Abstract
This study investigated whether pupils hold personal beliefs and attitudes which could affect their performance in mathematics lessons in such a way as to either facilitate or impede learning. There were four parts to the study which took place over three years. In the first part, personal constructs about all school subjects were elicited from a group of pupils in their first year of comprehensive school. The interviews were recorded and provided background data for the study. One year later, the same pupils were asked to rate eighteen mathematics topics on the constructs of like/dislike; easy/difficult and useful/not useful. The interviews were again recorded and used to develop categories of pupil beliefs. These were used to develop a number of questions which were later put to the same group. Six weeks later the pupils divided into groups of three and took part in videorecorded problem solving sessions. This provided triangulated observational and oral data to corroborate or refute data from other parts of the study. Finally, approximately one year later, each pupil was asked the questions developed from the second interview categories. These were posed in an open ended form and were also used to develop belief categories. These final categories provided the information on which to compare the beliefs of the study group pupils. The basis for comparison was the pupils' mathematical setting and their positions in yearly examinations. Data from across the study were used to provide case studies of three pupils. The main conclusions were that beliefs and attitudes do affect mathematics performance, but that the effect was not the same for high and low settings; that problem solving ability correlated poorly with setting, and that for individuals it was necessary to examine a constellation of beliefs rather than any single ones.