Verbal labels for math concepts influence multiple aspects of math learning. In this study, we examined the influence of point labels (e.g., 0.42 as point four two), decomposed labels (e.g., four tenths and two hun-dredths), and common-unit labels (e.g., forty-two hundredths) on children's processing and representation of decimal magnitudes. We randomly assigned 162 5th-and 6th-graders to briefly learn decomposed, common-unit, or point labels. Children then completed measures of decimal magnitude processing and representation. We found that the place-value labels (i.e., decomposed and common-unit labels) each showed unique advantages in reducing the whole-number bias, and common-unit labels also reduced componential processing. No difference was found in the ratio effect - which served as an index of the precision of decimal magnitude representation -among children from the three conditions. These findings add to our understanding of the role of verbal labels in math learning and have important implications for instructional practices.

Recently, there has been increasing evidence showing that males estimate whole numbers more accurately than females on the number line. However, relatively little is known about what factors contribute to this gender gap. The current study explored potential mediators of the gender difference in number line estimation, including spatial skills and spatial anxiety. In the Fall (time-point 1 [T1]), 490 children from kindergarten through fourth grade (274 girls) completed age-appropriate measures of number line estimation, spatial skills (including proportional reasoning, mental rotation, mental transformation, and visuospatial working memory), and spatial anxiety. About 5 month later in the Spring (time-point 2 [T2]), children completed the same measure of number line estimation again. Boys were more accurate on number line estimation, proportional reasoning, and mental rotation than girls, whereas girls showed higher levels of spatial anxiety. Critically, spatial skills (a latent variable constructed from proportional reasoning, mental rotation, mental transformation, and visuospatial working memory) at T1 mediated the gender difference in T2 number line estimation whereas spatial anxiety was not a significant mediator. These relationships held even after controlling for T1 number line estimation, reading achievement, and reading anxiety. Among the four spatial skills, proportional reasoning and mental rotation (but not mental transformation or visuospatial working memory) were mediators of the gender difference in T2 number line estimation. These findings constitute, to our knowledge, the first evidence regarding factors contributing to the gender difference in whole number line estimation.

Parents provide motivational and cognitive support within the same interaction, yet researchers have investigated these separately. We examined two key aspects of parental support, praise (motivational support) and spatial language (cognitive support), from fathers and mothers during three tasks with their first-grade children (6-7-year-olds; N = 107; 56 girls; 72.0% White, 23.4% Black). Parents' praise and spatial language varied by task but not child sex: Both parents produced more praise in the Etch-a-Sketch and block tasks than the card game and produced more spatial language in the Etch-a-Sketch task than other tasks. We further examined whether praise and spatial language in the two spatial tasks (Etch-a-Sketch and block construction) were related to children's later math and spatial skills. We found neither additive nor multiplicative effects of parents' praise or spatial language. We also did not see additive or multiplicative effects of fathers' and mothers' support. However, fathers' greater spatial language at first grade was negatively associated with boys' (but not girls') math achievement in third grade, with greater father spatial tokens related to their sons' lower math achievement. This suggests that boys may perceive fathers' support more negatively than girls do or that fathers may offer additional support for boys with lower abilities. Taken together, this study emphasizes the importance of considering contexts in examining parental support. The correlational nature of the study warrants future research to establish causal relations and to enhance our understanding of multifaceted parent-child interactions.

When students start learning decimals, they may incorrectly apply features of their prior numerical knowledge (e.g., whole-number or fraction rules). However, because whole numbers, fractions, and decimals all have their own unique features, these whole-number and fraction strategies do not always lead to correct solutions. We examined whether receiving immediate accuracy feedback while comparing decimal pairs that were either congruent with whole-number rules (e.g., decimals with more digits were larger in magnitude) or incongruent with whole-number rules (e.g., decimals with fewer digits were larger in magnitude) would lead students to change their decimal comparison strategies. We also examined whether students' potential improvement after feedback would generalize to decimal comparisons involving different numbers of digits. We found that sixthto eighth-grade students' use of the whole-number strategy declined and their use of the normative decimal strategy increased over the course of receiving feedback, whereas no significant strategy change was observed among students who did not receive any feedback. Students who received feedback were also less likely to use a whole-number strategy and more likely to use a decimal strategy in different decimal comparisons in an immediate posttest and a 2-week delayed posttest. Our exploratory analyses found that students' improvement on decimal comparisons did not transfer to decimal arithmetic. Moreover, students' inhibitory control also predicted strategy use in immediate and delayed posttests. Our study provides insights into the mechanisms of rapid strategy change and has implications for designing interventions to improve children's understanding of decimal magnitudes. (C) 2020 Elsevier Inc. All rights reserved.

Decades of research have established that spatial skills correlate with numerical skills. However, because both spatial and numerical skills are multidimensional, we sought to determine how specific spatial skills relate to specific numeracy skills. We used a cohort-sequential design, assessing a large diverse sample of students (N = 612, initially in pre-kindergarten [pre-K]-3rd grade, 4-9 years of age) at four time points spanning 2 years. We examined how initial levels of five spatial skills (visuospatial working memory [VSWM], mental transformation, mental rotation, proportional reasoning, and analog magnitude system [AMS] acuity) related to initial levels and growth rates in exact and approximate calculation skills, and we further investigated number line estimation as a potential mediator. We found unique patterns of relations between spatial skills and numeracy. Initial levels of mental rotation, proportional reasoning, and AMS acuity related to initial levels of exact calculation skill; initial levels of AMS acuity related to initial levels of approximate calculation; and initial levels of proportional reasoning related to initial levels of number line estimation. VSWM and mental transformation did not relate to numeracy skills after controlling for other spatial skills. Initial levels of number line estimation related to both exact and approximate calculation after controlling for spatial skills. Notably, neither spatial skills nor number line estimation predicted growth in exact or approximate calculation skills. These results indicate that there is specificity in the time-invariant relations between spatial skills and numeracy, and they suggest that researchers and educators should treat spatial skills and numeracy as multidimensional constructs with complex and unique interrelations. (c) 2021 Elsevier Inc. All rights reserved.

Young children are sensitive to both numerical and spatial magnitude cues early in development, but many questions remain about how children's attention to magnitudes relates to their early math achievement. In two studies, we tested three hypotheses related to the flexible attention to magnitudes (FAM) account, which suggests that young children's flexible attention to both numerical and spatial magnitudes is an important predictor of early math success. In Study 1, we recruited 318 preschool-age children (51.5% female; M-age = 54.7 months, SDage = 4.24 months) and assessed them at two time points on a battery of math, executive function, and language measures, including a novel assessment of FAM ability developed for this study. Consistent with our hypotheses, we found that young children had specific difficulty flexibly shifting between numerical and spatial magnitudes, that their FAM ability was related to both their executive function and math skills controlling for covariates, and finally that their FAM ability at the first time point was predictive of their math achievement growth over time controlling for executive function skills and covariates. In Study 2, we recruited 157 preschool-age children (47.4% female; M-age = 53.36 months, SDage = 7.17 months). We replicated the findings of Study 1 and extended them to account for children's non-symbolic numerical magnitude discrimination skills. Implications of the results of these studies for early math activities development are discussed.

Number lines and area models are both used pervasively in teaching fractions. Prior studies found that second and third graders demonstrated better magnitude knowledge of proper fractions after a 15-minute training using the number line as compared to using the area model. The current study aimed to extend these findings to improper fractions. We randomly assigned fourth and fifth graders to a number line training, an area model training, or a non-numerical control condition. The number line and area model trainings involved both proper and improper fractions and were closely modeled on the training procedures in prior studies. Fraction training with the area model produced improvements in children's area model estimation of proper and improper fractions. However, contrary to our expectations, training with the number line did not improve number line estimation, and neither training led to improvements in transfer tasks assessing fraction magnitude knowledge. These findings suggest that children can develop the skill to represent improper fractions on area models with brief training. Nevertheless, it is unclear whether this skill enhances a comprehensive understanding of fraction magnitudes.

Individual differences in children's number knowledge arise early and are associated with variation in parents' number talk. However, there exists little experimental evidence of a causal link between parent number talk and children's number knowledge. Parent number talk was manipulated by creating picture books which parents were asked to read with their children every day for 4 weeks.N = 100 two- to four-year olds and their parents were randomly assigned to read either Small Number (1-3), Large Number (4-6), or Control (non-numerical) books. Small Number books were particularly effective in promoting number knowledge relative to the Control books. However, children who began the study further along in their number development also benefited from reading the Large Number Books with their parents.

Children's ability to estimate fractions on a number line is strongly related to algebra and overall high school math achievement, and number line training leads to better fraction magnitude comparisons compared with area model training. Here, we asked whether unidimensionality is necessary for the number line to promote fraction magnitude concepts and whether left-to-right orientation and labeled endpoints are sufficient. We randomly assigned second and third-graders (N = 148) to one of four 15-min one-on-one, experimenter-led trainings. Three number line trainings had identical scripts, where the experimenter taught children to segment and shade the number line along the horizontal dimension. The number line conditions varied only in the vertical dimension of the training number line: pure unidimensional number line (17.5 cm horizontal line), hybrid unidimensional number line (17.5 x 0.6 cm rectangle), and square number line (17.5 x 17.5 cm). In the area model condition, children were taught to segment and shade a square (17.5 x 17.5 cm) along both dimensions. The conditions significantly differed in posttest fraction magnitude comparison accuracy (a transfer task), controlling for pretest accuracy, reading achievement, and age. In preregistered analyses, the hybrid unidimensional number line condition significantly outperformed the square area model condition and the square number line condition. In exploratory analyses accounting for training protocol fidelity, these results held and the pure unidimensional number line also outperformed the area model condition on fraction magnitude comparisons. We argue that unidimensionality is a critical feature of the number line for promoting fraction magnitude concepts because it aligns with a key concept that real numbers, including fractions, can be ordered along a single dimension. (C) 2019 Elsevier Inc. All rights reserved.

Elementary school students often lack a conceptual understanding of linear measurement, which is revealed by their poor performance when the object to be measured is not aligned with the start of the ruler. Instead of correctly counting the units that correspond to the object (e.g., inches or centimeters), children often use 1 of 2 incorrect strategies: reading off the number that corresponds to the end of the object (the least-mature, read-off strategy) and counting the hash marks that flank the object (a more mature, but still incorrect, hash-mark strategy). We hypothesized that shifting to a more mature linear measurement strategy would require the ability to inhibit less-mature prepotent responses, such as read-off and hash-mark responses. In the present study, we predicted that children with better inhibitory control would be more likely to improve in their linear measurement strategy use over one year. Participants (n = 317) were in 1st through 3rd grades when they completed a linear measurement task that required measuring objects that were not aligned with the start of the ruler; they also completed an inhibitory control task and control measures (visuospatial working memory, arithmetic calculations, and number line estimation). One year later, they repeated the linear measurement task. Students with higher initial inhibitory control were more likely to adopt a more mature strategy over time. Moreover, inhibitory control was a significant predictor of strategy improvement over and above other cognitive measures, including visuospatial working memory and arithmetic calculation skill.