Learning without representational change: development of numerical estimation in individuals with Williams syndrome.

Experience engenders learning, but not all learning involves representational change. In this paper, we provide a dramatic case study of the distinction between learning and representational change. Specifically, we examined long- and short-term changes in representations of numeric magnitudes by asking individuals with Williams syndrome (WS) and typically developing (TD) children to estimate the position of numbers on a number line. As with TD children, accuracy of WS children's numerical estimates improved with age (Experiment 1) and feedback (Experiment 2). Both long- and short-term changes in estimates of WS individuals, however, followed an atypical developmental trajectory: as TD children gained in age and experience, increases in accuracy were accompanied by a logarithmic-to-linear shift in estimates of numerical magnitudes, whereas in WS individuals, accuracy increased but logarithmic estimation patterns persisted well into adulthood and after extensive training. These findings suggest that development of numerical estimation in WS is both arrested and atypical.