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Abstract Non-rigid spatial thinking, or mental transformations where the distance between two points in an object changes (e.g., folding, breaking, bending), is required for many STEM fields but remains critically understudied. We developed and tested a non-rigid, ductile spatial skill measure based on reasoning about knots with 279 US adults (M = 30.90, SD 5.47 years; 76% White; 48% women). The resultant 54-item measure had good reliability (α = .88). Next, 147 US adults (M = 20.65, SD 2.80 years; 48% White; 56% women) completed existing spatial skills measures, the knot reasoning measure, a verbal skill measure, and surveys of current and childhood spatial activities. Knot reasoning performance was significantly, positively correlated with existing measures of spatial skill. Mental rotation and paper folding, but not bending, predicted knot reasoning task performance. We replicated work showing that men performed better than women on mental rotation and unexpectedly found that men also outperformed women on paper folding and knot reasoning, but not bending, tasks. Using structural equation modeling, we found several significant mediation effects. Men who reported less masculine-stereotyped spatial activity engagement had higher performance on the mental rotation and knot reasoning tasks. Women who reported greater engagement in feminine-stereotyped spatial activities had higher paper folding and backwards knot reasoning performance. Spatial skills did not differ among math-intensive STEM, non-math-intensive STEM, and non-STEM majors. The studies introduce a reliable measure of non-rigid, ductile string transformations and provide initial evidence of the role of gender and gendered spatial activities on non-rigid spatial skills. 

Spatial skills in early childhood are key predictors of mathematical achievement. Previous studies have found that training mental rotation can transfer to arithmetic skills; however, some studies have failed to replicate this transfer effect, or observed transfer effects only in certain types of arithmetic problems. Even in studies where transfer effects were observed, the underlying mechanisms of this transfer have not been explored. This study focused on the effect of short-duration (i.e., single-session) spatial training on arithmetic skills, and tested two underlying mechanisms. First, based on the spatial modeling account, short-duration spatial training may prime spatial processing, leading to a reduction in the use of counting strategies and an increase in spatially-related strategies following spatial training. Second, from a social-psychological account, short-duration spatial training may reduce children’s state anxiety, thus allowing them more cognitive resources in spatial and arithmetic tasks. We tested these mechanisms among 80 U.S. second- and third-graders using a pretest-intervention-posttest design, with 40 children in the spatial training group and 40 in an active control group. Short-duration spatial training improved children’s overall arithmetic performance; this effect did not differ by problem type (conventional, missing-term, or two-step problems). Spatial training also reduced children’s use of counting strategies. However, we did not find a significant increase in spatially-related strategies, nor did we observe a significant reduction in state anxiety. This study makes an important contribution to understanding the mechanisms underlying the transfer effects of short-duration spatial training on arithmetic skills, providing partial support for the spatial modeling account. 

To determine their academic strengths and weaknesses, students compare their own performance across domains (e.g., math versus English), a process referred to as dimensional comparisons. For example, individuals’ higher-scoring English performance may negatively affect their math motivational beliefs (competence self-concepts and intrinsic values), resulting in favoritism toward English. Students’ motivation can also be affected by praise from adults. However, praise in one domain (e.g., English) may have unexpected negative effects on motivation in the contrasting domain (e.g., math) through dimensional comparisons. We experimentally investigated the impact of receiving praise in only one domain on students’ domain-specific motivational beliefs. We hypothesized that students would have higher motivational beliefs in the praised domain and lower motivational beliefs in the non-praised domain compared to students who received no praise. Seventh-to-9th-graders (10-15-year-olds; N=108; 46 girls; 92 living in the U.S.; 84.8% White, 2.9% Asian or Asian American, 2.9% Black or African American, 9.5% multiple races; parents’ education range: 13-18 years) showed heightened verbal competence self-concepts after receiving praise on either verbal or math performance. College students (first-to-5th-year; N=109; 89 females; 105 living in the U.S.; 58.9% White, 21.5% Asian or Asian American, 10.3% Black or African American, 5.6% multiple races, 3.7% other races) showed higher verbal intrinsic values after receiving praise on verbal performance. Results supported positive effects of praise in the verbal domain only and were inconsistent with the predicted negative effects on the non-praised domain. We suggest that students’ verbal motivational beliefs are more malleable than math beliefs when receiving disproportionate praise. 

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, SD=.58 years) from the mid-Atlantic region of the US (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 versus process praise, or person-easy versus 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 that previously thought. 

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. 

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 4th grade (Study 1, 51% girls, 65.5% White, at least 43.2% below Federal poverty line) and at 1st 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 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. 

Verbal labels for math concepts influence multiple aspects of math learning. In this study, we examined the influence of point labels (e.g., .42 as “point four two”), decomposed labels (e.g., “four tenths and two hundredths”), 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.