Ability is a concept central to the current practice of mathematics teaching. However, the widespread view of mathematics learning as an ordered progression through a hierarchy of knowledge and skill, mediated by the stable cognitive capability of the individual pupil, can be sustained only as a gross global model, and is of limited value in describing and understanding the particular cognitive capabilities of individual pupils in order to plan, promote and evaluate their learning. In effect, individual pupils, and groups of pupils, are subject to ability stereotyping; characterisation in terms of a summary global judgement of cognitive capability, associated with overgeneralised and stereotyped expectations of mathematical behaviour, and stereotyped perceptions of an appropriate mathematics curriculum.