Under what conditions does the bar model support mathematical problem solving of two-step, real-life, word problems for autistic students?

The current PhD thesis explores the key conditions (factors) associated with mathematical problem solving amongst autistic pupils, with a focus on the use and application of the bar model. Previous research within mathematical problem solving identifies an uneven range of profiles amongst the autistic population. Furthermore, a lack of empirical evidence exists as to the success and best classroom practice within mathematical problem solving for this group of pupils. Previous studies identify individual conditions likely to be influential on mathematical problem solving, the aim of the current study was to explore the combinations of these conditions with respect to successful word problem solving amongst autistic pupils. Although the bar model is becoming more widely adopted within mathematics teaching and learning, there remains a paucity of empirical research around the conditions associated with its success. The research questions are answered through the exploratory use of qualitative comparative analysis (QCA) in small-N (N=9), educational research. Through the use of pupil discussions and observations of mathematical problem solving and teacher interviews, the analysis of individual conditions and configurations of conditions giving rise to successful mathematical word problem solving are explored. The findings from the study identify mathematical attainment and pupils’ self-perception of their own mathematical ability to be significant in mathematical problem solving. Through further analysis, the impact of the executive functions, particularly working memory and attention, are identified, along with the importance of pupils’ conceptual understanding within mathematical problem solving. The study suggests that teachers pay particular attention to the broader profiles of autistic pupils within the mathematics classroom and consider carefully the balance of procedural and conceptual teaching and learning, particularly when utilising the bar model. Through a range of data analysis techniques, the study provides encouraging data to advocate the use of QCA in small-N, educational research.