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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.

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.

Learning to read is a critical but often challenging academic task for young children. In the current study, we explore the relation between children's reading affect--particularly anxiety--and reading achievement in the early years of reading acquisition. We hypothesized that reading anxiety would relate to reading achievement across the school year and that boys and girls might show differential patterns in the relation between reading anxiety and achievement due to the common stereotype that boys underperform in reading. A sample of first and second grade students completed measures of reading anxiety, positive reading affect, math achievement, and reading achievement in the fall and spring. Results show that reading anxiety and reading achievement share a bi-directional relation in which fall reading anxiety predicts spring reading achievement and vice versa. Furthermore, the pattern of relation between reading anxiety and achievement differs by gender: boys appear more susceptible to the reciprocal damaging effects of reading anxiety on reading achievement across the school year. Finally, reading achievement shares a stronger relation with reading anxiety than with positive reading affect, perhaps because of the phenomenon in which negative relative to positive experiences have a greater psychological impact.

School-entry math achievement is a strong predictor of math achievement through high school. We asked whether reciprocal relations among math achievement, math anxiety, and entity motivational frameworks (believing that ability is fixed and a focus on performance) can help explain these persistent individual differences. We assessed 1st and 2nd graders' (N = 634) math achievement, motivational frameworks, and math anxiety 2 times, 6 months apart. Cross-lagged path analyses showed reciprocal relations between math anxiety and math achievement and between motivational frameworks and math achievement. Entity motivational frameworks predicted higher math anxiety. High math achievement was a particularly strong predictor of lower math anxiety and less entity-oriented motivational frameworks. We concluded that reciprocal effects are already present in the first 2 years of formal schooling, with math achievement and attitudes feeding off one another to produce either a vicious or virtuous cycle. Improving both math performance and math attitudes may set children onto a long-lasting, positive trajectory in math.

In a previous study, Mix et al. (2016) reported that spatial skill and mathematics were composed of 2 highly correlated, domain-specific factors, with a few cross-domain loadings. The overall structure was consistent across grade (kindergarten, 3rd grade, 6th grade), but the cross-domain loadings varied with age. The present study sought to replicate these patterns. Using the data from Wave 1 (n = 854) and data collected from a 2nd sample of kindergarten (n = 251), 3rd-grade (n = 247), and 6th-grade students (n = 241) with the same measures as in Wave 1, we carried out a multigroup confirmatory factor analysis to compare the 2 waves. We also completed several analyses of the Wave 2 data alone. The overall pattern obtained in Wave 1-2 highly correlated domain-specific factors--was clearly replicated in Wave 2. However, more subtle effects involving cross-domain loading were only partially replicated and generally appear fragile and context-specific. In Wave 2, we also included 2 new measures (i.e., proportion matching and fraction identification) that were analyzed in a separate model. Including these new measures did not change the overall pattern of factors and domain-specific factor loadings but did alter some of the cross-domain loadings.

Summer slide, uneven growth of academic skills during the calendar year, captures the fact that the learning gains children make during the school year do not continue at the same pace over the summer, when children are typically not in school. We compared growth of reading skills during the school year and during the summer months in children with prenatal or perinatal brain lesions (PL) and typically developing (TD) children from varying socioeconomic-status (SES) backgrounds as a new way to probe the role of structured environmental support in functional plasticity for reading skills in children with PL. Results showed that children with PL performed worse than TD children on both reading decoding and reading comprehension. Group differences were primarily driven by children with larger lesions and children with right-hemisphere lesions (RH). For reading comprehension, children with RH showed greater growth during the school year but more slide during the summer months than both TD children and children with left-hemisphere lesions, implicating a particularly strong role of structured input in supporting reading comprehension in this group. TD children from lower-SES backgrounds fell behind their TD peers from higher-SES backgrounds on decoding and reading comprehension but did not show differential patterns of school year and summer growth. Overall, results highlight the importance of considering the role of a host of factors interacting at multiple levels of analyses, including biological and environmental, in influencing developmental trajectories of TD children and atypically developing children.

Proportional reasoning involves thinking about parts and wholes (i.e., about fractional quantities). Yet, research on proportional reasoning and fraction learning has proceeded separately. This study assessed proportional reasoning and formal fraction knowledge in 8- to 10-year-olds. Participants (N = 52) saw combinations of cherry juice and water in displays that highlighted either part-whole or part-part relations. Their task was to indicate on a continuous rating scale how much each mixture would taste of cherries. Ratings suggested the use of a proportional integration rule for both kinds of displays, although more robustly and accurately for part-whole displays. The findings indicate that children may be more likely to scale proportional components when being presented with part-whole as compared with part-part displays. Crucially, ratings for part-whole problems correlated with fraction knowledge, even after controlling for age, suggesting that a sense of spatial proportions is associated with an understanding of fractional quantities.

Although math anxiety is associated with poor mathematical knowledge and low course grades (Ashcraft & Krause, 2007), research establishing a connection between math anxiety and math achievement has generally been conducted with young adults, ignoring the emergence of math anxiety in young children. In the current study, we explored whether math anxiety relates to young children's math achievement. One hundred and fifty-four first- and second-grade children (69 boys, 85 girls) were given a measure of math achievement and working memory (WM). Several days later, children's math anxiety was assessed using a newly developed scale. Paralleling work with adults (Beilock, 2008), we found a negative relation between math anxiety and math achievement for children who were higher but not lower in WM. High-WM individuals tend to rely on WM-intensive solution strategies, and these strategies are likely disrupted when WM capacity is co-opted by math anxiety. We argue that early identification and treatment of math anxieties is important because these early anxieties may snowball and eventually lead students with the highest potential (i.e., those with higher WM) to avoid math courses and math-related career choices. (Contains 3 figures, 1 table, and 2 footnotes.)

This study examines the development of children's ability to reason about proportions that involve either discrete entities or continuous amounts. Six-, 8- and 10-year olds were presented with a proportional reasoning task in the context of a game involving probability. Although all age groups failed when proportions involved discrete quantities, even the youngest age group showed some success when proportions involved continuous quantities. These findings indicate that quantity type strongly affects children's ability to make judgments of proportion. Children's greater success in judging proportions involving continuous quantities appears to be related to their use of different strategies in the presence of countable versus noncountable entities. In two discrete conditions, children--particularly 8- and 10-year-olds--adopted an erroneous counting strategy, considering the number of target elements but not the relation between target and nontarget elements, either in terms of number or amount. In contrast, in the continuous condition, when it was not possible to count, children may have relied on an early developing ability to code the relative amounts of target and nontarget regions. (Contains 3 figures and 5 tables.)

Two experiments tested the ability of 4- and 8-year-old children to encode the extent of a target dowel and later discriminate between the target and a foil having a novel extent. By manipulating the heights of containers in which we presented the stimuli we tested whether children used the relation between the dowels and containers for encoding extent. We found that 8-year-olds encoded extent without relying on the relation between the target dowel and container but 4-year-olds only encoded the extent of the target dowel relative to the container. This early ability to encode extent relative to an aligned standard may serve as a perceptual basis for the developing ability to measure. (Contains 1 figure and 1 table.)