Generalisation in students with autism spectrum disorder: an exploratory study of strategies

Abstract

Generalisation is a skill that enables learners to acquire knowledge in general, and mathematical knowledge in particular. It is a core aspect of algebraic thinking and, in particular, of functional thinking, as a type of algebraic thinking. Introducing primary school children to functional thinking fosters their ability to generalise, explain and reason with mathematical relationships. It also helps them overcome difficulties in understanding functions when they are exposed to the idea more formally in secondary education. Although more and more special education students are enrolled in mainstream schools, little is known about algebraic thinking in that community, especially in the case of students with autism spectrum disorder (ASD). Students with ASD often exhibit deficits that interfere directly with mathematical learning. The study discussed here, which was conducted in the context of algebraic reasoning, was aimed primarily at identifying and describing the strategies and representations observed in 26 ASD primary education students when performing a task that involved a linear function, and describing the generalisations they performed. The 26 participants were enrolled in 19 mainstream Spanish schools. The tools used, a questionnaire and semi-structured interview, were designed to explore their ability to generalise in a problem involving the function f(x) = 2x + 2. The strategies identified included: (a) bald answering; (b) modelling with manipulatives; (c) drawing; (d) counting and (e) operating. The strategy most frequently observed was operating, represented verbally or symbolically, followed by drawing. Only three students generalised but did not reach the highest level of functional thinking, namely, ‘functions as objects’. The results are compared with findings for mainstream students of similar ages. Conjectures around the possible relationships between some findings and the type of thinking characteristic of autism spectrum disorder are put forward. The results carry implications for research with and teaching of students with ASD.

Comparison of Mathematics Problem-Solving Abilities in Autistic and Non-autistic Children: the Influence of Cognitive Profile

“…The main difficulties are observed when faced with mathematical word problems that contain indirect language, superfluous information or require several steps to solve (Bae et al, 2015). Some studies show that, although ASD students without intellectual disability may use the same strategies as students without ASD diagnosis (from now on, non-ASD) when solving mathematical problems, in ASD students more rudimentary strategies like those based on drawing and counting persist (Alderson-Day, 2014;Bae et al, 2015;Goñi-Cervera et al, 2022;Polo-Blanco et al, 2019), while non-ASD children soon exhibit progress to more efficient strategies that require higher level of abstraction, like arithmetic operations (Brissiaud & Sander, 2010;Ivars & Fernández, 2016;Mulligan & Mitchelmore, 1997;Rodríguez Marcos et al, 2008;Siegler, 1988).…”