PGCE students and investigational approaches in secondary maths

Abstract

Several researchers have recently drawn attention to aspects of the teacher shortage in maths: both its causes (Smithers and Hill, 1989) and its consequences (Straker, 1987). In particular, there has been considerable concern about the quality and quantity of entrants to Post‐graduate Certificate in Education (PGCE) courses (Hayter, 1989). It is within this context that a move has occurred within secondary schools towards a greater use of investigative approaches in mathematics (HMSO, 1987).

This paper reports on one aspect of a qualitative study of a university cohort of PGCE mathematics students: their responses to investigational work in their teaching practice schools. These students had a variety of backgrounds. Some were recent graduates in maths or related disciplines, while others had taken their degrees nearly 20 years ago. All had experienced a largely algorithmic approach to maths teaching at school. Several had suffered the fairly typical experience for those who study maths at university of being warmed up at school and then being cooled out at university.

The paper briefly discusses the investigational approach. It then describes the school and undergraduate experience of the student group, in order to show that their university careers had resulted in many of them lacking confidence in themselves as ‘mathematicians’ (Bibby, 1985). It is suggested that, when faced with the new uncertainty represented by ‘investigations’, as well as the usual problems of classroom control experienced by PGCE students (Lacey, 1977), they might have been expected to have favoured the algorithmic approach to maths they had experienced, and largely succeeded with, at school.

The main body of the paper presents detailed case studies of four students, two of whom were placed in a very pro‐investigational school. The responses of these four to investigational approaches are described as they developed during the year. It is shown how, in some cases, a lack of confidence, either about undertaking less didactic classroom roles or about the mathematical content implicit in many investigations, would seem to account for students’ initial responses, some of which were characterized by high levels of anxiety and confusion. As some students’ confidence grew, and as they perceived the possible motivational advantages of an investigational approach, they began to be more positive about such methods. In other cases there would also seem to have been a value preference at work, and some students remained unhappy about various aspects of investigational work at the end of the course.

Additional information

Notes on contributors

Barry Cooper

Barry Cooper, Lecturer in Education, Institute of Continuing and Professional Education, University of Sussex, Falmer, Brighton, BN1 9RG, UK.