Using a sample of 883 Latiné engineering students, the present study explored the measurement characteristics of the Negative Outcome Expectations Scale for Engineers (NOES-E), applying advanced psychometric techniques, including bifactor and the exploratory structural equation modeling (ESEM) framework, to ascertain the scale's most suitable factor structure. Additionally, measurement invariance across Latino and Latina participants was tested to investigate if the scale operates equally across gender groups and whether the latent mean scores are invariant. The results suggested that the bi-factor ESEM provided the best model fit when contrasted with other possible factor structures. The findings generally highlighted the general factor as reflecting the negative outcome expectations, suggesting that the use of total score is advised over the use of individual subscale scores. Findings from the measurement invariance testing across men and women indicated the NOES-E score can be compared between both groups.

Infants begin to produce abstract “math” words – such as numbers (e.g., “two”), spatial terms (e.g., “down”), and magnitude words (e.g., “more”) – during their second postnatal year. Math words, as all words, are likely learned in the home setting during interactions with caregivers. However, everyday early exposure to math talk is understudied. What referents and social cues accompany caregivers' math-related speech to infants? We examined U.S. infants' (25 girls, 25 boys; ages 13 to 23 months; 60% white non-Latine) exposure to math words at home during everyday activities with their mothers. We documented three types of math words/phrases (i.e., number, spatial, and magnitude words), their referents (e.g., images in books), and the social cues that accompanied math talk (e.g., gestures). Math words appeared in 15% of mothers' utterances (13,000+ math utterances in aggregate), increased with child age, mostly specified spatial concepts (e.g., location and direction), and tended to refer to objects and actions in the environment that were relevant to the child, such as toys, books, and the child's body and behaviors. Social cues accompanied mothers' math talk about half the time. Notably, certain types of referents and social cues aligned with specific types of math talk (e.g., manual gestures such as points accompanied talk about spatial features such as shapes). In the everyday home environment, infants experience frequent and varied math words, across a variety of activities, in the presence of salient social and contextual cues.

Scientists and laypeople alike have long been inspired by infants' acquisition of skills-from walking to talking to interacting with objects. Indeed, complementary aims of developmental science are to characterize infants' changing skills and identify the experiences that propel learning. Our observations of infants' unconstrained behavior in the ecologically-valid home environment have led to new insights on learning that integrate theory at the intersection of Piaget's writings on embodied action and Vygotsky's writings on the socially embedded nature of learning. These insights formed the basis of my plenary talk at the Jean Piaget Society conference, at which I underscored the need to: (1) surmount soundbites that early learning is rapid and effortless by characterizing the immense amount of practice that infants generate across domains such as playing, walking, and talking; (2) reinforce Piaget's observation that cognition is grounded in sensorimotor action; (3) challenge assumptions that controlling the environment is the only way to identify learning mechanisms; and (4) elucidate the shared and unique developmental contexts that frame infants' learning across cultural communities. Objective documentation of the natural behaviors, cultural niches, and learning opportunities of infants around the world is fundamental to science.

Infants begin to produce abstract “math” words – such as numbers (e.g., “two”), spatial terms (e.g., “down”), and magnitude words (e.g., “more”) – during their second postnatal year. Math words, as all words, are likely learned in the home setting during interactions with caregivers. However, everyday early exposure to math talk is understudied. What referents and social cues accompany caregivers' math-related speech to infants? We examined U.S. infants' (25 girls, 25 boys; ages 13 to 23 months; 60% white non-Latine) exposure to math words at home during everyday activities with their mothers. We documented three types of math words/phrases (i.e., number, spatial, and magnitude words), their referents (e.g., images in books), and the social cues that accompanied math talk (e.g., gestures). Math words appeared in 15% of mothers' utterances (13,000+ math utterances in aggregate), increased with child age, mostly specified spatial concepts (e.g., location and direction), and tended to refer to objects and actions in the environment that were relevant to the child, such as toys, books, and the child's body and behaviors. Social cues accompanied mothers' math talk about half the time. Notably, certain types of referents and social cues aligned with specific types of math talk (e.g., manual gestures such as points accompanied talk about spatial features such as shapes). In the everyday home environment, infants experience frequent and varied math words, across a variety of activities, in the presence of salient social and contextual cues.

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Mounting evidence suggests that home engagement in mathematics is related to variability in early math skill. Although prior work has investigated parental predictors of home math engagement more broadly, it remains understudied whether the same factors relate to toddlers' home math environment, and if home math experiences are associated with toddlers' math skills. Here we asked whether parents' beliefs, attitudes, and experiences with math relate to their engagement in home numeracy and spatial activities with toddlers and are associated with toddlers' developing number and spatial skills (N = 189). We find that a broad range of parent factors, including parents' beliefs about the importance of math, math growth mindset beliefs, math anxiety, and math coursework, predicts parents' frequency of engaging in numeracy activities with toddlers. Furthermore, home number activities predicted toddlers' number skills. Parents' math beliefs, attitudes, and experiences all had positive indirect effects on toddlers' number skills through associations with number activities. However, none of these parent factors predicted home spatial activities, and we saw no association between home spatial activities and toddlers' spatial skills. Altogether, these results suggest that even at very young ages, parent factors shape the home environment and toddlers' early numeracy learning, but we did not detect associations for spatial skills.