INVESTIGATING THE MATHEMATICS LEARNING OF STUDENT TEACHERS: EXPLORATIONS AND DISCOVERIES?

This paper describes a single experiment from early stages of work in progress. It examines one student's work in depth following the analysis of a class set of solutions of first year teacher trainees and mathematics students for a well-known investigation. Backeround to the research. Changes to the mathematics curriculum that followed from the Cockcroft Report (Cockcroft 82) led to "Real " Problem-Solving and Investigations becoming part of the official content of mathematics. The inclusion of such activities as assessed coursework for GCSE has ensured their being common occurrences in UK schools, and influenced the ways in which these investigations are carried out. In the mathematics education literature and particularly the journals closest to the classroom teacher there has recently been a debate about the effectiveness of such mathematical investigations in compulsory education mathematics classrooms. Hewitt (Hewitt 92) has questioned whether the diversity and richness of the mathematics curriculum was being reduced to spotting patterns from tables. In response Andrews shows concern that if those who were attempting change "see their efforts undermined by such criticism, is there not a risk that they might revert to the didactic modes of operation that characterise all that is disappointing in mathematics education, but which both teachers and pupils seem to fin