Making numbers count: The early development of numerical inferences.

Abstract

Two experiments examined preschool children's ability to draw inferences about numerosity from correspondences between sets. In Experiment I, 3-and 4-year-old children made numerical inferences about a hidden set from their own counts of a corresponding visible set and also from numerical information about that set stated by the experimenter. Experiment 2 contrasted a count condition with a move condition, in which children's attention was not explicitly drawn to the numerosity of the visible set. Again, children were able to make numerical inferences as early as 3 years of age. However, differences between the 2 conditions implicate production deficiencies in young children's use of counting as a problem-solving strategy when they are not explicitly told to count.

Putting counting to work: preschoolers’ understanding of cardinal extension

“…The data from the two conditions were therefore pooled for subsequent analysis. This finding is in marked contrast to that obtained by Sophian et al (1995). Thus, the question remained as to why some children used counting and others did not.…”

“…Consequently our tests needed to eliminate the possibility that children would use spatial similarity as a means of establishing equivalence. We achieved this by modifying the procedure used by Sophian et al (1995) where children are shown animals that go to a party by boat (one animal per boat). In the present study the boats travelled down a narrow river (only one boat wide, thereby precluding the possibility that children would use spatial matching rather than their knowledge of cardinality to establish corresponding sets).…”

“…First, did children who successfully created equivalent sets do so because they had been prompted to count, by virtue of being asked to count the frogs first, as suggested by Sophian et al (1995)? If competence is masked by a 'production deficiency' there should be a significant difference between children who are prompted to count frogs and those not prompted.…”

“…To this end we devised two different tasks as measures of cardinality understanding. Our experiments use the child-friendly procedure of Sophian, Wood, and Vong (1995) in order to assess whether children can solve problems of numerical equivalence via counting and cardinal extension in two contexts. The first examines whether children use counting to ensure that sets are put in item-to-item correspondence.…”

Oral counting sequences: a theoretical discussion and analysis through the lens of representational redescription

“…A large body of Author's copy of the paper as accepted for publication 3 literature has explored the development of children's oral counting skills (e.g., Bruce & Threlfall, 2004;Fuson, 1992a;Fuson, 1992b;Threlfall, 2008), the development of children's counting competencies (e.g., Bialystok & Codd, 1997;Fuson, 1992b;Gelman & Greeno, 1989;Greeno, Riley & Gelman, 1984), and the use of counting as a calculation and problem solving strategy by children of different ages and attainment in mathematics (e.g., Lefevre et al, 2002;Siegler, 2006;Siegler & Robinson, 1982;Sophian, Wood & Vong, 1995). However, there has not been much attention to children's learning of oral counting in steps bigger than 1 (e.g., counting in steps of 2, 5 or 10) and to how children develop this skill into processes that can support their calculations, despite the acknowledged significance of such counting skills (often referred to as "step" or "skip" counting) for mental calculation (Anghileri, 2008;Thompson, 2008).…”