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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. Public Significance Statement: This research suggests that an optimal approach for parents in supporting early elementary children's numeracy learning is to use a combination of (a) prompts that reference relatively advanced numeracy concepts and (b) autonomy-supportive (vs. controlling) parenting practices in interacting with their children in the numeracy context. [ABSTRACT FROM AUTHOR]

Increasing evidence suggests that success in science, technology, engineering, and math (STEM) fields is not only dependent upon one's actual STEM-relevant abilities but also upon one's STEM-relevant attitudes—in particular, math and spatial attitudes. Here, we examine whether simply mentioning the math or spatial relevance of a task affects children's performance and the moderating role of children's math and spatial attitudes. Further, we examine gender differences in performance given pervasive gender gaps in STEM and early-emerging gender differences in math and spatial attitudes. Participants (221 first- to fourth-grade children from the United States; 113 girls, 108 boys; 52% White, 16% Black, 14% Asian, 9% Hispanic or Latinx, 18% multiple races/ethnicities) were introduced to a novel task framed as tapping into math or spatial abilities (or no framing [control condition]). Children then completed math and spatial anxiety and self-concept measures. Results indicate that children who heard the math task framing were less accurate relative to children in the control condition, and the effect was larger for those with higher math anxiety or lower math self-concept, but it was not different for boys and girls. Children who heard the spatial task framing, however, performed comparably to children in the control condition. Though both math and spatial attitudes revealed identical patterns of gender differences (with higher anxiety and lower self-concept in girls than boys), there were no gender differences in performance. This study highlights the salient role of math attitudes early in development and provides key insights for future work aimed at increasing STEM outcomes. Public Significance Statement: Findings reveal that children perform worse on a novel task when it is described as being related to math—but not spatial—skills, and this effect is strongest for children with more negative math attitudes. Moreover, girls had more negative math and spatial attitudes than did boys, but gender differences were not observed in performance on the task. Findings provide key insights into processes implicated in science, technology, engineering, and math outcomes. [ABSTRACT FROM AUTHOR]

The relation to operands (RO) principles describe the relation between operands and answers in arithmetic problems (e.g., the sum is always larger than its positive addends). Despite being a fundamental property of arithmetic, its empirical relation with arithmetic/algebraic problem solving has seldom been investigated. The current longitudinal study aimed to address this issue. Two-hundred-and-two Chinese fifth graders (57% boys) were assessed on their RO understanding. Their arithmetic/algebraic problem solving were assessed multiple times over 2 years. Results from latent growth curve modeling showed that RO understanding predicted the growth in arithmetic/algebraic problem solving when other known predictors of arithmetic/algebraic problem solving were controlled. The findings highlight the role of RO understanding in children's mathematical development. Interventions should be developed to enhance children's RO understanding. Public Significance Statement: The relation to operands (RO) principles, which describe the relation between operands and answers in arithmetic problems (e.g., A + B > A for all positive B), have received little attention in the literature. The current findings illustrate that children's understanding of the RO principles is related to the growth in children's arithmetic/algebraic problem solving performance. Educators should pay more attention to this construct and develop relevant interventions to ensure that children understand these arithmetic principles. [ABSTRACT FROM AUTHOR]

A longitudinal study was conducted to identify unique sources of individual differences in later understanding of the equal sign as a relational symbol of equivalence (i.e., formal understanding of mathematical equivalence). The sample included 141 children from a mid-sized city in the Midwestern United States (Mage = 6 years, 2 months in kindergarten; 88 boys, 53 girls; 71% white, 8% Hispanic or Latine, 7% Black, 3% Asian, 11% multiracial or other race/ethnicity; 42% qualified for free/reduced lunch). Children were assessed on three categories of skills in kindergarten including number knowledge, relational thinking, and executive functioning. These skills were hypothesized to provide a foundation for a formal understanding of mathematical equivalence (assessed in second grade) by preventing a specific, narrow misunderstanding of the equal sign that hinders learning. Results showed that kindergarten relational thinking, particularly tasks assessing nonsymbolic equivalence understanding, uniquely and positively predicted formal understanding of mathematical equivalence and negatively predicted the specific misunderstanding of the equal sign in second grade, controlling for IQ, gender, and free/reduced lunch status. Exploratory analyses unpacking the categories of skills into individual tasks also indicated specific areas of kindergarten instructional focus that may help children construct understanding of mathematical equivalence in future years. Public Significance Statement: Understanding the equal sign as a relational symbol of equivalence is a foundational pre-algebra concept. We found that children who had higher relational thinking skills in kindergarten had a better understanding of the equal sign by second grade than their peers with lower relational thinking skills in kindergarten. Our findings identify early relational thinking as a potential topic of interest for future research on kindergarten instruction aimed at improving later pre-algebraic learning. [ABSTRACT FROM AUTHOR]

This research examined how parents' math anxiety is associated with their controlling and autonomy-supportive involvement in children's math learning; the contribution of such involvement to children's math achievement was also evaluated. Parents (N = 562; 62% White, 21% Black; 65% with at least a bachelor's degree) of young elementary school children (Mage = 7.48 years; 50% girls) reported on their math anxiety as well as controlling and autonomy-supportive involvement in children's math learning; observations were also made. At the same time and a year later, children's math achievement was assessed. Parents with higher math anxiety were more controlling (in both parents' reports and the observations) and less autonomy supportive (only in the observations) with children who had poorer math achievement. Notably, controlling parenting (in both parents' reports and the observations) was most likely to predict lower math achievement a year later among such children. The findings suggest math-anxious parents are prone to using practices with children struggling in math that further undermine their math achievement, which can create an unconstructive cycle for children's math learning. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Research on the associations among adversity, executive function (EF), and academic outcomes in low- and middle-income countries, where developmental risk factors are more prevalent and impoverished environments are more widespread than in high income countries, is sparse. This study examines the relations among cumulative risk. EF, and learning outcomes measured 2-years later in Ghanaian third- and fourth-graders (N = 371,49% female), shedding light on underlying mechanisms of how risk can undermine learning. A cumulative risk index was created based on a set of four child-reported risk factors: home aggression, unsafe home neighborhood, hunger. and having worked for pay. Cumulative risk and EF were negatively correlated. Learning outcomes (literacy and math test scores) were negatively correlated with earlier measures of cumulative risk and positively correlated with earlier measures of EF. EF mediated the association between cumulative risk and later learning outcomes, accounting for 65.3% of the total effect for literacy and 100% for math. This mediated pathway was robust to controls for child and household sociodemographic characteristics. The findings contribute to a small evidence base on the mediating role of EF in linking adversity and learning outcomes in a global context. [ABSTRACT FROM AUTHOR]

The sustaining environments hypothesis theorizes that the lasting effects of PreK programs are contingent on the quality of the subsequent learning environment in early elementary school. The current study tests this theory by leveraging data from students (N = 462) who did and did not enroll in the Boston Public Schools (BPS) prekindergarten (PreK) program as well as features of their kindergarten instruction measured at the child- and classroom-levels using surveys and observations. Taken together, findings revealed limited evidence for the sustaining environments hypothesis. The bulk of the results were null, indicating that in general, associations between enrollment in BPS PreK and language, literacy, and math skills through the spring of kindergarten did not vary by kindergarten instructional experiences. When examining distinct types of instructional experiences, there were some inklings that child-level observational measures of kindergarten learning experiences--particularly those capturing constrained versus unconstrained instruction--were more predictive of PreK persistence than observed global classroom quality measures or survey-based measures of advanced instruction. However, these associations were not always specific to outcomes matching the content delivered during this instruction (math vs. literacy), consistent with the possibility of either cross-domain effects or that instructional variables are proxies for more general instruction;il practices. Findings for future research and theory are discussed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]