Date on Senior Honors Thesis


Document Type

Senior Honors Thesis

Degree Name



Psychological and Brain Sciences

Degree Program

College of Arts and Sciences

Author's Keywords

Williams syndrome; math; cognitive; IDD; development


Williams syndrome (WS) is a genetic neurodevelopmental disorder associated with relative strengths in concrete vocabulary, nonverbal reasoning, and verbal short-term memory and considerable weaknesses in visuospatial construction and relational language. While the cognitive profile of WS has been studied extensively, there have been few studies of the early mathematical abilities of children with WS and the cognitive predictors of these abilities. The purpose of this study was to describe the early mathematical abilities of 48-month-olds with WS and determine the concurrent cognitive predictors of these abilities. The Differential Ability Scales–second edition (DAS-II) was used to determine cognitive and mathematical abilities for seventy-two 48-month-old children with WS. The DAS-II Early Number Concepts subtest was administered to determine the mathematical abilities of the participants. The cognitive predictors for mathematical abilities were DAS-II Verbal Ability standard score (SS), DAS-II Nonverbal Reasoning Ability SS, and DAS-II Spatial Ability SS. The results showed that the majority of the participants understood the concept of “one,” could count by rote to 10, and comprehended the relational concepts “big” and “little”. Significant delays in mathematical abilities, including counting with one–to–one correspondence, cardinality, and understanding of relational concepts, were identified. Regression analysis indicated that verbal ability contributed significant unique variance to individual differences in mathematical ability for 48-month-olds with WS. Implications of these findings are discussed.

Lay Summary

Williams syndrome (WS) is a neurodevelopmental disorder characterized by intellectual disability and a uniquely distinct cognitive profile which includes relative strengths in concrete vocabulary, non-verbal reasoning, and verbal short-term memory, and considerable weakness in visuospatial construction and relational language. The mathematical abilities in children with WS are delayed as compared to typically developing (TD) individuals, but the scope of these delays has not been adequately studied. The purpose of this study was to describe the mathematical abilities of 48-month-olds with WS and determine the relations between their mathematical ability and other areas of their cognitive development. The progression of mathematics throughout childhood is expected to follow a particular pattern in which certain skills develop first and more complex abilities develop later. Individuals with WS may not be equally impaired in all areas of mathematics such that they are better at answering certain types of questions than others.

Seventy-two 48-month-old children with WS were assessed using the Differential Ability ScalesSecond Edition (DAS-II), which is a standardized measure that quantifies various cognitive abilities such as verbal ability, non-verbal reasoning ability, spatial ability, and early mathematical ability. The subtest within the DAS-II that assessed mathematics is called the Early Number Concepts (ENC) subtest. First, an itemized assessment of the ENC was performed to characterize individual skills within mathematics. These skills were split into three categories that addressed different components of mathematics including counting ability, number recognition and manipulation, and relational language.

A wide range of mathematical ability was observed in the participants ranging from the lowest possible score for 48-month-olds to nearing the average for TD children of the same age. However, the overall average on the ENC was well below the average for 48-month-old TD populations. Certain mathematical abilities were more advanced in children with WS than others, but the general pattern of development was consistent with TD populations. All three cognitive predictors correlated to mathematical ability. However, verbal ability was most strongly correlated with mathematical ability and accounted for a significant amount of unique variance in the subject. The findings indicate that children with WS may rely on their relative strengths in verbal ability to construct their understanding of various mathematical concepts and that mathematical concepts that rely heavily on verbal ability may be stronger than those that rely on other cognitive abilities. Therefore, it may be appropriate to employ individualized approaches to teaching mathematics that include verbal strategies as well as allocating support to the development of spatial and nonverbal abilities that may benefit the development of various mathematical skills.