Thursday, May 20, 2010
Franklin Hall B Level 4 (Philadelphia Marriott Downtown)
Asperger (1944) asserted that observing how individuals think is as important as establishing the level at which individuals think. In studies of cognitive development, assessing strategy use has been a productive avenue for understanding how children think (Pressley & Hilden, 2006; Siegler, 2005). Variability in generating and using strategies when solving math problems is associated with increased generalization (Alibali, 1999; Siegler, 2006). Therefore, investigating strategy generation and use is proposed as a way to describe how children with ASD think and eventually, as a way to investigate generalization – a difficult process for children with ASD (Klin et al., 2005).
Both Asperger (1944) and Kanner (1943) provided limited descriptions of how children with ASD solved math problems. Since the 1940s studies of math in ASD have been focused on standardized measures of math skills (reviewed by Chiang & Lin, 2007) or on savant skills such as calendar calculation (e.g., Thioux et al., 2007). There has been little, if any, work on how children with ASD learn about math or if they show the same kind of strategy generation, use, and variability observed in typically developing children.
To investigate the development of mathematical thinking in children with high functioning autism (HFA) by exploring their performance, reasoning, and strategy use on tasks that are well-characterized in typical development such as equivalence problems (e.g., 6 + 3 + 7 = ___ + 7) (Alibali et al., 2009) and the principle of inversion where a + b – b must equal a (Bisanz et al., 2009; Siegler & Stern, 1998).
Measures of mathematical thinking including counting, estimation, equivalence, and inversion were given during play-based sessions that were video-taped. Two boys (ages 6 and 9 years-old) with HFA, both recruited from the community and both in mainstream classrooms, have participated. Recruitment continues.
Both boys showed robust math abilities and used distinct strategies. For example, when solving two-digit arithmetic problems presented either numerically or in the context of word problems, W.K., age 6, used two strategies in combination, a counting-on strategy and keeping track of his counting by using parallel number lines (i.e., for 31 minus 12, counting “13, 1, 14, 2, 15, 3…” and so on until 31) instead of using another means, such as his fingers. In another example, R.A., age 9, was able to explain correct use of the shortcut inversion strategy (e.g., for 13 + 24 – 24 explaining that adding and subtracting the same thing leaves 13) when solving inversion problems presented both with Arabic numerals and arbitrary non-numeric symbols.
This study is the first to explore the strategies children with HFA use as they solve math problems. As the study continues we will be able to document the range and effectiveness of strategies used by children with HFA. In addition, self-reports of the strategies used by both boys suggest that children with HFA may be able to reflect on and describe their problem-solving approach.