Mathematical skills in Williams syndrome: insight into the importance of underlying representations.

Williams syndrome (WS) is a developmental disorder characterized by relatively spared verbal skills and severe visuospatial deficits. Serious impairments in mathematics have also been reported. This article reviews the evidence on mathematical ability in WS, focusing on the integrity and developmental path of two fundamental representations, namely those that support judgments of "how much" (i.e., magnitude) and "how many" (i.e., number of objects). Studies on magnitude or "number line" representation in WS suggest that this core aspect of mathematical ability, is atypical in WS throughout development, causing differences on some but not all aspects of math. Studies on the representation of small numbers of objects in WS are also reviewed, given the proposed links between this type of representation and early number skills such as counting. In WS, representation appears to be relatively typical in infancy but limitations become evident by maturity, suggesting a truncated developmental trajectory. The math deficits in WS are consistent with neurological data indicating decreased gray matter and hypoactivation in parietal areas in WS, as these areas are implicated in mathematical processing as well as visuospatial abilities and visual attention. In spite of their deficits in core mathematical representations, people with WS can learn many mathematical skills and show some strengths, such as reading numbers. Thus individuals with WS may be able to take advantage of their relatively strong verbal skills when learning some mathematical tasks. The uneven mathematical abilities found in persons with WS provide insight into not only appropriate remediation for this developmental disorder but also into the precursors of mathematical ability, their neural substrates, and their developmental importance.