We report on a small scale study with six experienced teachers of mathematics in which we have applied a general theoretical model of expert practice (developed by the second author) to explore the nature of the knowledge base that enables teachers to operate effectively in the complexity of a class of 30 pupils. This model uses the notion of attention-dependent knowledge, which is derived through the use of specialised attentional skills. A methodology was developed which enabled us both to investigate the role of attention-dependent knowledge and to develop a basic vocabulary to articulate aspects of expert classroom practice.