Mathematics researchers put considerable cognitive effort into trying to expand the body of mathematical knowledge. In so doing, is their cognitive behaviour different from those who work on more standard mathematical problems? This paper attempts to examine some aspects of mathematical cognition at the highest level of formal functioning. It illustrates how the structure of a mathematician's output--and, to a certain extent, its cognitive complexity--can be characterised by the SOLO taxonomy. A number of cognitive and philosophical issues concerning mathematical functioning at the research level will also be discussed.

Twenty-seven Grade 5/6 students working in triads considered a supplied data set. They were asked to hypothesise about associations in the data and to represent these. Each student was classified according to the level of interpreting the information, the level of representing the chosen data, and the type of collaboration observed in the group. Levels of interpretation and representation skills were related and there was some indication of a possible association with the type of collaboration. There was no association of type of collaboration and students' views on group work. Implications for future research and the classroom are considered.

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