John Opfer
Ohio State University

Development of Numerical Estimation:
Evidence for Adaptive Choice in Representations of Numerical Quantity

Beyond a very small number, humans and other animals can only 
approximately quantify objects without counting them. This ability to 
estimate quantities seems to rely on a mental number line, which 
represents increasing numeric values by means of increasing spatial 
quantities. Two studies examined short- and long-term developments in 
children's numerical estimates, the representations that gave rise to 
those estimates, and the general hypothesis that the magnitude of 
difference between children's representations and adult feedback affects 
children's choice of numerical representations. Results indicated that the 
fine-grained, microgenetic changes observed in second graders' estimates 
mirrored coarse-grained changes observed to occur between second and 
fourth grade. In particular, between second and fourth grades, patterns of 
estimates progressed from a logarithmic to a linear series, and feedback 
accelerated this progression. Most strikingly, the magnitude of this 
acceleration was directly tied to experimental condition, in which 
feedback was manipulated to differentially impact the magnitude of 
discrepancy between a linear representation of numerical quantity and 
children's hypothesized logarithmic representation.