Children learn math concepts long before they enter school. Across all cultures, children are exposed to number and spatial language to varying degrees during everyday home routines. Yet most studies of math talk occur in the lab and target non-Hispanic, English-speaking families. We expanded inquiry to the spontaneous math language (i.e., number and spatial language) of Spanish-speaking mothers and their 1- to 2-year-olds (N = 50) during home activities. Mothers varied enormously in their use of math language, and mother math language related to toddler math language, whereas mother non-math language did not. Children's math language both preceded and followed mother math talk, suggesting imitation and reinforcement as important processes in children's math language learning. Children also produced math language outside the context of mother input. Findings advance an understanding of children's early math language in natural settings and have implications for interventions aimed at promoting math skills in toddlers from diverse backgrounds.

Early mathematics skills relate to later mathematics achievement and educational attainment, which in turn predict career choice, income, health and financial decision-making. Critically, large differences exist among children in early mathematics performance, with parental mathematics engagement being a key predictor. However, most prior work has examined mothers' mathematics engagement with their preschool- and school-aged children. In this Registered Report, we tested concurrent associations between mothers' and fathers' engagement in mathematics activities with their 2- to 3-year-old toddlers and children's mathematics performance. Mothers and fathers did not differ in their engagement in mathematics activities, and both parents' mathematics engagement related to toddlers' mathematics skills. Fathers' mathematics engagement was associated with toddlers' number and mathematics language skills, but not their spatial skills. Mothers' mathematics engagement was only associated with toddlers' mathematics language skills. Critically, associations may be domain-specific, as parents' literacy engagement did not relate to measures of mathematics performance above their mathematics engagement. Mothers' and fathers' mathematics activities uniquely relate to toddlers' developing mathematics skills, and future work on the nuances of these associations is needed.

Development is complex. It encompasses interacting domains, at multiple levels, across nested time scales. Embracing the complexity of development-while addressing the challenges inherent to studying infants-requires researchers to make tough decisions about what to study, why, how, where, and when. My own view is inspired by a developmental systems approach, and echoed in Esther Thelen's (2005) mountain stream metaphor. Like a river that carves its course, the active infant navigates the social and physical environment and generates rich inputs that propel learning and development. Drawing from my experiences, I offer some recommendations to guide research on infants. I encourage researchers to embrace discovery science; to observe infants in ecologically valid settings; to recognize the active and adaptive nature of infant behavior; to break down silos and consider the nonobvious; and to adopt full transparency in all aspects of research. I draw on cascading influences in infant play, language, and motor domains to illustrate the value of a bottom-up, cross-domain, collaborative approach.

Parents’ beliefs about the importance of math predicts their math engagement with their children. However, most work focuses on mothers’ math engagement with preschool- and school-aged children, leaving gaps in knowledge about fathers and the experiences of toddlers. We examined differences in mothers’ and fathers’ ( N = 94) engagement in math- and non-math activities with their two-year-old girls and boys. Parents reported their beliefs about the importance of math and literacy for young children and their frequency of home learning activities. Parents of sons did not differ in their engagement in math activities from parents of daughters. Mothers reported engaging more frequently in math activities with their toddlers than fathers did, but the difference reduced when parents endorsed stronger beliefs about the importance of math for children. Even at very early ages, children experience vastly different opportunities to learn math in the home, with math-related experiences being shaped by both parent gender and parents’ beliefs.

Recent evidence suggests that infants and toddlers may recognize counting as numerically relevant long before they are able to count or understand the cardinal meaning of number words. The Give-N task, which asks children to produce sets of objects in different quantities, is commonly used to test children’s cardinal number knowledge and understanding of exact number words but does not capture children’s preliminary understanding of number words and is difficult to administer remotely. Here, we asked whether toddlers correctly map number words to the referred quantities in a two-alternative forced choice Point-to-X task (e.g., “Which has three?”). Two- to three-year-old toddlers ( N = 100) completed a Give-N task and a Point-to-X task through in-person testing or online via videoconferencing software. Across number-word trials in Point-to-X, toddlers pointed to the correct image more often than predicted by chance, indicating that they had some understanding of the prompted number word that allowed them to rule out incorrect responses, despite limited understanding of exact cardinal values. No differences in Point-to-X performance were seen for children tested in-person versus remotely. Children with better understanding of exact number words as indicated on the Give-N task also answered more trials correctly in Point-to-X. Critically, in-depth analyses of Point-to-X performance for children who were identified as 1- or 2-knowers on Give-N showed that 1-knowers do not show a preliminary understanding of numbers above their knower-level, whereas 2-knowers do. As researchers move to administering assessments remotely, the Point-to-X task promises to be an easy-to-administer alternative to Give-N for measuring children’s emerging number knowledge and capturing nuances in children’s number-word knowledge that Give-N may miss.

Play offers an unparalleled opportunity for young children to gain cognitive skills in informal settings. Block play in particular-including interactions with parents around block constructions-teaches children about intrinsic spatial features of objects (size, shape) and extrinsic spatial relations. In turn, early spatial cognition paves the way for later competencies in math and science. We assessed 4- and 5-year-old children's spatial skill on a set of block-building constructions and examined mother-child block building interactions in 167 U.S. dyads from African American, Dominican, Mexican, and Chinese backgrounds. At both ages, children were instructed to copy several 3D block constructions, followed by a break during which mothers and children were left alone with the blocks. A form that contained pictures of test items was left on the table. Video-recordings of mother-child interactions during the break were coded for two types of building behaviors - test-specific construction (building structures on the test form) or free-form construction (building structures not on the test form). Chinese children outperformed Mexican, African American, and Dominican children on the block-building assessment. Further, Chinese and Mexican mother-child dyads spent more time building test-specific constructions than did African American and Dominican dyads. At an individual level, mothers' time spent building test-specific constructions at the 4-year (but not 5-year) assessment, but not mothers' initiation of block building interactions or verbal instructions, related to children's performance, when controlling for ethnicity. Ethnic differences in children's block-building performance and experiences emerge prior to formal schooling and provide a valuable window into sources of individual differences in early spatial cognition.