Dave Sherratt and Gill Donald teach children with autism at Mowbray School, North Yorkshire. Dave Sherratt also teaches at the University of Birmingham and is honorary research fellow at the University College of York St John. Gill Donald is also a specialist speech and language therapist for Hambleton and Richmondshire Primary Care Trust. In this article, Dave Sherratt and Gill Donald outline an approach to teaching children who are on the autistic spectrum. They describe the social construction of understanding in normally developing children and suggest ways in which this differs in children with autism. These children may have difficulties in attributing relevance to the aspects of experience that are regarded as significant by most learners. The authors suggest that this may account for the poverty in social engagement or connectedness commonly observed in children with autism. Illustrating their propositions with vivid examples from practice, Dave Sherratt and Gill Donald go on to describe ten teaching structures promoting progress from early social engagement; through a shared understanding of objects and observable processes; to a shared understanding of symbolic representation in play, ideas and language. These structures, rooted in a fascinating evocation of theory, will help practitioners striving to develop a shared understanding of self, others and the environment in children with autistic spectrum disorders.