This chapter provides an overview of the challenges facing young children as they acquire early number concepts, and the power of domain general processes to support this learning. Four specific domain general cognitive processes are reviewed—statistical learning, structure mapping, language acquisition, and spatial cognition. For each one, there is evidence presented for the process itself in the literature on early childhood learning, and evidence presented for its contribution to number learning in the literature on number concept development. These processes alone might explain the origins of numeracy without appealing to inborn enumeration or quantitative representations. In either case, these processes clearly play a major role and may be useful leverage points for teachers, caregivers, and parents seeking to support children's learning.
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Years before children receive formal instruction in mathematics, they begin constructing concepts for number meanings and basic arithmetic. These early concepts are built from parental input (Berkowitz, Schaeffer, Maloney, Peterson et al., 2018; Zippert & Rittle-Johnson, 2020), preschool instruction (Brenneman, Stevenson-Boyd, & Frede, 2009; Lehrl, Kluczniok, & Rossbach, 2016), explorations during play (Hassinger-Das, Bustamante, Hirsh-Pasek, & Golinkoff, 2018; Ramani & Eason, 2015) and everyday mathematics experiences, such as shopping (MacDonald, Fenton, & Davidson, 2018). Well-articulated early childhood mathematics curricula exist (e.g., Montessori, 1917; Clements & Sarama, 2007), but not all children have access to these curricula and at least basic number concepts seem to emerge for most children without targeted instruction, using only sparse and incidental information (e.g., Mix, Prather, Smith, & Stockton, 2014; Yuan, Xiang, Crandell, & Smith, 2020). By what cognitive mechanisms might this informal learning occur?
Understanding these mechanisms is critical to address the well-known early childhood achievement gap in mathematics that follows children from kindergarten into adolescence (e.g., Watts, Duncan, Siegler, & Davis-Kean, 2014). Although researchers are learning more about the mathematics input preschool children receive (Gunderson & Levine, 2011; Klibanoff, Levine, Huttenlocher, Vasilyeva, & Hedges, 2006; Ramani, Rowe, Eason, & Leech, 2015), less is known about the cognitive processes through which they build these key concepts. Yet, innovation in early childhood education depends on a deep mechanistic understanding of these processes—the means by which children move from one skill level to another. This chapter offers a framework focused on four candidate processes —statistical learning, structure mapping, language acquisition, and spatial cognition. By understanding how these processes operate, and specifically, how they might operate on early childhood number input, we can gain insight into both how children acquire these concepts with sparse data, and effective ways adults can support and expand this learning.