An Exploration of Using Children's Reasoning about Math to Identify Cognitive Profiles In Autism Spectrum Disorders

Background: Research on autism spectrum disorders (ASD) has moved toward mapping the variability in ASD (Happé et al., 2006; Szatmari, 2003; Volkmar & Klin, 2005). The search for meaningful profiles within that variability extends across multiple levels including genes, clinical presentation, and cognition. Research into cognitive profiles in ASD has been limited to performance measures on standardized tests. Investigating how children with ASD think will further enrich our understanding of cognitive profiles in ASD (Asperger, 1944). 

Mathematics is a useful domain for exploring how children with ASD think because a body of research investigating how typically developing children think about mathematical concepts is available (De Corte & Verschaffel, 2006).  For example, four different cognitive profiles of strategy discovery and generalization were revealed in Luwel et al.’s study (2005) of typically developing children’s discovery and use of strategies for subtraction. There are very few studies of mathematical thinking in children with ASD, but Jones et al. (2009) showed evidence for cognitive profiles marked by “peaks” and “dips” in reading and mathematical performance relative to full-scale IQ scores.  Little work has been done, however, on how children with ASD learn about math or whether they show the same kinds of cognitive profiles as typically developing children.  Cognitive profiles in ASD will provide rich descriptions that may complement the detailed investigations ongoing in areas such as genetics.

Objectives: The purpose of this study is to probe the reasoning of children with ASD on several math tasks, well-characterized in the literature from typical development, in order to explore math as a vehicle for establishing cognitive profiles in ASD.   

Methods: Eight children (6-14 years) with clinical diagnoses of ASD participated.  Each child completed a standardized measure of math achievement (Woodcock Johnson-III) and engaged in several tasks probing their mathematical reasoning, including number line estimation (Booth & Siegler, 2006), insightful subtraction (Luwel et al., 2005), and inversion (Bisanz et al., 2009).    

Results: Children with ASD differed from each other in both math performance and how they think about math. Not only did some children with ASD show a “math peak” relative to an overall measure of cognitive ability, but some children also showed relative “peaks” and “dips” within math. Across math tasks, three potential cognitive profiles emerged. One profile is characterized by consistently using more rote, procedurally based strategies across math tasks. A second profile is represented by consistently using more insightful, conceptually based strategies across math tasks, and a third profile is characterized by  using both kinds of strategies across tasks .  

Conclusions: Being able to map the cognitive terrain in ASD is important for understanding the variability observed in ASD. Previous studies of cognition in ASD have focused on outcome measures of thinking to the exclusion of information about the process of thinking. This study is the first to explore reasoning about math as a vehicle for examining profiles of cognition in ASD. Targeted studies of performance and reasoning on specific math tasks in children with ASD are planned.