Number sense at 12 months predicts 4-year-olds' maths skills.

Preverbal infants spontaneously represent the number of objects in collections. Is this 'sense of number' (also referred to as Approximate Number System, ANS) part of the cognitive foundations of mathematical skills? Multiple studies reported a correlation between the ANS and mathematical achievement in children. However, some have suggested that such correlation might be mediated by general-purpose inhibitory skills. We addressed the question using a longitudinal approach: we tested the ANS of 60 12 months old infants and, when they were 4 years old (final N = 40), their symbolic math achievement as well as general intelligence and inhibitory skills. Results showed that the ANS at 12 months is a specific predictor of later maths skills independent from general intelligence or inhibitory skills. The correlation between ANS and maths persists when both abilities are measured at four years. These results confirm that the ANS has an early, specific and longstanding relation with mathematical abilities in childhood. RESEARCH HIGHLIGHTS: In the literature there is a lively debate about the correlation between the ANS and maths skills. We longitudinally tested a sample of 60 preverbal infants at 12 months and rested them at 4 years (final sample of 40 infants). The ANS tested at 12 months predicted later symbolic mathematical skills at 4 years, even when controlling for inhibition, general intelligence and perceptual skills. The ANS tested at 4 years remained linked with symbolic maths skills, confirming this early and longstanding relation in childhood.

Preschool language and visuospatial skills respectively predict multiplication and addition/subtraction skills in middle school children.

A converging body of evidence from neuroimaging, behavioral, and neuropsychology studies suggests that different arithmetic operations rely on distinct neuro-cognitive processes: while addition and subtraction may rely more on visuospatial reasoning, multiplication would depend more on verbal abilities. In this paper, we tested this hypothesis in a longitudinal study measuring language and visuospatial skills in 358 preschoolers, and testing their mental calculation skills at the beginning of middle school. Language skills at 5.5 years significantly predicted multiplication, but not addition nor subtraction scores at 11.5 years. Conversely, early visuospatial skills predicted addition and subtraction, but not multiplication scores. These results provide strong support for the existence of a double dissociation in mental arithmetic operations, and demonstrate the existence of long-lasting links between language/visuospatial skills and specific calculation abilities.

Are infants' preferences in the number change detection paradigm driven by sequence patterns?

Inter-individual differences in infants' numerosity processing have been assessed using a change detection paradigm, where participants were presented with two concurrent streams of images, one alternating between two numerosities and the other showing one constant numerosity. While most infants look longer at the changing stream in this paradigm, the reasons underlying these preferences have remained unclear. We suggest that, besides being attracted by numerosity changes, infants perhaps also respond to the alternating pattern of the changing stream. We conducted two experiments (N = 32) with 6-month-old infants to assess this hypothesis. In the first experiment, infants responded to changes in numerosity even when the changing stream showed numerosities in an unpredictable random order. In the second experiment, infants did not display any preference when an alternating stream was pitted against a random stream. These findings do not provide evidence that the alternating pattern of the changing stream contributes to drive infants' preferences. Instead, around the age of 6 months, infants' responses in the numerosity change detection paradigm appear to be mainly driven by changes in numerosity, with different levels of preference reflecting inter-individual difference in the acuity of numerosity perception.

Cortical route for facelike pattern processing in human newborns.

Humans are endowed with an exceptional ability for detecting faces, a competence that, in adults, is supported by a set of face-specific cortical patches. Human newborns, already shortly after birth, preferentially orient to faces, even when they are presented in the form of highly schematic geometrical patterns vs. perceptually equivalent nonfacelike stimuli. The neural substrates underlying this early preference are still largely unexplored. Is the adult face-specific cortical circuit already active at birth, or does its specialization develop slowly as a function of experience and/or maturation? We measured EEG responses in 1- to 4-day-old awake, attentive human newborns to schematic facelike patterns and nonfacelike control stimuli, visually presented with slow oscillatory "peekaboo" dynamics (0.8 Hz) in a frequency-tagging design. Despite the limited duration of newborns' attention, reliable frequency-tagged responses could be estimated for each stimulus from the peak of the EEG power spectrum at the stimulation frequency. Upright facelike stimuli elicited a significantly stronger frequency-tagged response than inverted facelike controls in a large set of electrodes. Source reconstruction of the underlying cortical activity revealed the recruitment of a partially right-lateralized network comprising lateral occipitotemporal and medial parietal areas overlapping with the adult face-processing circuit. This result suggests that the cortical route specialized in face processing is already functional at birth.

Distance and Direction Codes Underlie Navigation of a Novel Semantic Space in the Human Brain.

A recent proposal posits that humans might use the same neuronal machinery to support the representation of both spatial and nonspatial information, organizing concepts and memories using spatial codes. This view predicts that the same neuronal coding schemes characterizing navigation in the physical space (tuned to distance and direction) should underlie navigation of abstract semantic spaces, even if they are categorical and labeled by symbols. We constructed an artificial semantic environment by parsing a bidimensional audiovisual object space into four labeled categories. Before and after a nonspatial symbolic categorization training, 25 adults (15 females) were presented with pseudorandom sequences of objects and words during a functional MRI session. We reasoned that subsequent presentations of stimuli (either objects or words) referring to different categories implied implicit movements in the novel semantic space, and that such movements subtended specific distances and directions. Using whole-brain fMRI adaptation and searchlight model-based representational similarity analysis, we found evidence of both distance-based and direction-based responses in brain regions typically involved in spatial navigation: the medial prefrontal cortex and the right entorhinal cortex (EHC). After training, both regions encoded the distances between concepts, making it possible to recover a faithful bidimensional representation of the semantic space directly from their multivariate activity patterns, whereas the right EHC also exhibited a periodic modulation as a function of traveled direction. Our results indicate that the brain regions and coding schemes supporting relations and movements between spatial locations in mammals are "recycled" in humans to represent a bidimensional multisensory conceptual space during a symbolic categorization task.SIGNIFICANCE STATEMENT The hippocampal formation and the medial prefrontal cortex of mammals represent the surrounding physical space by encoding distances and directions between locations. Recent works suggested that humans use the same neural machinery to organize their memories as points of an internal map of experiences. We asked whether the same brain regions and neural codes supporting spatial navigation are recruited when humans use language to organize their knowledge of the world in categorical semantic representations. Using fMRI, we show that the medial prefrontal cortex and the entorhinal portion of the hippocampal formation represent the distances and the movement directions between concepts of a novel audiovisual semantic space, and that it was possible to reconstruct, from neural data, their relationships in memory.

Symbolic categorization of novel multisensory stimuli in the human brain.

When primates (both human and non-human) learn to categorize simple visual or acoustic stimuli by means of non-verbal matching tasks, two types of changes occur in their brain: early sensory cortices increase the precision with which they encode sensory information, and parietal and lateral prefrontal cortices develop a categorical response to the stimuli. Contrary to non-human animals, however, our species mostly constructs categories using linguistic labels. Moreover, we naturally tend to define categories by means of multiple sensory features of the stimuli. Here we trained adult subjects to parse a novel audiovisual stimulus space into 4 orthogonal categories, by associating each category to a specific symbol. We then used multi-voxel pattern analysis (MVPA) to show that during a cross-format category repetition detection task three neural representational changes were detectable. First, visual and acoustic cortices increased both precision and selectivity to their preferred sensory feature, displaying increased sensory segregation. Second, a frontoparietal network developed a multisensory object-specific response. Third, the right hippocampus and, at least to some extent, the left angular gyrus, developed a shared representational code common to symbols and objects. In particular, the right hippocampus displayed the highest level of abstraction and generalization from a format to the other, and also predicted symbolic categorization performance outside the scanner. Taken together, these results indicate that when humans categorize multisensory objects by means of language the set of changes occurring in the brain only partially overlaps with that described by classical models of non-verbal unisensory categorization in primates.

Grid-like and distance codes for representing word meaning in the human brain.

Relational information about items in memory is thought to be represented in our brain thanks to an internal comprehensive model, also referred to as a "cognitive map". In the human neuroimaging literature, two signatures of bi-dimensional cognitive maps have been reported: the grid-like code and the distance-dependent code. While these kinds of representation were previously observed during spatial navigation and, more recently, during processing of perceptual stimuli, it is still an open question whether they also underlie the representation of the most basic items of language: words. Here we taught human participants the meaning of novel words as arbitrary labels for a set of audiovisual objects varying orthogonally in size and sound. The novel words were therefore conceivable as points in a navigable 2D map of meaning. While subjects performed a word comparison task, we recorded their brain activity using functional magnetic resonance imaging (fMRI). By applying a combination of representational similarity and fMRI-adaptation analyses, we found evidence of (i) a grid-like code, in the right postero-medial entorhinal cortex, representing the relative angular positions of words in the word space, and (ii) a distance-dependent code, in medial prefrontal, orbitofrontal, and mid-cingulate cortices, representing the Euclidean distance between words. Additionally, we found evidence that the brain also separately represents the single dimensions of word meaning: their implied size, encoded in visual areas, and their implied sound, in Heschl's gyrus/Insula. These results support the idea that the meaning of words, when they are organized along two dimensions, is represented in the human brain across multiple maps of different dimensionality. SIGNIFICANT STATEMENT: How do we represent the meaning of words and perform comparative judgements on them in our brain? According to influential theories, concepts are conceivable as points of an internal map (where distance represents similarity) that, as the physical space, can be mentally navigated. Here we use fMRI to show that when humans compare newly learnt words, they recruit a grid-like and a distance code, the same types of neural codes that, in mammals, represent relations between locations in the environment and support physical navigation between them.

The hippocampal-entorhinal system represents nested hierarchical relations between words during concept learning.

A fundamental skill of an intelligent mind is that of being able to rapidly discover the structural organization underlying the relations across the objects or the events in the world. Humans, thanks to language, master this skill. For example, a child learning that dolphins and cats can also be referred to as mammals, not only will infer the presence of a hierarchical organization for which dolphins and cats are subordinate exemplars of the category mammals, but will also derive that dolphins are, at least at one conceptual level, more similar to cats than to sharks, despite their indisputable higher perceptual similarity to the latter. The hippocampal-entorhinal system, classically known for its involvement in relational and inferential memory, is a likely candidate to construct and hold these complex relational structures between concepts. To test this hypothesis, we trained healthy human adults to organize a novel audio-visual object space into categories labeled with novel words. Crucially, a hierarchical taxonomy existed between the object categories, and participants discovered it via inference during a simple associative object-to-word training. Using functional MRI after learning, and a combination of ROI-based multivariate analyses, we found that both the mid-anterior hippocampus and the entorhinal cortex represented the inferred hierarchical structure between words: subordinate-level words were represented more similarly to their related superordinate than to unrelated ones. This was paired, in the entorhinal cortex, by an additional signature of internalized structural representation of nested hierarchy: words referring to subordinate concepts belonging to the same superordinate category were represented more similarly compared with those not belonging to the same superordinate level: interestingly, this similarity was never directly taught to subjects nor it was made explicit during the task, but only indirectly derived through a logical inferential process and, crucially, contrasted the evidence coming from the definitional perceptual properties of the concepts. None of these results were observed before learning, when the same words were not yet semantically organized. A whole-brain searchlight revealed that the effect in the entorhinal cortex extends to a wider network of areas, encompassing the prefrontal, temporal, and parietal cortices, partially overlapping with the semantic network.

Infants' use of motion cues in object individuation processes.

We investigated 10-month-old infants' and adults' numerical expectations in scenarios where information on self-motion and static object features may give rise to numerically incongruent representations. A red circle or a blue box with yellow stripes appeared on the left side of a screen, moved autonomously sideways and then moved back behind the screen. Next, on the opposite side, an identical object was first brought in view by a hand and then pushed back behind the screen (Experiments 1 and 2). The screen was finally removed, revealing either one or two objects. Infants looked longer at one-object test events, suggesting that they expected to find two objects. Adults were also shown these animations and were asked for their numerical expectations. Contrary to infants, they expected one single object (Experiment 3). Whereas preverbal infants' numerical expectations appeared to be dominated by information on object autonomous and induced motion, adults' expectations were mainly guided by information about object shape, size, and color. These findings were discussed in relation to current models on the development of object individuation processes.

Excessive visual crowding effects in developmental dyscalculia.

Visual crowding refers to the inability to identify objects when surrounded by other similar items. Crowding-like mechanisms are thought to play a key role in numerical perception by determining the sensory mechanisms through which ensembles are perceived. Enhanced visual crowding might hence prevent the normal development of a system involved in segregating and perceiving discrete numbers of items and ultimately the acquisition of more abstract numerical skills. Here, we investigated whether excessive crowding occurs in developmental dyscalculia (DD), a neurodevelopmental disorder characterized by difficulty in learning the most basic numerical and arithmetical concepts, and whether it is found independently of associated major reading and attentional difficulties. We measured spatial crowding in two groups of adult individuals with DD and control subjects. In separate experiments, participants were asked to discriminate the orientation of a Gabor patch either in isolation or under spatial crowding. Orientation discrimination thresholds were comparable across groups when stimuli were shown in isolation, yet they were much higher for the DD group with respect to the control group when the target was crowded by closely neighbouring flanking gratings. The difficulty in discriminating orientation (as reflected by the combination of accuracy and reaction times) in the DD compared to the control group persisted over several larger target flanker distances. Finally, we found that the degree of such spatial crowding correlated with impairments in mathematical abilities even when controlling for visual attention and reading skills. These results suggest that excessive crowding effects might be a characteristic of DD, independent of other associated neurodevelopmental disorders.

Conceptual and Perceptual Dimensions of Word Meaning Are Recovered Rapidly and in Parallel during Reading.

A single word (the noun "elephant") encapsulates a complex multidimensional meaning, including both perceptual ("big", "gray", "trumpeting") and conceptual ("mammal", "can be found in India") features. Opposing theories make different predictions as to whether different features (also conceivable as dimensions of the semantic space) are stored in similar neural regions and recovered with similar temporal dynamics during word reading. In this magnetoencephalography study, we tracked the brain activity of healthy human participants while reading single words varying orthogonally across three semantic dimensions: two perceptual ones (i.e., the average implied real-world size and the average strength of association with a prototypical sound) and a conceptual one (i.e., the semantic category). The results indicate that perceptual and conceptual representations are supported by partially segregated neural networks: Whereas visual and auditory dimensions are encoded in the phase coherence of low-frequency oscillations of occipital and superior temporal regions, respectively, semantic features are encoded in the power of low-frequency oscillations of anterior temporal and inferior parietal areas. However, despite the differences, these representations appear to emerge at the same latency: around 200 msec after stimulus onset. Taken together, these findings suggest that perceptual and conceptual dimensions of the semantic space are recovered automatically, rapidly, and in parallel during word reading.

Word meaning in the ventral visual path: a perceptual to conceptual gradient of semantic coding.

The meaning of words referring to concrete items is thought of as a multidimensional representation that includes both perceptual (e.g., average size, prototypical color) and conceptual (e.g., taxonomic class) dimensions. Are these different dimensions coded in different brain regions? In healthy human subjects, we tested the presence of a mapping between the implied real object size (a perceptual dimension) and the taxonomic categories at different levels of specificity (conceptual dimensions) of a series of words, and the patterns of brain activity recorded with functional magnetic resonance imaging in six areas along the ventral occipito-temporal cortical path. Combining multivariate pattern classification and representational similarity analysis, we found that the real object size implied by a word appears to be primarily encoded in early visual regions, while the taxonomic category and sub-categorical cluster in more anterior temporal regions. This anteroposterior gradient of information content indicates that different areas along the ventral stream encode complementary dimensions of the semantic space.

A shared, flexible neural map architecture reflects capacity limits in both visual short-term memory and enumeration.

Human cognition is characterized by severe capacity limits: we can accurately track, enumerate, or hold in mind only a small number of items at a time. It remains debated whether capacity limitations across tasks are determined by a common system. Here we measure brain activation of adult subjects performing either a visual short-term memory (vSTM) task consisting of holding in mind precise information about the orientation and position of a variable number of items, or an enumeration task consisting of assessing the number of items in those sets. We show that task-specific capacity limits (three to four items in enumeration and two to three in vSTM) are neurally reflected in the activity of the posterior parietal cortex (PPC): an identical set of voxels in this region, commonly activated during the two tasks, changed its overall response profile reflecting task-specific capacity limitations. These results, replicated in a second experiment, were further supported by multivariate pattern analysis in which we could decode the number of items presented over a larger range during enumeration than during vSTM. Finally, we simulated our results with a computational model of PPC using a saliency map architecture in which the level of mutual inhibition between nodes gives rise to capacity limitations and reflects the task-dependent precision with which objects need to be encoded (high precision for vSTM, lower precision for enumeration). Together, our work supports the existence of a common, flexible system underlying capacity limits across tasks in PPC that may take the form of a saliency map.

Mind, brain, and teaching: Some directions for future research.

In line with Kline's taxonomy, highlighting teaching as an array of behaviors with different cognitive underpinnings, we advocate the expansion of a specific line of research on mind, brain, and teaching. This research program is devoted to the understanding of the neurocognitive mechanisms and the evolutionary determinants of teaching skills, with the ultimate goal of helping teachers improve teaching quality.

Staphylococcus aureus toxic shock syndrome toxin-1 endocarditis with muscular metastatic abscesses.

A 42-year-old woman, living in a nursing home for the mentally disabled, with congenital ventricular septal defect and multiple comorbidities, developed endocarditis with vegetations of the interventricular septum and the right coronary aortic leaflet. The main feature of this case was the metastatic embolism leading to multiple and muscular abscesses. Methicillin-sensitive S. aureus, spa type 253 and ST30, producing toxin shock syndrome toxin-1 was isolated from blood cultures. The patient was initially treated with beta-lactam antibiotics without showing clinical response and subsequently with daptomycin and linezolid that improved the patient's clinical symptoms. The effectiveness of treatment with daptomycin and linezolid was partly due to the ability of linezolid to reduce TSST-1 secretion. The portal of entry of the infection was not recognized. TSST-1 production by the strain might have favoured the formation of large cardiac vegetations and the subsequent metastatic dissemination to the muscles.

Education enhances the acuity of the nonverbal approximate number system.

All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the numbers of objects in sets with ratio-limited precision. Interindividual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucú, who have a very restricted numerical lexicon and highly variable access to mathematics education. By comparing Mundurucú subjects with and without access to schooling, we found that education significantly enhances the acuity with which sets of concrete objects are estimated. These results indicate that culture and education have an important effect on basic number perception. We hypothesize that symbolic and nonsymbolic numerical thinking mutually enhance one another over the course of mathematics instruction.

Objects, numbers, fingers, space: clustering of ventral and dorsal functions in young children and adults.

In the primate brain, sensory information is processed along two partially segregated cortical streams: the ventral stream, mainly coding for objects' shape and identity, and the dorsal stream, mainly coding for objects' quantitative information (including size, number, and spatial position). Neurophysiological measures indicate that such functional segregation is present early on in infancy, and that the two streams follow independent maturational trajectories during childhood. Here we collected, in a large sample of young children and adults, behavioural measures on an extensive set of functions typically associated with either the dorsal or the ventral stream. We then used a correlational approach to investigate the presence of inter-individual variability resulting in clustering of functions. Results show that dorsal- and ventral-related functions follow two uncorrelated developmental trajectories. Moreover, within each stream, some functions show age-independent correlations: finger gnosis, non-symbolic numerical abilities and spatial abilities within the dorsal stream, and object and face recognition abilities within the ventral stream. This pattern of clear within-stream cross-task correlation seems to be lost in adults, with two notable exceptions: performance in face and object recognition on one side, and in symbolic and non-symbolic comparison on the other, remain correlated, pointing to distinct shape recognition and quantity comparison systems.

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.

A magnitude code common to numerosities and number symbols in human intraparietal cortex.

Activation of the horizontal segment of the intraparietal sulcus (hIPS) has been observed in various number-processing tasks, whether numbers were conveyed by symbolic numerals (digits, number words) or by nonsymbolic displays (dot patterns). This suggests an abstract coding of numerical magnitude. Here, we critically tested this hypothesis using fMRI adaptation to demonstrate notation-independent coding of numerical quantity in the hIPS. Once subjects were adapted either to dot patterns or to Arabic digits, activation in the hIPS and in frontal regions recovered in a distance-dependent fashion whenever a new number was presented, irrespective of notation changes. This remained unchanged when analyzing the hIPS peaks from an independent localizer scan of mental calculation. These results suggest an abstract coding of approximate number common to dots, digits, and number words. They support the idea that symbols acquire meaning by linking neural populations coding symbol shapes to those holding nonsymbolic representations of quantities.