Children's strategies for numerosity judgement in square grids of different sizes

Abstract

This study investigates the development of subjects' strategies for the judgement of numerosity from the theoretical perspective of "strategic change" (Lemaire & Siegler, 1995) as initiated by Verschaffel, De Corte, Lamote and Dherdt (1998). In the present study we assessed second and sixth graders' strategy use in determining numerosities of colored blocks in square grids of three different sizes. Converging evidence from response times and error rates showed that three distinct major numerosity judgement strategies were used: (a) an addition strategy by means of which (groups of) blocks are counted (and added), (b) a subtraction strategy in which the number of empty squares is subtracted from the (estimated or computed) total number of squares in the grid, and (c) a rough estimation strategy, whereby the number of blocks is determined in a quick but imprecise way. In terms of Lemaire and Siegler's model of strategic change, second and sixth graders did not differ in the kind of strategies used but in the efficiency with which they applied them. From a methodological point of view, this study demonstrates the potential of Beem's (1993, 1999) two- and three-phase segmented curve model for detecting subjects' strategy use in cognitive tasks.