Problem-Based Learning and Teacher Training in Mathematics: How to Design a Math Laboratory

A long tradition of educational research has promoted the use of active learner-centred methodologies at school, especially with the use of pedagogical laboratories. When mathematics is concerned, it seems that PBL (Problem-Based learning) is the most suitable approach for a more effective long-life learning. Nevertheless these recommendations do not seem to find their proper location in school practice, where self-perpetuating "traditional" methods impose themselves. In order to discourage the misuse of such so called "traditional" methods, many authors observe that teacher training should adopt, at least in part, the exact methods that are pleaded in the lectures. This very notion inspires the teacher training program at the University of Milano-Bicocca, during which prospective primary school teachers are required to attend PBL laboratories, that accompany the "theoretical" discussion on the potential of this instructional method. This contribution will present the structure of one of these laboratories and the achievements obtained by the students. The laboratory we will describe is specifically aimed at stimulating the students in the understanding, through their experience, of how PBL really works and to train them to design PBL activities they could use in a maths laboratory once they become teachers. A qualitative analysis of the final essays of 80 students attending the laboratory will be provided with particular attention to: - the ability to observe the activation of their own mathematical knowledge by mean of the PBL approach; - the ability to transpose the lab activities, without distorting their essential mathematical content, to a level suitable for primary school children.