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Math experiences during the preschool years play an important role in children's later math learning. Preschool teachers exhibit considerable variability in the amount and types of mathematics activities they engage in with their students; one potentially important source of these individual differences is adults' knowledge of early math development. The current study aimed to describe preschool teachers' knowledge of numeracy, patterning, and spatial/geometric skills developed in preschool and its relation to their reported mathematics instruction. Participants (N = 83) completed a survey in which they judged whether particular early math skills could be observed in typically developing 4-year-olds in the United States and reported their frequency of engaging in different math instructional activities. Pre- and in-service preschool teachers' knowledge varied across the different domains (i.e., numeracy, patterning, and spatial/geometric) of mathematical thinking, but their reported frequency of instruction did not. Teachers who were found to be more accurate in their knowledge of early math development were more likely to report higher frequency of math instruction; looking specifically at the domains, the strength of association between knowledge and instruction was the strongest for numeracy. Such findings highlight the possibility that supporting preschool teachers' knowledge of the range of math skills their students can be developing may be one component of improving early math teaching and learning.

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Parents' knowledge about the math skills that most preschool-aged children can develop might be an important component of the Home Math Environment (HME) as it might shape their math beliefs and efforts to support their preschoolers' math development. This study aimed to systematically develop measures of parents' knowledge about two critical early math topics, numeracy, and patterning, across five studies conducted with a total of 616 U.S. parents of 3- to 5-year-olds (66% mothers, 54% sons, 73% White, 60% college-educated). Parents were recruited via CloudResearch or a university database. Study 1 focused on item generation to revise a previous measure to capture a wider set of children's early math skills and analysis of the psychometric properties of the measure after it was completed by 161 parents via a survey. Study 2 included an analysis of a new sample of parents (n = 21) who responded to the measures twice across two weeks to explore test-retest reliability. The measures were iteratively revised, administered to new samples, and analyzed in Studies 3 (n = 45), 4 (n = 46), and 5 (n = 344). The measures demonstrated adequate internal consistency and validity (construct, convergent, and discriminant) in Study 5 such as being positively related to parents' numeracy and patterning beliefs about their children. Overall, the newly developed measures satisfy standards for the development of an adequate measure and can be used to better understand what parents know about early math development and how this relates to the HME that they facilitate.

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Parents' academic beliefs influence the academic support they provide to their children. In this chapter, we review the published literature on empirical studies conducted with parents of preschoolers and propose a conceptual model for how different parental numeracy beliefs uniquely and differentially influence parents' early numeracy support and vary with their demographic characteristics. Parents' numeracy beliefs about their children were more consistently related to their numeracy support than their other numeracy beliefs but were inconsistently related to demographic characteristics. Parents' numeracy beliefs about themselves were significantly related to their socioeconomic status and the extent to which their numeracy support focused on advanced early numeracy skills, but were not significantly related to how often they provided numeracy support. We also discuss parents' beliefs regarding where and how children should learn numeracy. Overall, evidence to date highlights the role of parents' beliefs about their children as well as their socioeconomic status. We discuss several future directions.

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Both recent evidence and research-based early mathematics curricula indicate that repeating patterns-predictable sequences that follow a rule-are a topic of major importance for mathematics development. The purpose of the current study was to help build a theory for how early repeating patterning knowledge contributes to early math development, focusing on development in children aged 4-6 years. The current study examined the relation between 65 preschool children's repeating patterning knowledge (via a fast, teacher-friendly measure) and their end-of-kindergarten broad math and numeracy knowledge, controlling for verbal and visual-spatial working memory (WM) skills as well as end-of-pre-K (pre-kindergarten) broad math knowledge. Relations were also examined between repeating patterning and specific aspects of numeracy knowledge-knowledge of the count sequence to 100 and the successor principle. Children's repeating patterning knowledge was significantly predictive of their broad math and general numeracy knowledge, as well as one specific aspect of their numeracy knowledge (counting to 100), even after controlling for verbal and visual-spatial WM skills. Further, repeating patterning knowledge remained a unique predictor of general numeracy knowledge and counting to 100 after controlling for end-of-pre-K broad math knowledge. The relation between repeating patterning and mathematics may be explained by the central role that identifying predictable sequences based on underlying rules plays in both. Theories of math development and early math instruction standards should thus give even greater attention to the role of children's repeating patterning knowledge.

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The current study broadens our understanding of preschoolers' early math experiences with parents, recognizing that math knowledge and experiences are inclusive of numeracy as well as non-numeracy domains. Parents and preschoolers (N = 45) were observed exploring three domains of early mathematics knowledge (i.e., number, space, and pattern) during play in three activities (playing cards, building with blocks, and stringing beads, all with activity suggestions). Children were administered a broad math and numeracy measure and individual measures of spatial and patterning skills concurrently and 7 months later. Dyads explored math broadly across most activities but emphasized number more than space or patterning. In addition, there was more overall math exploration during card and bead play than during block play, with the greatest parent support during card play. Parent support was not linked to children's skills, although children's exploration of space and patterns related moderately to their concurrent spatial and pattern skills. Overall, parents and young children explored a variety of early math domains in guided play contexts, with an emphasis on numeracy. Future work should aim to increase the breadth and rigor of individual concepts that parents and preschoolers explore during play.

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