By Julie Sarama
This significant new e-book synthesizes correct examine at the studying of arithmetic from beginning into the first grades from the total variety of those complementary views. on the center of early math specialists Julie Sarama and Douglas Clements's theoretical and empirical frameworks are studying trajectories—detailed descriptions of children’s pondering as they learn how to in attaining particular ambitions in a mathematical area, along a comparable set of educational initiatives designed to engender these psychological procedures and circulate young children via a developmental development of degrees of considering. Rooted in simple problems with pondering, studying, and educating, this groundbreaking physique of analysis illuminates foundational subject matters at the studying of arithmetic with functional and theoretical implications for every age. these implications are in particular vital in addressing fairness matters, as figuring out the extent of taking into consideration the category and the contributors inside it, is essential in serving the wishes of all young children.
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Extra resources for Early Childhood Mathematics Education Research: Learning Trajectories for Young Children
1. Developmental progression. , Clements, Wilson, & Sarama, 2004; Steﬀe & Cobb, 1988). These actions-on-objects are children’s main way of operating on, knowing, and learning about, the world, including the world of mathematics. 2. Domain speciﬁc progression. These developmental progressions often are most propitiously characterized within a speciﬁc mathematical domain or topic (see also Dowker, 2005; Karmiloﬀ-Smith, 1992; cf. Resnick’s “conceptual rationalism,” 1994; Van de Rijt & Van Luit, 1999).
An intermediate position appears warranted, such as interactionalist theories that recognize the interacting roles of the nature and nurture (Newcombe, 2002). In interactionalist, constructivist theories, children actively and recursively create knowledge. Structure and content of this knowledge are intertwined and each structure constitutes the organization and components from which the child builds the next, more sophisticated, structure. In comparison to nativism’s initial representational cognition, children’s early structures are prerepresentational.
Supporting this position, Fitzhugh (1978) found that some children could subitize sets of one or two, but were not able to count them. None of these very young children, however, were able to count any sets that they could not subitize. She concluded that subitizing is a necessary precursor to counting. Research with infants similarly suggested that young children possess and spontaneously use subitizing to represent the number contained in small sets, and that subitizing emerges before counting (A.