Representations and generalization in early algebra: a comparative study of autistic students and their non-autistic peers

Abstract This study explores ASD (Autism Spectrum Disorder) students’ early algebraic thinking abilities by comparing them to their non-ASD peers. The first aim was to examine whether possible significant differences between ASD and non-ASD students in arithmetic also extend to early algebra. The second aim focused further on early algebraic thinking, examining whether ASD students differ from their non-ASD peers in the modes of representation they use (concrete, figural, arithmetical, and symbolic) and the levels of generalization they achieve (factual, contextual, and symbolic) when engaging with early algebra tasks. Using a mixed-methods approach, we analyzed data from 26 ASD and 26 non-ASD students aged from 6 to 12 years old. Statistical analyses revealed that while ASD students’ performance in the arithmetic test was lower than non-ASD students, their performance on the early algebra test was comparable. For ASD students, the figural mode of representation was a significant predictor of their total score in the early algebra test. For non-ASD students, no specific mode of representation significantly predicted their total score in the early algebra test. At the same time, factual generalizations were a significant predictor of ASD students’ total scores in the early algebra test, whereas contextual and symbolic generalizations were significant predictors for non-ASD students. These findings suggest that while ASD and non-ASD students achieve similar total scores on the early algebra test, they differ in their use of specific modes of representation and the level of generalization they attain. ASD students seem to benefit from creating figural representations and tend to achieve more basic levels of generalization, compared to their non-ASD peers, who demonstrate greater flexibility in using various modes of representation and reach more advanced levels of generalization.