that infants built expectations about the upcoming label based on the triplet structure and were surprised when it happened to be incongruent. Preverbal infants were thus able to recode the incoming triplets into abstract mental variables to which arbitrary labels were flexibly assigned. Importantly, infants also generalized to novel trials in which the pairing order was reversed (with the label preceding the auditory structure). Beyond conditioned associations, infants instantly inferred a bidirectional mapping between the abstract structures and the following label, a foundational operation for any symbolic system.

Computational models of motivated frontal function

Computational models of frontal function have made important contributions to understanding how the frontal lobes support a wide range of important functions, in their interactions with other brain areas including, critically, the basal ganglia (BG). We focus here on the specific case of how different frontal areas support goal-directed, motivated decision-making, by representing three essential types of information: possible plans of action (in more dorsal and lateral frontal areas), affectively significant outcomes of those action plans (in ventral, medial frontal areas including the orbital frontal cortex), and the overall utility of a given plan compared to other possible courses of action (in anterior cingulate cortex). Computational models of goal-directed action selection at multiple different levels of analysis provide insight into the nature of learning and processing in these areas and the relative contributions of the frontal cortex versus the BG. The most common neurologic disorders implicate these areas, and understanding their precise function and modes of dysfunction can contribute to the new field of computational psychiatry, within the broader field of computational neuroscience.

Numerical and Non-numerical Predictors of First Graders' Number-Line Estimation Ability

Children’s ability to map numbers into a spatial context has been shown to be a powerful predictor of math performance. Here, we investigate how three types of cognitive abilities – approximate number processing ability, symbolic number processing ability, and non-numerical cognitive abilities – predict 0–100 number-line estimation performance in first graders. While each type of measure predicts number-line performance when considered individually, when considered together, only symbolic number comparison and non-verbal reasoning predicted unique variance in number-line estimation. Moreover, the relation between symbolic number comparison and number-line ability was stronger for male students than for female students, suggesting potential gender differences in the way boys and girls accomplish mapping numbers into space. These results suggest that number-line estimation ability is largely reflective of the precision with which symbolic magnitudes are represented (at least among boys). Our findings therefore suggest that promoting children’s understanding of symbolic, rather than non-symbolic, numerical magnitudes may help children learn better from number-lines in the classroom.

Fronto-parietal numerical networks in relation with early numeracy in young children

Early numeracy provides the foundation of acquiring mathematical skills that is essential for future academic success. This study examined numerical functional networks in relation to counting and number relational skills in preschoolers at 4 and 6 years of age. The counting and number relational skills were assessed using school readiness test (SRT). Resting-state fMRI (rs-fMRI) was acquired in 123 4-year-olds and 146 6-year-olds. Among them, 61 were scanned twice over the course of 2 years. Meta-analysis on existing task-based numeracy fMRI studies identified the left parietal-dominant network for both counting and number relational skills and the right parietal-dominant network only for number relational skills in adults. We showed that the fronto-parietal numerical networks, observed in adults, already exist in 4-year and 6-year-olds. The counting skills were associated with the bilateral fronto-parietal network in 4-year-olds and with the right parietal-dominant network in 6-year-olds. Moreover, the number relational skills were related to the bilateral fronto-parietal and right parietal-dominant networks in 4-year-olds and had a trend of the significant relationship with the right parietal-dominant network in 6-year-olds. Our findings suggested that neural fine-tuning of the fronto-parietal numerical networks may subserve the maturation of numeracy in early childhood.

Distinct neural mechanisms for reading Arabic vs. verbal numbers: An ERP study

In this electroencephalogram/event-related potential (EEG/ERP) study, 16 volunteers were asked to compare the numerical equality of 360 pairs of multidigit numbers presented in Arabic or verbal format. Behavioural data showed faster and more accurate responses for digit targets, with a right hand/left hemisphere advantage only for verbal numerals. Occipito-temporal N1, peaking at approximately 180 ms, was strongly left-lateralized during verbal number processing and bilateral during digit processing. A LORETA (low-resolution electromagnetic tomography) source reconstruction performed at the N1 latency stage (155-185 ms) revealed greater brain activation during coding of Arabic than of verbal stimuli. Digit perceptual coding was associated with the activation of the right angular gyrus (rAG), the left fusiform gyrus (FG,BA37), and left and right superior and medial frontal areas. N1 sources for verbal numerals included the left FG (BA37), the precuneus (BA31), the parahippocampal area and a small right prefrontal activation. In addition, verbal numerals elicited a late frontocentral negativity, possibly reflecting stimulus unfamiliarity or complexity. Overall, the data suggest distinct mechanisms for number reading through ciphers (digits) or words. Information about quantity was accessed earlier and more accurately if numbers were in a nonlinguistic code. Indeed, it can be speculated that numerosity processing would involve circuits originally involved in processing space (i.e., rAG/rIPS).

A random-matrix theory of the number sense

Number sense, a spontaneous ability to process approximate numbers, has been documented in human adults, infants and newborns, and many other animals. Species as distant as monkeys and crows exhibit very similar neurons tuned to specific numerosities. How number sense can emerge in the absence of learning or fine tuning is currently unknown. We introduce a random-matrix theory of self-organized neural states where numbers are coded by vectors of activation across multiple units, and where the vector codes for successive integers are obtained through multiplication by a fixed but random matrix. This cortical implementation of the 'von Mises' algorithm explains many otherwise disconnected observations ranging from neural tuning curves in monkeys to looking times in neonates and cortical numerotopy in adults. The theory clarifies the origin of Weber-Fechner's Law and yields a novel and empirically validated prediction of multi-peak number neurons. Random matrices constitute a novel mechanism for the emergence of brain states coding for quantity.This article is part of a discussion meeting issue 'The origins of numerical abilities'.

The search of "canonical" explanations for the cerebral cortex

This paper addresses a fundamental line of research in neuroscience: the identification of a putative neural processing core of the cerebral cortex, often claimed to be "canonical". This "canonical" core would be shared by the entire cortex, and would explain why it is so powerful and diversified in tasks and functions, yet so uniform in architecture. The purpose of this paper is to analyze the search for canonical explanations over the past 40 years, discussing the theoretical frameworks informing this research. It will highlight a bias that, in my opinion, has limited the success of this research project, that of overlooking the dimension of cortical development. The earliest explanation of the cerebral cortex as canonical was attempted by David Marr, deriving putative cortical circuits from general mathematical laws, loosely following a deductive-nomological account. Although Marr's theory turned out to be incorrect, one of its merits was to have put the issue of cortical circuit development at the top of his agenda. This aspect has been largely neglected in much of the research on canonical models that has followed. Models proposed in the 1980s were conceived as mechanistic. They identified a small number of components that interacted as a basic circuit, with each component defined as a function. More recent models have been presented as idealized canonical computations, distinct from mechanistic explanations, due to the lack of identifiable cortical components. Currently, the entire enterprise of coming up with a single canonical explanation has been criticized as being misguided, and the premise of the uniformity of the cortex has been strongly challenged. This debate is analyzed here. The legacy of the canonical circuit concept is reflected in both positive and negative ways in recent large-scale brain projects, such as the Human Brain Project. One positive aspect is that these projects might achieve the aim of producing detailed simulations of cortical electrical activity, a negative one regards whether they will be able to find ways of simulating how circuits actually develop.

Developmental changes of cognitive vocal control in monkeys

The evolutionary origins of human language are obscured by the scarcity of essential linguistic characteristics in non-human primate communication systems. Volitional control of vocal utterances is one such indispensable feature of language. We investigated the ability of two monkeys to volitionally utter species-specific calls over many years. Both monkeys reliably vocalized on command during juvenile periods, but discontinued this controlled vocal behavior in adulthood. This emerging disability was confined to volitional vocal production, as the monkeys continued to vocalize spontaneously. In addition, they continued to use hand movements as instructed responses during adulthood. This greater vocal flexibility of monkeys early in ontogeny supports the neoteny hypothesis in human evolution. This suggests that linguistic capabilities were enabled via an expansion of the juvenile period during the development of humans.

Neural Tuning to Numerosity Relates to Perceptual Tuning in 3-6-Year-Old Children

Neural representations of approximate numerical value, or numerosity, have been observed in the intraparietal sulcus (IPS) in monkeys and humans, including children. Using functional magnetic resonance imaging, we show that children as young as 3-4 years old exhibit neural tuning to cardinal numerosities in the IPS and that their neural responses are accounted for by a model of numerosity coding that has been used to explain neural responses in the adult IPS. We also found that the sensitivity of children's neural tuning to number in the right IPS was comparable to their numerical discrimination sensitivity observed behaviorally, outside of the scanner. Children's neural tuning curves in the right IPS were significantly sharper than in the left IPS, indicating that numerical representations are more precise and mature more rapidly in the right hemisphere than in the left. Further, we show that children's perceptual sensitivity to numerosity can be predicted by the development of their neural sensitivity to numerosity. This research provides novel evidence of developmental continuity in the neural code underlying numerical representation and demonstrates that children's neural sensitivity to numerosity is related to their cognitive development.

SIGNIFICANCE STATEMENT

Here we test for the existence of neural tuning to numerosity in the developing brain in the youngest sample of children tested with fMRI to date. Although previous research shows evidence of numerical distance effects in the intraparietal sulcus of the developing brain, those effects could be explained by patterns of neural activity that do not represent neural tuning to numerosity. These data provide the first robust evidence that from as early as 3-4 years of age there is developmental continuity in how the intraparietal sulcus represents the values of numerosities. Moreover, the study goes beyond previous research by examining the relation between neural tuning and perceptual tuning in children.

Magnitude Codes for Cross-Modal Working Memory in the Primate Frontal Association Cortex

Quantitative features of stimuli may be ordered along a magnitude continuum, or line. Magnitude refers to parameters of different types of stimulus properties. For instance, the frequency of a sound relates to sensory and continuous stimulus properties, whereas the number of items in a set is an abstract and discrete property. In addition, within a stimulus property, magnitudes need to be processed not only in one modality, but across multiple modalities. In the sensory domain, for example, magnitude applies to both to the frequency of auditory sounds and tactile vibrations. Similarly, both the number of visual items and acoustic events constitute numerical quantity, or numerosity. To support goal-directed behavior and executive functions across time, magnitudes need to be held in working memory, the ability to briefly retain and manipulate information in mind. How different types of magnitudes across multiple modalities are represented in working memory by single neurons has only recently been explored in primates. These studies show that neurons in the frontal lobe can encode the same magnitude type across sensory modalities. However, while multimodal sensory magnitude in relative comparison tasks is represented by monotonically increasing or decreasing response functions ("summation code"), multimodal numerical quantity in absolute matching tasks is encoded by neurons tuned to preferred numerosities ("labeled-line code"). These findings indicate that most likely there is not a single type of cross-modal working-memory code for magnitudes, but rather a flexible code that depends on the stimulus dimension as well as on the task requirements.

Primitive Concepts of Number and the Developing Human Brain

Counting is an evolutionarily recent cultural invention of the human species. In order for humans to have conceived of counting in the first place, certain representational and logical abilities must have already been in place. The focus of this review is the origins and nature of those fundamental mechanisms that promoted the emergence of the human number concept. Five claims are presented that support an evolutionary view of numerical development: 1) number is an abstract concept with an innate basis in humans, 2) maturational processes constrain the development of humans' numerical representations between infancy and adulthood, 3) there is evolutionary continuity in the neural processes of numerical cognition in primates, 4) primitive logical abilities support verbal counting development in humans, and 5) primitive neural processes provide the foundation for symbolic numerical development in the human brain. We support these claims by examining current evidence from animal cognition, child development, and human brain function. The data show that at the basis of human numerical concepts are primitive perceptual and logical mechanisms that have evolutionary homologs in other primates and form the basis of numerical development in the human brain. In the final section of the review, we discuss some hypotheses for what makes human numerical reasoning unique by drawing on evidence from human and non-human primate neuroimaging research.

Heterogeneity of Developmental Dyscalculia: Cases with Different Deficit Profiles

Developmental Dyscalculia (DD) has long been thought to be a monolithic learning disorder that can be attributed to a specific neurocognitive dysfunction. However, recent research has increasingly recognized the heterogeneity of DD, where DD can be differentiated into subtypes in which the underlying cognitive deficits and neural dysfunctions may differ. The aim was to further understand the heterogeneity of developmental dyscalculia (DD) from a cognitive psychological perspective. Utilizing four children (8–9 year-old) we administered a comprehensive cognitive test battery that shed light on the cognitive-behavioral profile of each child. The children were compared against norm groups of aged-matched peers. Performance was then contrasted against predominant hypotheses of DD, which would also give insight into candidate neurocognitive correlates. Despite showing similar mathematical deficits, these children showed remarkable interindividual variability regarding cognitive profile and deficits. Two cases were consistent with the approximate number system deficit account and also the general magnitude-processing deficit account. These cases showed indications of having domain-general deficits as well. One case had an access deficit in combination with a general cognitive deficit. One case suffered from general cognitive deficits only. The results showed that DD cannot be attributed to a single explanatory factor. These findings support a multiple deficits account of DD and suggest that some cases have multiple deficits, whereas other cases have a single deficit. We discuss a previously proposed distinction between primary DD and secondary DD, and suggest hypotheses of dysfunctional neurocognitive correlates responsible for the displayed deficits.

The Symbol Grounding Problem Revisited: A Thorough Evaluation of the ANS Mapping Account and the Proposal of an Alternative Account Based on Symbol-Symbol Associations

Recently, a lot of studies in the domain of numerical cognition have been published demonstrating a robust association between numerical symbol processing and individual differences in mathematics achievement. Because numerical symbols are so important for mathematics achievement, many researchers want to provide an answer on the ‘symbol grounding problem,’ i.e., how does a symbol acquires its numerical meaning? The most popular account, the approximate number system (ANS) mapping account, assumes that a symbol acquires its numerical meaning by being mapped on a non-verbal and ANS. Here, we critically evaluate four arguments that are supposed to support this account, i.e., (1) there is an evolutionary system for approximate number processing, (2) non-symbolic and symbolic number processing show the same behavioral effects, (3) non-symbolic and symbolic numbers activate the same brain regions which are also involved in more advanced calculation and (4) non-symbolic comparison is related to the performance on symbolic mathematics achievement tasks. Based on this evaluation, we conclude that all of these arguments and consequently also the mapping account are questionable. Next we explored less popular alternative, where small numerical symbols are initially mapped on a precise representation and then, in combination with increasing knowledge of the counting list result in an independent and exact symbolic system based on order relations between symbols. We evaluate this account by reviewing evidence on order judgment tasks following the same four arguments. Although further research is necessary, the available evidence so far suggests that this symbol–symbol association account should be considered as a worthy alternative of how symbols acquire their meaning.

On The Evolutionary Origin of Symbolic Communication

The emergence of symbolic communication is often cited as a critical step in the evolution of Homo sapiens, language, and human-level cognition. It is a widely held assumption that humans are the only species that possess natural symbolic communication schemes, although a variety of other species can be taught to use symbols. The origin of symbolic communication remains a controversial open problem, obfuscated by the lack of a fossil record. Here we demonstrate an unbroken evolutionary pathway from a population of initially noncommunicating robots to the spontaneous emergence of symbolic communication. Robots evolve in a simulated world and are supplied with only a single channel of communication. When their ability to reproduce is motivated by the need to find a mate, robots evolve indexical communication schemes from initially noncommunicating populations in 99% of all experiments. Furthermore, 9% of the populations evolve a symbolic communication scheme allowing pairs of robots to exchange information about two independent spatial dimensions over a one-dimensional channel, thereby increasing their chance of reproduction. These results suggest that the ability for symbolic communication could have emerged spontaneously under natural selection, without requiring cognitive preadaptations or preexisting iconic communication schemes as previously conjectured.

Using cognitive training studies to unravel the mechanisms by which the approximate number system supports symbolic math ability

A picture is emerging that preverbal nonsymbolic numerical representations derived from the approximate number system (ANS) play an important role in mathematical development and sustained mathematical thinking. Functional imaging studies are revealing developmental trends in how the brain represents number. We propose that combining behavioral and neuroimaging techniques with cognitive training approaches will help identify the fundamental relationship between the ANS and symbolic mathematics. Understanding this relationship should ultimately benefit educators by providing ways to harness the ANS and hopefully improve math readiness in young children.

Cognitive and brain systems underlying early mathematical development

We review current debate regarding the core competencies that support early mathematics learning, focusing on the contributions of the inherent system for representing approximate magnitudes, and domain-general systems that facilitate learning across academic domains. The latter include the executive control system that enables explicit processing of quantitative symbols, such as Arabic numerals, and the logical problem-solving abilities (intelligence) that facilitate learning the relations among numerals. The neural systems that underlie these abilities, as related to mathematical learning, are also discussed, albeit briefly. We place the contributions of inherent quantitative abilities and domain-general mechanisms in an evolutionary context and provide some discussion as to how they interact during the learning of evolutionarily novel mathematics.

Developmental bias for number words in the intraparietal sulcus

Children and adults show behavioral evidence of psychological overlap between their early, non-symbolic numerical concepts and their later-developing symbolic numerical concepts. An open question is to what extent the common cognitive signatures observed between different numerical notations are coupled with physical overlap in neural processes. We show that from 8 years of age, regions of the intraparietal sulcus (IPS) that exhibit a numerical ratio effect during non-symbolic numerical judgments also show a semantic distance effect for symbolic number words. In both children and adults, the IPS showed a semantic distance effect during magnitude judgments of number words (i.e. larger/smaller number) but not for magnitude judgments of object words (i.e. larger/smaller object size). The results provide novel evidence of conceptual overlap between neural representations of symbolic and non-symbolic numerical values that cannot be explained by a general process, and present the first demonstration of an early-developing dissociation between number words and object words in the human brain.

Number Processing and Heterogeneity of Developmental Dyscalculia: Subtypes With Different Cognitive Profiles and Deficits

This study investigated if developmental dyscalculia (DD) in children with different profiles of mathematical deficits has the same or different cognitive origins. The defective approximate number system hypothesis and the access deficit hypothesis were tested using two different groups of children with DD (11-13 years old): a group with arithmetic fact dyscalculia (AFD) and a group with general dyscalculia (GD). Several different aspects of number magnitude processing were assessed in these two groups and compared with age-matched typically achieving children. The GD group displayed weaknesses with both symbolic and nonsymbolic number processing, whereas the AFD group displayed problems only with symbolic number processing. These findings provide evidence that the origins of DD in children with different profiles of mathematical problems diverge. Children with GD have impairment in the innate approximate number system, whereas children with AFD suffer from an access deficit. These findings have implications for researchers' selection procedures when studying dyscalculia, and also for practitioners in the educational setting.

Individual differences in algebraic cognition: Relation to the approximate number and semantic memory systems

The relation between performance on measures of algebraic cognition and acuity of the approximate number system (ANS) and memory for addition facts was assessed for 171 ninth graders (92 girls) while controlling for parental education, sex, reading achievement, speed of numeral processing, fluency of symbolic number processing, intelligence, and the central executive component of working memory. The algebraic tasks assessed accuracy in placing x,y pairs in the coordinate plane, speed and accuracy of expression evaluation, and schema memory for algebra equations. ANS acuity was related to accuracy of placements in the coordinate plane and expression evaluation but not to schema memory. Frequency of fact retrieval errors was related to schema memory but not to coordinate plane or expression evaluation accuracy. The results suggest that the ANS may contribute to or be influenced by spatial-numerical and numerical-only quantity judgments in algebraic contexts, whereas difficulties in committing addition facts to long-term memory may presage slow formation of memories for the basic structure of algebra equations. More generally, the results suggest that different brain and cognitive systems are engaged during the learning of different components of algebraic competence while controlling for demographic and domain general abilities.