ABSTRACT
In the case study synopsis that follows, the mathematical task set was designed to challenge pupils within the context of their current scheme of work. The teacher-researcher (so called because the pupils are being taught as well as observed — not simply being tested), uses a questioning approach, which serves to facilitate learning and to reveal aspects of pupils' mathematical approaches and understanding. Occasionally pupils are asked to summarise their thinking as a check on both of these points. Although on this occasion no attempt was made to record the discussion between pupils themselves it is clearly a further source of data about their mathematical characteristics. The interpretation of the pupils' responses is interwoven in the text and makes use of Krutetskii's categories where appropriate.
