The acquisition and use of an adaptive strategy for estimating numerosity

This study investigates the development of an adaptive strategy for the estimation of numerosity from the theoretical perspective of “strategic change” (Lemaire & Siegler, 1995; Siegler & Shipley, 1995). A simple estimation task was used in which participants of three different age groups (20 university students, 20 sixth-graders and 10 second-graders) had to estimate 100 numerosities of (colored) blocks presented in a 10x10 rectangular grid. Generally speaking, this task allows for two distinct estimation procedures: either repeatedly adding estimations of groups of blocks (=addition procedure) or subtracting the estimated number of empty squares from the (estimated) total number of squares in the grid (=subtraction procedure). A rational task analysis indicates that the most efficient overall estimation strategy consists of the adaptive use of both procedures, depending on the ratio of the blocks to the empty squares. The first hypothesis was that there will be a developmental difference in the adaptive use of the two procedures, and according to the second hypothesis this adaptive use will result in better estimation accuracy. Converging evidence from different kinds of data (i.e., response times, error rates, and retrospective reports) supported both hypotheses. From a methodological point of view, the study shows the potential of Beem’s (1995a, 1995b) “segmentation analysis” for unravelling subjects’ adaptive choices between different procedures in cognitive tasks, and for examining the relationship between these adaptive choices and performance.