JUSTIFYING AND PROVING IN THE MATHEMATICS CLASSROOM

The pilot study The school chosen for the pilot study was a large suburban secondary school. The school's mathematics department has for many years enthusiastically used and contributed to the SMILE individualised scheme for learning mathematics whose curriculum approach places much emphasis on guided discovery, problem solving, and investigations. A major proportion of the learners tasks are about establishing or identifying generalities and the potential for explaining or justifying them is frequently present even if the requirement to do so is not. In 7 separate visits to the school I talked to 22 learners from different classes but mainly from year 10. These were chosen by their class teachers to represent a range of abilities. I tape-recorded one-to-one conversations with learners about their attitudes to discovery and investigation type mathematics and their reasons for believing the rules and formulae they discovered