In the 21st century, there is no disagreement that a math education is considered important for all students, including those with disabilities or Autism Spectrum Disorder (ASD), so that their access and success contribute to the development of skills necessary for an independent life. Good performance in the discipline of math has a significant impact on academic and work opportunities (Bouck et al., 2021).
However, the academic research on math teaching and evidence-based interventions for people with ASD still has important gaps and is very limited (Tonizzi & Usai, 2023). These gaps may be due to the idea that individuals with ASD have extraordinary math skills, but their good performance in math assessments seems to be mainly anecdotal. That is, only a limited number of them have excellent performance in this discipline, and math difficulties seem to be more common among these students than among their peers with typical development (Tonizzi & Usai, 2023).
ASD is characterized by high heterogeneity due to the different levels of intellectual and linguistic abilities and the presence of comorbidities (Zeidan et al., 2022). Such students may face barriers that affect their learning abilities, such as not having developed executive function, which includes working memory, inhibitory control, and cognitive flexibility (Demetriou et al., 2018).
Another significant barrier is related to communication. When a child with ASD does not develop language skills, understanding instructions and responding to school demands, which are mostly based on verbal instructions, will interfere with the development of math skills. This includes number sequence formation, calculation skills, fact retrieval, and problem-solving involving words. Additionally, difficulties may arise in generalizing properties and procedures, as well as recognizing multiple strategies for solving a problem (Cox et al., 2021).
Rottmann et al. (2020) state that it is essential for mathematical content to be taught effectively in early childhood. Learning pre-arithmetic skills (major/minor, plus/less, large/small, first/last, before/after) builds a solid foundation of repertoires that will be used in the development of new concepts in the subsequent years. Neglecting the teaching of this set of content can create gaps that will worsen as students progress through school. According to these authors, to make math teaching effective, it is necessary to prioritize the assessment of learners’ repertoires.
An assessment model of the math repertoire is proposed by Costa et al. (2017), who evaluated the mathematical skills of children with Down syndrome and typical development in pre-arithmetic (relations of greater, lesser, equality, addition, and subtraction), counting and measuring, numerical sequence production skills, and recognition of geometric figures, using the Protocol for Registration and Evaluation of Mathematical Skills (PRAHM). The PRAHM has 34 questions.
After its publication, the PRAHM was used to assess the repertoire of 35 children aged 6 to 12 years with ASD in recent years, including six females and 29 males (Costa et al., 2021; Picharillo & Postalli, 2021; Moura et al., 2023; Benitez et al., 2023; Vernini, 2023; Picharillo, 2024). Three of the 35 children could not respond to the PRAHM due to language barriers. Data from the other 32 children indicated an average of 69.2% correct responses (15 children presented at least 80.1% correct responses, and only nine of them presented less than 50% correct responses). The authors observed that there was no relation between age and performance, as children of different ages had the same performance. The poorer performances can be explained by language barriers caused by the instructions (Cox et al., 2021).
Protocols such as PRAHM are still rare in international literature regarding children with ASD but are fundamental to establishing the strengths and weaknesses of knowledge of basic mathematical skills. Furthermore, understanding the input repertoire is essential for the development of content planning and the choice of assertive strategies, leading to a successful teaching procedure.
Ailton B. Costa, PhD, is Postdoctoral in the Department of Psychology at The Federal University of São Carlos, Brazil. He has autism, ADHD, and giftedness, conducts research on teaching and assessing mathematics for people with visual impairments and people with autism. He can be reached at ailton.barcelos@ufscar.br, +55 16 3351-8357.
Alessandra D. M. Picharillo, PhD, is Postdoctoral Student in the Department of Psychology at The Federal University of São Carlos, Brazil. She is a scientist who conducts research on teaching and assessing mathematics for people with autism. She can be reached by email at alessandrapicharillo@estudante.ufscar.br, +55 16 3351-8357.
Nassim C. Elias, PhD, is Professor in the Department of Psychology at The Federal University of São Carlos, Brazil, who conducts research on autism and behavior analysis-related topics. He can be reached by email at nassim@ufscar.br, +55 16 3351-8357.
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