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Success in science, technology, engineering, and mathematics (STEM) fields is often believed to require intellectual talent ("brilliance"). Given that many cultures associate men more than women with brilliance, this belief poses an obstacle to women's STEM pursuits. Here, we investigated the developmental roots of this phenomenon, focusing specifically on young children's beliefs about math (N = 174 U.S. students in Grades 1-4; 93 girls, 81 boys; 52% White, 17% Asian, 13% Hispanic/Latinx). We found that field-specific ability beliefs (FABs) that associate success in math (vs. reading/writing) with brilliance are already present in early elementary school. We also found that brilliance-oriented FABs about math are negatively associated with elementary school students' (and particularly girls') math motivation--specifically, their math self-efficacy and interest. The early emergence of brilliance-oriented FABs about math and the negative relation between FABs and math motivation underscore the need to understand the sources and long-term effects of these beliefs.

Prior research shows that when parents monitor, check, and assist in completing homework without an invitation, their children's motivation and academic achievement often decline. We propose that intrusive support from parents might also send the message that children are incompetent, especially if they believe their intelligence is fixed. We tested whether children's mindsets moderate the negative link between parents' intrusive homework support and achievement among first- and second-grade students followed for one academic year (Study 1, N = 563) and middle and high school students for two academic years (Study 2, N = 1,613). The samples were obtained from large urban areas in the United States. In both studies, intrusive homework support more strongly predicted a decrease in achievement over time for children with a fixed mindset. These findings suggest that the belief that intellectual ability cannot be changed may exacerbate the detrimental effects of uninvited help on academic work.

The relation of various math attitudes to math achievement has been extensively studied in adolescents and adults. Recently, researchers have begun to examine the math attitude-math achievement relation in young children. We review theories and research on four attitudes relevant to early math learning--math anxiety, math self-concept, mindset, and math-gender stereotype. These attitudes emerge and are related to math achievement by early elementary school. Our review suggests that early math achievement plays an important role in the initial development of either positive or negative math attitudes, which in turn, may initiate a vicious or virtuous cycle that can enhance or undermine math learning. Additionally, gender differences in math attitudes (favoring boys) emerge by early to mid-elementary school. An important future direction involves understanding how early attitudes about math relate to each other, and whether certain constellations of attitudes are prevalent. We also consider three types of math attitudes that key socializers--parents and teachers--hold: general (math-gender stereotypes and mindsets), self-relevant (math anxiety), and child-specific (expectations and value of math for their child or student). Our review highlights a link between key socializers' math attitudes and associated behaviors, and their children's math attitudes and math achievement. Based on these findings, we propose the Early Math Achievement-Attitude model (EMAA). An important future direction involves increasing our understanding of how key socializers with different math attitude constellations engage with children around math. Finally, based on our review of these topics as well as intervention studies, we discuss intervention approaches that hold promise for improving young children's math achievement and math attitudes.

Researchers have long been interested in the origins of humans' understanding of symbolic number, focusing primarily on how children learn the meanings of number words (e.g., "one", "two", etc.). However, recent evidence indicates that children learn the meanings of number gestures before learning number words. In the present set of experiments, we ask whether children's early knowledge of number gestures resembles their knowledge of nonsymbolic number. In four experiments, we show that preschool children (n = 139 in total; age M = 4.14 years, SD = 0.71, range = 2.75-6.20) do not view number gestures in the same the way that they view nonsymbolic representations of quantity (i.e., arrays of shapes), which opens the door for the possibility that young children view number gestures as symbolic, as adults and older children do. A video abstract of this article can be viewed at https://youtu.be/WtVziFN1yuI.

Students who experience mathematics anxiety have long been suggested to engage in avoidance behaviors that negatively impact their mathematics performance. However, little is known about how these avoidance behaviors manifest for highly anxious students within the context of a mathematics course. Since the use of effortful study strategies has been shown to be an important predictor of students' academic outcomes, we investigated whether highly mathematics-anxious college students would be less likely to utilize such strategies during exam preparation compared to their less-anxious peers. To measure this, we asked college students (N = 72) enrolled in introductory Calculus to complete a battery of anxiety-related surveys and to retrospectively report how they studied for the final exam in their Calculus course. Using theories of achievement emotion as well as recent research showing a relation between mathematics anxiety and students' planned exam preparation behavior, we hypothesized that students experiencing mathematics anxiety would retrospectively report less engagement with effortful study strategies during exam preparation compared to their less-anxious peers. In line with our hypothesis, we found that solving practice problems was viewed by students as being one of the most effortful ways to prepare for a mathematics examination, and that mathematics anxiety was negatively associated with the proportion of study time students allocated to solving practice problems during exam preparation. These findings highlight the significant relation between mathematics anxiety and students' self-regulated exam preparation behaviors, marking it as an important topic to consider when investigating ways to improve the mathematics performance of highly mathematics-anxious individuals.

Background: Use of numerical and spatial language, also known as math talk, is critical to the development of foundational number and spatial skills in early childhood. However, caregivers and children of low socioeconomic status (SES) tend to use less math talk than their higher-SES peers. Objective: The current efficacy study tested the hypothesis that quantity of math talk among low-SES caregivers and children is increased via a caregiver education curriculum aimed at improving caregivers' language input to children. Methods: Caregiver-child dyads (n = 37; children aged 17 to 36 months) participated in either the language input or a control intervention. Math talk (operationalized as number and spatial word tokens) was coded from video recordings of each dyad engaging in free play at three time points: baseline, post-intervention, and follow-up. Results: The language input curriculum significantly increased caregivers' amount of spatial talk and children's amount of number and spatial talk for up to 4 months after the intervention. Conclusions A caregiver education intervention increased caregivers' use of math talk, which resulted in higher math talk usage by their children. Further verification is needed through an adequately powered longitudinal randomized controlled trial.

Myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS) is a chronic and debilitating disease characterized by unexplained physical fatigue, cognitive and sensory dysfunction, sleeping disturbances, orthostatic intolerance, and gastrointestinal problems. People with ME/CFS often report a prodrome consistent with infections. Using regression, Bayesian and enrichment analyses, we conducted targeted and untargeted metabolomic analysis of plasma from 106 ME/CFS cases and 91 frequency-matched healthy controls. Subjects in the ME/CFS group had significantly decreased levels of plasmalogens and phospholipid ethers (p < 0.001), phosphatidylcholines (p < 0.001) and sphingomyelins (p < 0.001), and elevated levels of dicarboxylic acids (p = 0.013). Using machine learning algorithms, we were able to differentiate ME/CFS or subgroups of ME/CFS from controls with area under the receiver operating characteristic curve (AUC) values up to 0.873. Our findings provide the first metabolomic evidence of peroxisomal dysfunction, and are consistent with dysregulation of lipid remodeling and the tricarboxylic acid cycle. These findings, if validated in other cohorts, could provide new insights into the pathogenesis of ME/CFS and highlight the potential use of the plasma metabolome as a source of biomarkers for the disease.

Math anxiety negatively predicts young children's math achievement. While some researchers have suggested that math anxiety may stem from poor math ability, others have argued that math anxiety occurs at all levels of math ability. An important question is whether math anxiety predicts math achievement over and above foundational math skills. We sought to address this issue by examining whether math anxiety predicts future math achievement, controlling for number line estimation, a foundational math skill that predicts future math achievement. We found that 1st graders' math anxiety predicts their math achievement in 1st through 3rd grade, controlling for their number line estimation at the beginning of 1st grade. This finding suggests that math anxiety contributes to future math learning over and above an important foundational math skill. Additionally, we examined whether there are age differences in the relation of first-grade math anxiety to number line estimation at various scales in order to test the hypothesis that the negative effect of early math anxiety on math performance depends on task difficulty. In support of this hypothesis, early math anxiety more closely related to the 0--100 number line task in 1st graders but to the 0-1000 number line task in 3rd graders, suggesting that math anxiety most strongly relates to math skills that are at the cusp of children's understanding at particular grade levels. Together, these findings underscore the importance of fostering young children's positive emotions toward math in addition to providing them with a strong cognitive foundation for math learning. [This article was published in "Journal of Cognition and Development" (EJ1276583).]

Fractions are a challenging mathematics topic for many elementary and middle school students, and even for adults. However, a growing body of developmental research suggests that young children can reason about visually presented proportions, well before fraction instruction, providing insight into how fractions might be introduced to improve learning. We designed a card game to teach first and second grade children (N = 195, including a racially and economically diverse sample from the United States) about fractions in one of three ways. In the Actively Divided condition we iteratively divided an area model into equal-sized units, in the Predivided condition we used an area model with the end-state of the Actively Divided condition, and in the Nondivided condition we used a continuous representation of the fraction magnitude that was not divided into unit-sized parts. Children in the actively divided condition demonstrated larger improvements matching symbolic fractions and visual fractions (i.e., pie charts) than children in the other two conditions. Posthoc analyses of children's gameplay revealed that the actively divided condition may have provided a more optimal level of difficulty for young children than the predivided condition, which was particularly difficult, and the nondivided condition, which was trivially easy. These differences in gameplay performance provide insights into possible mechanisms for our results. We discuss open research questions highlighted by this work and implications of these findings for both the development of proportional reasoning and fraction learning.

The use of higher-order thinking talk (HOTT), where speakers identify relations between representations (e.g., comparison, causality, abstraction) is examined in the spontaneous language produced by 64 typically developing (TD) and 46 brain-injured children, observed from 14-58 months at home. HOTT is less frequent in lower-income children and children with brain injuries, but effects differed depending on HOTT complexity and type of brain injury. Controlling for income, children with larger and later-occurring cerebrovascular infarcts produce fewer "surface" (where relations are more perceptual) and "structure" (where relations are more abstract) HOTT utterances than TD children. In contrast, children with smaller and earlier occurring periventricular lesions produce HOTT at comparable rates to TD children. This suggests that examining HOTT development may be an important tool for understanding the impacts of brain injury in children. Theoretically, these data reveal that both neurological (size and timing of brain injury) and environmental (family income) factors contribute to these skills.

We present a case of a 14-year-old girl born without the left hemisphere due to prenatal left internal carotid occlusion. We combined longitudinal language and cognitive assessments with functional and structural neuroimaging data to situate the case within age-matched, typically developing children. Despite having had a delay in getting language off the ground during the preschool years, our case performed within the normal range on a variety of standardized language tests, and exceptionally well on phonology and word reading, during the elementary and middle school years. Moreover, her spatial, number, and reasoning skills also fell in the average to above-average range based on assessments during these time periods. Functional MRI data revealed activation in right fronto-temporal areas when listening to short stories, resembling the bilateral activation patterns in age-matched typically developing children. Diffusion MRI data showed significantly larger dorsal white matter association tracts (the direct and anterior segments of the arcuate fasciculus) connecting areas active during language processing in her remaining right hemisphere, compared to either hemisphere in control children. We hypothesize that these changes in functional and structural brain organization are the result of compensatory brain plasticity, manifesting in unusually large right dorsal tracts, and exceptional performance in phonology, speech repetition, and decoding. More specifically, we posit that our case's large white matter connections might have played a compensatory role by providing fast and reliable transfer of information between cortical areas for language in the right hemisphere.

Although substantial work investigates childrens understanding of ordinal and magnitude-based relations, little work hasinvestigated childrens understanding of the vocabulary used for these relations and how relational language knowledgemay be constrained by symbolic number knowledge. In the current study, children were asked which of two numbers wasbigger/smaller than or before/after five. On close trials, the correct answer was 4 or 6 (one away from 5) and on far trials,the correct answer was 3 or 7 (two away from 5). We hypothesized that 4- to 6-year-olds understanding of ordinal relations(before/after) are initially constrained to refer to numbers immediately before/after (i.e., close values), but that this is notthe case for bigger/smaller comparisons. Preliminary results suggest this to be the case, with children performing betteron close trials than far trials for ordinal relations, but not magnitude relations.

A solid foundation in math is important for children's long-term academic success. Many factors influence children's math learning--including the math content students are taught in school, the quality of their instruction, and the math attitudes of students' teachers. Using a large and diverse sample of first-grade students (n = 551), we conducted a large-scale replication of a previous study (Proceedings of the National Academy of Sciences of the USA, 2010, 1860; n = 117), which found that girls in classes with highly math anxious teachers learned less math during the school year, as compared to girls whose math teachers were less anxious about math. With a larger sample, we found a negative relation between teachers' math anxiety and students' math achievement for both girls and boys, even after accounting for teachers' math ability and children's beginning of year math knowledge, replicating and extending those previous results. Our findings strengthen the support for the hypothesis that teachers' math anxiety is one factor that undermines children's math learning and could push students off-track during their initial exposure to math in early elementary school.

Differences in children's math knowledge emerge as early as the start of kindergarten, and persist throughout schooling. Previous research implicates the importance of early parent number talk in the development of math competency. Yet we understand little about the factors that relate to variation in early parent number talk. The current study examined the relation of parent math anxiety and family socioeconomic status (SES) to parent number talk with children under the age of three (n = 36 dyads). For the first time, we show preliminary evidence that parent math anxiety (MA) predicts the amount of number talk children hear at home, beyond differences accounted for by SES. We also found a significant SES by parent MA interaction such that parent MA was predictive of higher-SES parents' number talk but not that of lower-SES parents. Furthermore, we found that these relations were specific to parents' cardinal number talk (but not counting), which has been shown to be particularly important in children's math development.

Young children show remarkably sophisticated abilities to evaluate others. Yet their abilities to engage in proportional moral evaluation undergoes protracted development. Namely, young children evaluate someone who shares "absolutely" more as being "nicer" than someone who shares "proportionally" more (e.g., sharing 3-out-of-6 is nicer than sharing 2-out-of-3, because 3 > 2, even though 3/6 < 2/3), whereas adults think the opposite. We investigate the hypothesis that this prior work underestimates children's proportional social reasoning by relying on discrete and spatially separated quantities (e.g., individual stickers), which can hinder proportional reasoning even outside social contexts. In three experiments we examine whether 4- and 5-year-old children's social evaluations are impacted by the discreteness and spatial separation of the resource and compare their behavior to adults (18 to 63 years; across all samples: 38% girls/women, 62% boys/men; no other demographic data was collected). We find that children are sensitive to these features: when the resource was divided into discrete units (Experiment 1) or spatially separated (Experiment 2) children were more likely to use absolute amount, as opposed to proportion, relative to when the resources were not divided and remained spatially connected. However, adults were highly sensitive to proportion regardless of the display's perceptual features (Experiment 3), and children's use of proportion remained below adult-levels. These results suggest that perceptual features influence children's use of absolute versus proportional information in their social evaluations, which has theoretical and methodological implications for understanding children's conceptions of fairness.

The pathogenesis of ME/CFS, a disease characterized by fatigue, cognitive dysfunction, sleep disturbances, orthostatic intolerance, fever, irritable bowel syndrome (IBS), and lymphadenopathy, is poorly understood. We report biomarker discovery and topological analysis of plasma metabolomic, fecal bacterial metagenomic, and clinical data from 50 ME/CFS patients and 50 healthy controls. We confirm reports of altered plasma levels of choline, carnitine and complex lipid metabolites and demonstrate that patients with ME/CFS and IBS have increased plasma levels of ceramide. Integration of fecal metagenomic and plasma metabolomic data resulted in a stronger predictive model of ME/CFS (cross-validated AUC = 0.836) than either metagenomic (cross-validated AUC = 0.745) or metabolomic (cross-validated AUC = 0.820) analysis alone. Our findings may provide insights into the pathogenesis of ME/CFS and its subtypes and suggest pathways for the development of diagnostic and therapeutic strategies.

Shape puzzles can elicit parent-child math talk, which is critical for early math learning. However, little is known abouthow the features of the puzzles impact parent-child interactions through parents math talk. Two- to four-year-old chil-dren and their parents (current N=30; target N=128) completed two shape puzzles. The control puzzle was typical ofcommercial puzzles, including nine distinct shapes. The experimental puzzle included multiple exemplars of shapes (e.g.,three different triangles, three different quadrilaterals). We hypothesized that parents would use richer math talk with theexperimental puzzle. We coded quantity and quality of parent math talk during the interactions. Preliminary results indi-cate that parents mostly used low-level math talk (naming shapes) for both puzzles, but they used more high-level mathtalk (comparing shapes, providing shape definitions) for the experimental than the control puzzle (p=0.054). We discussparticular puzzle features that can stimulate high-quality math talk during parent-child interactions.