Effects of praise and "easy" feedback on children's persistence and self-evaluations.

Praise is thought to affect children's responses to failure, yet other potentially impactful messages about effort have been rarely studied. We experimentally investigated the effects of praise and "easy" feedback after success on children's persistence and self-evaluations after failure. Children (N = 150; Mage = 7.97 years, SD = 0.58) from the mid-Atlantic region of the United States (73 girls; 79% White) heard one of five types of feedback from an experimenter after success on online tangram puzzles: process praise ("You must have worked hard on that puzzle"), person praise ("You must be good at puzzles"), process-easy feedback ("It must have been easy to rotate and fit those pieces together"), person-easy feedback ("It must have been an easy puzzle for you"), or a control. Next, children failed to complete a harder tangram puzzle. Preregistered primary analyses revealed no differences in persistence and self-evaluation between person and process praise or between person-easy and process-easy feedback. Exploratory analyses showed that hearing process praise led to greater persistence after failure than the control condition (d = .61) and that process-easy feedback led to greater strategy generation than the control condition. The effects of adult feedback after success may be more context dependent than previously thought.

Tracing the origins of the STEM gender gap: The contribution of childhood spatial skills.

Despite some gains, women continue to be underrepresented in many science, technology, engineering, and math (STEM) fields. Using a national longitudinal dataset of 690 participants born in 1991, we tested whether spatial skills, measured in middle childhood, would help explain this gender gap. We modeled the relation between 4th-grade spatial skills and STEM majors while simultaneously accounting for competing cognitive and motivational mechanisms. Strong spatial skills in 4th grade directly increased the likelihood of choosing STEM college majors, above and beyond math achievement and motivation, verbal achievement and motivation, and family background. Additionally, 4th-grade spatial skills indirectly predicted STEM major choice via math achievement and motivation in the intervening years. Further, our findings suggest that gender differences in 4th-grade spatial skills contribute to women's underrepresentation in STEM majors. RESEARCH HIGHLIGHTS: Using a national longitudinal dataset, we found 4th-grade spatial skills directly predicted STEM college major choice after accounting for multiple cognitive and motivational mechanisms. Strong spatial skills in 4th grade also elevated STEM major choice via enhanced math achievement and motivation in the intervening years. Gender differences in 4th-grade spatial skills contributed to women's underrepresentation in STEM college majors.

Relations among spatial skills, number line estimation, and exact and approximate calculation in young children.

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.

The dynamic nature of children's strategy use after receiving accuracy feedback in decimal comparisons.

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 sixth- to 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.

Causal Effects of Parent Number Talk on Preschoolers' Number Knowledge.

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.

Number gestures predict learning of number words.

When asked to explain their solutions to a problem, children often gesture and, at times, these gestures convey information that is different from the information conveyed in speech. Children who produce these gesture-speech "mismatches" on a particular task have been found to profit from instruction on that task. We have recently found that some children produce gesture-speech mismatches when identifying numbers at the cusp of their knowledge, for example, a child incorrectly labels a set of two objects with the word "three" and simultaneously holds up two fingers. These mismatches differ from previously studied mismatches (where the information conveyed in gesture has the potential to be integrated with the information conveyed in speech) in that the gestured response contradicts the spoken response. Here, we ask whether these contradictory number mismatches predict which learners will profit from number-word instruction. We used the Give-a-Number task to measure number knowledge in 47 children (Mage  = 4.1 years, SD = 0.58), and used the What's on this Card task to assess whether children produced gesture-speech mismatches above their knower level. Children who were early in their number learning trajectories ("one-knowers" and "two-knowers") were then randomly assigned, within knower level, to one of two training conditions: a Counting condition in which children practiced counting objects; or an Enriched Number Talk condition containing counting, labeling set sizes, spatial alignment of neighboring sets, and comparison of these sets. Controlling for counting ability, we found that children were more likely to learn the meaning of new number words in the Enriched Number Talk condition than in the Counting condition, but only if they had produced gesture-speech mismatches at pretest. The findings suggest that numerical gesture-speech mismatches are a reliable signal that a child is ready to profit from rich number instruction and provide evidence, for the first time, that cardinal number gestures have a role to play in number-learning.

Number line unidimensionality is a critical feature for promoting fraction magnitude concepts.

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 × 0.6 cm rectangle), and square number line (17.5 × 17.5 cm). In the area model condition, children were taught to segment and shade a square (17.5 × 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.

The specificity of parenting effects: Differential relations of parent praise and criticism to children's theories of intelligence and learning goals.

Individuals who believe that intelligence can be improved with effort (an incremental theory of intelligence) and who approach challenges with the goal of improving their understanding (a learning goal) tend to have higher academic achievement. Furthermore, parent praise is associated with children's incremental theories and learning goals. However, the influences of parental criticism, as well as different forms of praise and criticism (e.g., process vs. person), have received less attention. We examine these associations by analyzing two existing datasets (Study 1: N = 317 first to eighth graders; Study 2: N = 282 fifth and eighth graders). In both studies, older children held more incremental theories of intelligence, but lower learning goals, than younger children. Unexpectedly, the relation between theories of intelligence and learning goals was nonsignificant and did not vary with children's grade level. In both studies, overall perceived parent praise positively related to children's learning goals, whereas perceived parent criticism negatively related to incremental theories of intelligence. In Study 2, perceived parent process praise was the only significant (positive) predictor of children's learning goals, whereas perceived parent person criticism was the only significant (negative) predictor of incremental theories of intelligence. Finally, Study 2 provided some support for our hypothesis that age-related differences in perceived parent praise and criticism can explain age-related differences in children's learning goals. Results suggest that incremental theories of intelligence and learning goals might not be strongly related during childhood and that perceived parent praise and criticism have important, but distinct, relations with each motivational construct.

A parent-directed language intervention for children of low socioeconomic status: a randomized controlled pilot study.

We designed a parent-directed home-visiting intervention targeting socioeconomic status (SES) disparities in children's early language environments. A randomized controlled trial was used to evaluate whether the intervention improved parents' knowledge of child language development and increased the amount and diversity of parent talk. Twenty-three mother-child dyads (12 experimental, 11 control, aged 1;5-3;0) participated in eight weekly hour-long home-visits. In the experimental group, but not the control group, parent knowledge of language development increased significantly one week and four months after the intervention. In lab-based observations, parent word types and tokens and child word types increased significantly one week, but not four months, post-intervention. In home-based observations, adult word tokens, conversational turn counts, and child vocalization counts increased significantly during the intervention, but not post-intervention. The results demonstrate the malleability of child-directed language behaviors and knowledge of child language development among low-SES parents.

Intergenerational Effects of Parents' Math Anxiety on Children's Math Achievement and Anxiety.

A large field study of children in first and second grade explored how parents' anxiety about math relates to their children's math achievement. The goal of the study was to better understand why some students perform worse in math than others. We tested whether parents' math anxiety predicts their children's math achievement across the school year. We found that when parents are more math anxious, their children learn significantly less math over the school year and have more math anxiety by the school year's end-but only if math-anxious parents report providing frequent help with math homework. Notably, when parents reported helping with math homework less often, children's math achievement and attitudes were not related to parents' math anxiety. Parents' math anxiety did not predict children's reading achievement, which suggests that the effects of parents' math anxiety are specific to children's math achievement. These findings provide evidence of a mechanism for intergenerational transmission of low math achievement and high math anxiety.

Approximate number word knowledge before the cardinal principle.

Approximate number word knowledge-understanding the relation between the count words and the approximate magnitudes of sets-is a critical piece of knowledge that predicts later math achievement. However, researchers disagree about when children first show evidence of approximate number word knowledge-before, or only after, they have learned the cardinal principle. In two studies, children who had not yet learned the cardinal principle (subset-knowers) produced sets in response to number words (verbal comprehension task) and produced number words in response to set sizes (verbal production task). As evidence of approximate number word knowledge, we examined whether children's numerical responses increased with increasing numerosity of the stimulus. In Study 1, subset-knowers (ages 3.0-4.2 years) showed approximate number word knowledge above their knower-level on both tasks, but this effect did not extend to numbers above 4. In Study 2, we collected data from a broader age range of subset-knowers (ages 3.1-5.6 years). In this sample, children showed approximate number word knowledge on the verbal production task even when only examining set sizes above 4. Across studies, children's age predicted approximate number word knowledge (above 4) on the verbal production task when controlling for their knower-level, study (1 or 2), and parents' education, none of which predicted approximation ability. Thus, children can develop approximate knowledge of number words up to 10 before learning the cardinal principle. Furthermore, approximate number word knowledge increases with age and might not be closely related to the development of exact number word knowledge.

Parent praise to 1- to 3-year-olds predicts children's motivational frameworks 5 years later.

In laboratory studies, praising children's effort encourages them to adopt incremental motivational frameworks--they believe ability is malleable, attribute success to hard work, enjoy challenges, and generate strategies for improvement. In contrast, praising children's inherent abilities encourages them to adopt fixed-ability frameworks. Does the praise parents spontaneously give children at home show the same effects? Although parents' early praise of inherent characteristics was not associated with children's later fixed-ability frameworks, parents' praise of children's effort at 14-38 months (N = 53) did predict incremental frameworks at 7-8 years, suggesting that causal mechanisms identified in experimental work may be operating in home environments.

Female teachers' math anxiety affects girls' math achievement.

People's fear and anxiety about doing math--over and above actual math ability--can be an impediment to their math achievement. We show that when the math-anxious individuals are female elementary school teachers, their math anxiety carries negative consequences for the math achievement of their female students. Early elementary school teachers in the United States are almost exclusively female (>90%), and we provide evidence that these female teachers' anxieties relate to girls' math achievement via girls' beliefs about who is good at math. First- and second-grade female teachers completed measures of math anxiety. The math achievement of the students in these teachers' classrooms was also assessed. There was no relation between a teacher's math anxiety and her students' math achievement at the beginning of the school year. By the school year's end, however, the more anxious teachers were about math, the more likely girls (but not boys) were to endorse the commonly held stereotype that "boys are good at math, and girls are good at reading" and the lower these girls' math achievement. Indeed, by the end of the school year, girls who endorsed this stereotype had significantly worse math achievement than girls who did not and than boys overall. In early elementary school, where the teachers are almost all female, teachers' math anxiety carries consequences for girls' math achievement by influencing girls' beliefs about who is good at math.

"This is hard!" Children's and parents' talk about difficulty during dyadic interactions.

Children's beliefs about the contribution of effort and ability to success and failure shape their decisions to persist or give up on challenging tasks, with consequences for their academic success. But how do children learn about the concept of "challenge"? Prior work has shown that parents' verbal responses to success and failure shape children's motivational beliefs. In this study, we explore another type of talk-parent and child talk about difficulty-which could contribute to children's motivational beliefs. We performed secondary analyses of two observational studies of parent-child interactions in the United States (Boston and Philadelphia) from age 3 to fourth grade (Study 1, 51% girls, 65.5% White, at least 43.2% below Federal poverty line) and at first grade (Study 2, 54% girls, 72% White, family income-to-needs ratio M [SD] = 4.41 [2.95]) to identify talk about difficulty, characterize the content of those statements, and assess whether task context, child and parent gender, child age, and other parent motivational talk were associated with the quantity of child and parent difficulty talk. We found that many families did discuss difficulty, with variation among families. Parents and children tended to use general statements to talk about difficulty (e.g., "That was hard!"), and task context affected child and parent difficulty talk. In the NICHD-SECCYD dataset, mothers' highlighting how task features contributed to task difficulty was positively correlated with their process praise, suggesting that this talk could be motivationally relevant. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

A Growth Mindset Message Leads Parents to Choose More Challenging Learning Activities.

Prior research has shown that the home learning environment (HLE) is critical in the development of spatial skills and that various parental beliefs influence the HLE. However, a comprehensive analysis of the impact of different parental beliefs on the spatial HLE remains lacking, leaving unanswered questions about which specific parental beliefs are most influential and whether inducing a growth mindset can enhance the spatial HLE. To address these gaps, we conducted an online study with parents of 3- to 5-year-olds. We found that parents' growth mindset about their children's ability strongly predicted the spatial HLE after controlling for parents' motivational beliefs about their children, beliefs about their own ability, children's age, children's gender, and family SES. Further, reading an article about growth mindset led parents to choose more challenging spatial learning activities for their children. These findings highlight the critical role of parents' growth mindset in the spatial HLE. Crucially, these findings demonstrate that general growth mindset messages without specific suggestions for parental practices can influence parental behavior intentions. Further, these effects were also observed in the control domain of literacy, underscoring the broad relevance of the growth mindset in the HLE.

Parental intrusive homework support and math achievement: Does the child's mindset matter?

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. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Spatial skills, but not spatial anxiety, mediate the gender difference in number line estimation.

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. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Fathers' and mothers' praise and spatial language during play with first graders: Patterns of interaction and relations to math achievement.

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. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Some types of parent number talk count more than others: relations between parents' input and children's cardinal-number knowledge.

Before they enter preschool, children vary greatly in their numerical and mathematical knowledge, and this knowledge predicts their achievement throughout elementary school (e.g. Duncan et al., 2007; Ginsburg & Russell, 1981). Therefore, it is critical that we look to the home environment for parental inputs that may lead to these early variations. Recent work has shown that the amount of number talk that parents engage in with their children is robustly related to a critical aspect of mathematical development - cardinal-number knowledge (e.g. knowing that the word 'three' refers to sets of three entities; Levine, Suriyakham, Rowe, Huttenlocher & Gunderson, 2010). The present study characterizes the different types of number talk that parents produce and investigates which types are most predictive of children's later cardinal-number knowledge. We find that parents' number talk involving counting or labeling sets of present, visible objects is related to children's later cardinal-number knowledge, whereas other types of parent number talk are not. In addition, number talk that refers to large sets of present objects (i.e. sets of size 4 to 10 that fall outside children's ability to track individual objects) is more robustly predictive of children's later cardinal-number knowledge than talk about smaller sets. The relation between parents' number talk about large sets of present objects and children's cardinal-number knowledge remains significant even when controlling for factors such as parents' socioeconomic status and other measures of parents' number and non-number talk.

Malleability of whole-number and fraction biases in decimal comparison.

Children and adults often have difficulties comparing decimal magnitudes. Although individuals attempt to reconcile decimals with prior whole-number and fraction knowledge, conceptual and procedural differences between decimals and prior knowledge of whole numbers and fractions can lead to incorrect strategies. The dynamic strategy choice account has proposed that saliency, recency, prior knowledge, and other factors contribute to strategy use when reasoning about decimals. We experimentally tested this theory using a priming technique to manipulate the saliency of different strategies prior to completion of a decimal magnitude comparison task. We hypothesized that whole-number priming (practicing whole-number comparisons with feedback) would increase whole-number bias in decimal comparisons (treating decimals with more digits as larger in magnitude), whereas fraction priming would increase fraction bias (treating decimals with fewer digits as larger in magnitude). We also explored participants' performance in decimal comparisons after being primed by decimal comparisons with feedback. Sixth to eighth graders (N = 149) and adults (N = 175) were randomly assigned to 1 of 4 priming conditions: whole-number, fraction, decimal, or a control (flanker) task. Participants first completed numerical magnitude comparisons according to their priming condition (or control task) with feedback, then all conditions completed decimal comparisons without feedback. In both children and adults, fraction priming significantly reduced whole-number bias compared with the control. Among children, fraction priming significantly increased fraction bias. Moreover, children's performance in the control and whole-number-priming conditions was characterized by strong whole-number bias, but in the decimal-priming condition, relatively brief feedback substantially improved decimal comparison performance. (PsycINFO Database Record (c) 2019 APA, all rights reserved).