Strategic aspects of children's numerosity judgement

A previous study (Luwel, Verschaffel Onghena, & De Corte, 2000) revealed that 2nd and 6th graders use at least 3 different kinds of strategies for determining different numerosities of blocks presented in square grids: (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 total number of blocks in the grid (i.e. the anchor), and (c) an estimation strategy, whereby the number of blocks is determined in a quick but imprecise way. Although 6th as well as 2nd graders used the clever subtraction strategy, the majority of 2nd graders had serious trouble with the correct determination of the anchor, resulting in huge numerosity judgement errors. Since this finding seriously complicated the testing of a number of hypotheses in that study, we replicated the above study but presented the children information about the grid size. This manipulation led to a substantial increase in the proportion of appropriate subtraction strategy users and made it possible to investigate the effect of several subject and task variables on the frequency, accuracy, and adaptiveness with which the different strategies were applied. Results are discussed in terms of the conceptual framework of Lemaire and Siegler (1995) regarding strategic change.