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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. 

The frequency of home spatial activities (e.g., puzzles and blocks) correlates with young children's spatial skills, but causal evidence is limited. We addressed this issue by comparing the effects of a parent‐led intervention aimed at increasing spatial activities to an active control targeting narrative activities (preregistered:https://osf.io/u7qrx). Parents of 80 4‐ and 5‐year‐old children were randomly assigned to either a spatial or narrative condition. Parents learned about the importance and malleability of spatial or narrative skills and engaged their children in spatial or narrative activities provided by the researchers for a month. Unexpectedly, the spatial intervention did not significantly enhance children's spatial skills or parents' motivational beliefs regarding children's spatial abilities. These findings do not support the hypothesis that spatial play causally influences children's skills. However, we note that the families in our sample had high socioeconomic status, and their children may have already benefited from rich spatial environments. 

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. 

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.