Cognitive and motivational numeracy parenting practices: Implications for children's numeracy engagement during early elementary school.

Parents are considered a major resource in children's numeracy development. The relative role of cognitive and motivational parenting practices, however, is unclear given that the two types of practices have largely been studied in isolation. The current study simultaneously estimated the contributions of several cognitive and motivational parenting practices hypothesized to be important, but which may have overlapping effects. To capture parents' cognitive practices, the level and structure (i.e., prompts vs. statements) of 529 American parents' (80% mothers; 65% White, 20% Black; 33% less than a bachelor's degree) numeracy talk was coded during a challenging numeracy activity. Parents' motivational practices were assessed by coding their autonomy support and control in the activity. Children's (Mage = 7.5 years; 49% girls) engagement of numeracy strategies was also coded. Multilevel minute-to-minute modeling predicting children's engagement from both cognitive and motivational parenting practices indicated that parents' cognitive practices, particularly advanced prompts, predicted children's subsequent engagement of numeracy strategies, which were often advanced. Parents' motivational practices, as reflected in their autonomy support (vs. control), also foreshadowed children's engagement. These effects of the two types of practices were independent of one another. Taken together, the findings are consistent with the idea that cognitive and motivational parenting practices provide distinct resources that can benefit children's math learning. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

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.

Cognitive neuroscience: An abstract sense of number in the infant brain.

The human infant brain automatically extracts number from the environment. A new study recovers an abstract code for number from the brain electrophysiology of sleeping infants.

Signatures of emotional face processing measured by event-related potentials in 7-month-old infants.

The ability to distinguish facial emotions emerges in infancy. Although this ability has been shown to emerge between 5 and 7 months of age, the literature is less clear regarding the extent to which neural correlates of perception and attention play a role in processing of specific emotions. This study's main goal was to examine this question among infants. To this end, we presented angry, fearful, and happy faces to 7-month-old infants (N = 107, 51% female) while recording event-related brain potentials. The perceptual N290 component showed a heightened response for fearful and happy relative to angry faces. Attentional processing, indexed by the P400, showed some evidence of a heightened response for fearful relative to happy and angry faces. We did not observe robust differences by emotion in the negative central (Nc) component, although trends were consistent with previous work suggesting a heightened response to negatively valenced expressions. Results suggest that perceptual (N290) and attentional (P400) processing is sensitive to emotions in faces, but these processes do not provide evidence for a fear-specific bias across components.

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 (Mage  = 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 ß = .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 (ß = -.07) or mathematics abilities (average ß = .10). These results suggest that learning about verbal numbers is associated with a sharpening of pre-existing non-verbal numerical abilities.

Comparing fixed-array and functionally-defined channel of interest approaches to infant functional near-infrared spectroscopy data.

Functional near-infrared spectroscopy (fNIRS) is increasingly used to study brain function in infants, but the development and standardization of analysis techniques for use with infant fNIRS data have not paced other technical advances. Here we quantify and compare the effects of different methods of analysis of infant fNIRS data on two independent fNIRS datasets involving 6-9-month-old infants and a third simulated infant fNIRS dataset. With each, we contrast results from a traditional, fixed-array analysis with several functional channel of interest (fCOI) analysis approaches. In addition, we tested the effects of varying the number and anatomical location of potential data channels to be included in the fCOI definition. Over three studies we find that fCOI approaches are more sensitive than fixed-array analyses, especially when channels of interests were defined within-subjects. Applying anatomical restriction and/or including multiple channels in the fCOI definition does not decrease and in some cases increases sensitivity of fCOI methods. Based on these results, we recommend that researchers consider employing fCOI approaches to the analysis of infant fNIRS data and provide some guidelines for choosing between particular fCOI approaches and settings for the study of infant brain function and development.

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.

Associations between brain and behavioral processing of facial expressions of emotion and sensory reactivity in young children.

The ability to decode and accurately identify information from facial emotions may advantage young children socially. This capacity to decode emotional information may likewise be influenced by individual differences in children's temperament. This study investigated whether sensory reactivity and perceptual awareness, two dimensions of temperament, as well as children's ability to accurately label emotions relates to the neural processing of emotional content in faces. Event related potentials (ERPs) of 4 to 6 year-old children (N  = 119) were elicited from static displays of anger, happy, fearful, sad, and neutral emotion faces. Children, as a group, exhibited differential early (N290) and mid-latency (P400) event-related potentials (ERPs) in response to facial expressions of emotion. Individual differences in children's sensory reactivity were associated with enhanced P400 amplitudes to neutral, sad, and fearful faces. In a separate task, children were asked to provide an emotional label for the same images. Interestingly, children less accurately labeled the same neutral, sad, and fearful faces, suggesting that, contrary to previous work showing enhanced attentional processing to threatening cues (i.e., fear), children higher in sensory reactivity may deploy more attentional resources when decoding ambiguous emotional cues.

Hemispheric asymmetries in processing numerical meaning in arithmetic.

Hemispheric asymmetries in arithmetic have been hypothesized based on neuropsychological, developmental, and neuroimaging work. However, it has been challenging to separate asymmetries related to arithmetic specifically, from those associated general cognitive or linguistic processes. Here we attempt to experimentally isolate the processing of numerical meaning in arithmetic problems from language and memory retrieval by employing novel non-symbolic addition problems, where participants estimated the sum of two dot arrays and judged whether a probe dot array was the correct sum of the first two arrays. Furthermore, we experimentally manipulated which hemisphere receive the probe array first using a visual half-field paradigm while recording event-related potentials (ERP). We find that neural sensitivity to numerical meaning in arithmetic arises under left but not right visual field presentation during early and middle portions of the late positive complex (LPC, 400-800 ms). Furthermore, we find that subsequent accuracy for judgements of whether the probe is the correct sum is better under right visual field presentation than left, suggesting a left hemisphere advantage for integrating information for categorization or decision making related to arithmetic. Finally, neural signatures of operational momentum, or differential sensitivity to whether the probe was greater or less than the sum, occurred at a later portion of the LPC (800-1000 ms) and regardless of visual field of presentation, suggesting a temporal and functional dissociation between magnitude and ordinal processing in arithmetic. Together these results provide novel evidence for differences in timing and hemispheric lateralization for several cognitive processes involved in arithmetic thinking.

Functional Organization of the Temporal-Parietal Junction for Theory of Mind in Preverbal Infants: A Near-Infrared Spectroscopy Study.

Successful human social life requires imagining what others believe or think to understand and predict behavior. This ability, often referred to as theory of mind (ToM), reliably engages a specialized network of temporal and prefrontal brain regions in older children and adults, including selective recruitment of the temporal-parietal junction (TPJ). To date, how and when this specialized brain organization for ToM arises is unknown due to limitations in functional neuroimaging at younger ages. Here, we used the emerging technique of functional near-infrared spectroscopy to measure the functional brain response across parietal, temporal, and prefrontal regions in 7-month-old male and female infants as they viewed different video scenarios of a person searching for a hidden object. Over different conditions, we manipulated whether the person held an accurate (true) or inaccurate (false) belief about the location of the hidden object in the videos. In two separate experiments, we observed that activity from the TPJ, but not other temporal and prefrontal regions, spontaneously tracked with the beliefs of the other person, responding more during scenarios when the other person's belief regarding the location of the object was false compared with scenarios when her belief was true. These results mirror those obtained with adults to show that the TPJ already shows some functional organization relevant to high-level social cognition by around 7 months of age. Furthermore, these results suggest that infants may draw on similar core mechanisms to implicitly track beliefs, as adults do when reasoning explicitly about them.SIGNIFICANCE STATEMENT Humans selectively engage a network of brain regions, including the temporal-parietal junction (TPJ), to track what others think, an ability referred to as theory of mind. How and when this specialized brain organization for high-level social cognition arises is unknown. Using the emerging technique of near-infrared spectroscopy with 7-month-old infants, we observed that activity of the TPJ, but not other temporal and frontal regions, distinguished between scenarios when another person's belief about the location of the object was false compared with scenarios when the belief was true. These results suggest that a basic neural architecture to understand and predict the actions of others based on their beliefs may be present from the first year of life.

What counts in preschool number knowledge? A Bayes factor analytic approach toward theoretical model development.

Preschool children vary tremendously in their numerical knowledge, and these individual differences strongly predict later mathematics achievement. To better understand the sources of these individual differences, we measured a variety of cognitive and linguistic abilities motivated by previous literature to be important and then analyzed which combination of these variables best explained individual differences in actual number knowledge. Through various data-driven Bayesian model comparison and selection strategies on competing multiple regression models, our analyses identified five variables of unique importance to explaining individual differences in preschool children's symbolic number knowledge: knowledge of the count list, nonverbal approximate numerical ability, working memory, executive conflict processing, and knowledge of letters and words. Furthermore, our analyses revealed that knowledge of the count list, likely a proxy for explicit practice or experience with numbers, and nonverbal approximate numerical ability were much more important to explaining individual differences in number knowledge than general cognitive and language abilities. These findings suggest that children use a diverse set of number-specific, general cognitive, and language abilities to learn about symbolic numbers, but the contribution of number-specific abilities may overshadow that of more general cognitive abilities in the learning process.

The relationship between non-verbal systems of number and counting development: a neural signatures approach.

Two non-verbal cognitive systems, an approximate number system (ANS) for extracting the numerosity of a set and a parallel individuation (PI) system for distinguishing between individual items, are hypothesized to be foundational to symbolic number and mathematics abilities. However, the exact role of each remains unclear and highly debated. Here we used an individual differences approach to test for a relationship between the spontaneously evoked brain signatures (using event-related potentials) of PI and the ANS and initial development of symbolic number concepts in preschool children as displayed by counting. We observed that individual differences in the neural signatures of the PI system, but not the ANS, explained a unique portion of variance in counting proficiency after extensively controlling for general cognitive factors. These results suggest that differences in early attentional processing of objects between children are related to higher-level symbolic number concept development.

Magnitude rather than number: More evidence needed.

Leibovich et al. do not present enough empirical support to overturn decades of work supporting a number sense nor to convince the reader that a magnitude sense provides a better explanation of the literature. Here we highlight what we feel are the main points of weakness and the types of evidence that could be provided to be more convincing.

Effects of Non-Symbolic Approximate Number Practice on Symbolic Numerical Abilities in Pakistani Children.

Current theories of numerical cognition posit that uniquely human symbolic number abilities connect to an early developing cognitive system for representing approximate numerical magnitudes, the approximate number system (ANS). In support of this proposal, recent laboratory-based training experiments with U.S. children show enhanced performance on symbolic addition after brief practice comparing or adding arrays of dots without counting: tasks that engage the ANS. Here we explore the nature and generality of this effect through two brief training experiments. In Experiment 1, elementary school children in Pakistan practiced either a non-symbolic numerical addition task or a line-length addition task with no numerical content, and then were tested on symbolic addition. After training, children in the numerical training group completed the symbolic addition test faster than children in the line length training group, suggesting a causal role of brief, non-symbolic numerical training on exact, symbolic addition. These findings replicate and extend the core findings of a recent U.S. laboratory-based study to non-Western children tested in a school setting, attesting to the robustness and generalizability of the observed training effects. Experiment 2 tested whether ANS training would also enhance the consistency of performance on a symbolic number line task. Over several analyses of the data there was some evidence that approximate number training enhanced symbolic number line placements relative to control conditions. Together, the findings suggest that engagement of the ANS through brief training procedures enhances children's immediate attention to number and engagement with symbolic number tasks.

Behavioral and Neural Foundations of Multisensory Face-Voice Perception in Infancy.

In this article, we describe behavioral and neurophysiological evidence for infants' multimodal face-voice perception. We argue that the behavioral development of face-voice perception, like multimodal perception more broadly, is consistent with the intersensory redundancy hypothesis (IRH). Furthermore, we highlight that several recently observed features of the neural responses in infants converge with the behavioral predictions of the intersensory redundancy hypothesis. Finally, we discuss the potential benefits of combining brain and behavioral measures to study multisensory processing, as well as some applications of this work for atypical development.

Functional brain organization for number processing in pre-verbal infants.

Humans are born with the ability to mentally represent the approximate numerosity of a set of objects, but little is known about the brain systems that sub-serve this ability early in life and their relation to the brain systems underlying symbolic number and mathematics later in development. Here we investigate processing of numerical magnitudes before the acquisition of a symbolic numerical system or even spoken language, by measuring the brain response to numerosity changes in pre-verbal infants using functional near-infrared spectroscopy (fNIRS). To do this, we presented infants with two types of numerical stimulus blocks: number change blocks that presented dot arrays alternating in numerosity and no change blocks that presented dot arrays all with the same number. Images were carefully constructed to rule out the possibility that responses to number changes could be due to non-numerical stimulus properties that tend to co-vary with number. Interleaved with the two types of numerical blocks were audio-visual animations designed to increase attention. We observed that number change blocks evoked an increase in oxygenated hemoglobin over a focal right parietal region that was greater than that observed during no change blocks and during audio-visual attention blocks. The location of this effect was consistent with intra-parietal activity seen in older children and adults for both symbolic and non-symbolic numerical tasks. A distinct set of bilateral occipital and middle parietal channels responded more to the attention-grabbing animations than to either of the types of numerical stimuli, further dissociating the specific right parietal response to number from a more general bilateral visual or attentional response. These results provide the strongest evidence to date that the right parietal cortex is specialized for numerical processing in infancy, as the response to number is dissociated from visual change processing and general attentional processing.

Human temporal-parietal junction spontaneously tracks others' beliefs: A functional near-infrared spectroscopy study.

Humans have the unique capacity to actively reflect on the thoughts, beliefs, and knowledge of others, but do we also track mental states spontaneously when observing other people? We asked this question by monitoring brain activity in belief-sensitive cortex using functional near-infrared spectroscopy (fNIRS) during free-viewing of social videos. More specifically, we identified a portion of the right temporal-parietal junction (rTPJ) selective for mental state processing using an established, explicit theory of mind task, and then analyzed the brain response in that region of interest (ROI) during free-viewing of video clips involving people producing goal-directed actions. We found a significant increase in oxygenated hemoglobin concentration in our rTPJ ROI during free-viewing for all of our test videos. Activity in this region was further modulated by the extent to which the knowledge state, or beliefs, of the protagonist regarding the location of an object contrasted with the reality of where the object was hidden. Open-ended questioning suggested our participants were not explicitly focusing on belief states of the characters during free-viewing. Further analyses ruled out lower-level details of the video clips or general attentional differences between conditions as likely explanations for the results. As such, these results call into question the traditional characterization of theory of mind as a resource intensive, deliberate process, and, instead, support an emerging view of theory of mind as a foundation for, rather than the pinnacle of, human social cognition.

Children's expectations about training the approximate number system.

Humans possess a developmentally precocious and evolutionarily ancient approximate number system (ANS) whose sensitivity correlates with uniquely human symbolic arithmetic skills. Recent studies suggest that ANS training improves symbolic arithmetic, but such studies may engender performance expectations in their participants that in turn produce the improvement. Here, we assessed 6- to 8-year-old children's expectations about the effects of numerical and non-numerical magnitude training, as well as states of satiety and restfulness, in the context of a study linking children's ANS practice to their improved symbolic arithmetic. We found that children did not expect gains in symbolic arithmetic after exercising the ANS, although they did expect gains in ANS acuity after training on any magnitude task. Moreover, children expected gains in symbolic arithmetic after a good night's sleep and their favourite breakfast. Thus, children's improved symbolic arithmetic after ANS training cannot be explained by their expectations about that training.