Origins of Quantitative Competence

Children's developing numerical notations: The impact of input display, numerical size and operational complexity

“…The present results support the view that numerical notations constitute a functional instrument in the child's negotiation with the environment (Donald, 1991;Miller, 1996;Olson, 1995;Tolchinsky, 2003;Vygotsky, 1978) and suggest that this occurs earlier than had previously been claimed (Bialystok & Codd, 1996). The results confirm the trend from iterative to digital notation that had previously been described (Bialystok & Codd, 1996;Sinclair et al, 1988) and also the coexistence of several notational 'strategies' at one time.…”

“…A number of authors have argued that conceptual mathematical knowledge should precede children's exposure to mathematical symbols since they assume that the ability to produce and understand notation is contingent upon conceptual understanding (Kamii, 1986;Lehrer, Schauble, Carpenter, & Penner, 2000). In contrast, others have argued that there is coevolution between conceptual and notational aspects in the development of children's mathematical thinking (Bowers, 2000;Miller, 1996;Sfard, 2000). Tolchinsky (2003) proposes a constructivist approach to the developmental study of notations, suggesting that drawing, writing or numerals deserve to be studied in their own right, rather than as a derivative.…”

“…Children are differentially familiar with these purposes (Ewers-Rogers & Cowan, 1996). Numerals in the environment could provide the child with elements to support mathematical development (Miller, 1996;Sinclair & Sinclair, 1984;Tolchinsky, 2003). The current study considers young children's ability to use numerical notations symbolically and the ways in which their developing skills are influenced by the form of the external representation that the child is presented with and the characteristics of the task she is involved in.…”

The Whorfian hypothesis and numerical cognition: is `twenty-four' processed in the same way as `four-and-twenty'?

“…There is now repeated evidence that this notation helps Asian children to understand the number system more quickly and more profoundly (e.g. Miller, 1996;Miura et al, 1993). For instance, when young Asian children are asked to represent numbers with two types of blocks that stand for tens and units, they are likely to use both types of blocks, whereas Western children of the same age have a higher tendency to represent the numbers by an equivalent amount of unit blocks.…”

Does the Coordination of Verbal and Motor Information Explain the Development of Counting in Children?

“…Speed and accuracy of saying the number words depend on retrieving them in the correct order ("un" to "seize," one to sixteen; Fuson, Richards, & Briars, 1982;Miller, 1996) and elaborating them ("dix-sept," "dixhuit," . .…”