Problem-based learning and teacher training in mathematics: how to evaluate a math laboratory effectiveness

As in other papers presented at previous IATED conferences, we start from the assumption that the use of active learner-centered methotologies at school, especially with the use of pedagogical laboratories, is essential for an effective teaching of mathematics. In order to stimulate the use of active methodologies in future teachers, the pre-service teacher training program at the university of Milano-Bicocca includes compulsory laboratories, that, at least for the math discipline, are implemented according to Problem-based learning (PBL) principles. The high number of students requires the implementation in parallel of many laboratories each year. These laboratories can be very different one from the other, thus making the offer for students extremely heterogeneous. Therefore we felt the need to set up a monitoring of the effectiveness of the various laboratories. The evaluation model that we will describe is based on an analysis of the careers of students who have attended these laboratories during the 2017-18 academic year. Data on about 380 students were collected and for each student the grades in university mathematical exams were taken into account. By comparing the students' performance before and after attending the laboratories, we created 4 indices that allow for a ranking of some characteristic each laboratory. Differences in "performance" between the different laboratories emerged. Clearly a quantitative analysis of this type needs further investigation (e.g. we plan to take a similar analysis for the laboratories held in the 2018-19 academic year, as soon as students' grades will be available). However, this kind of analysis lays the groundwork for a subsequent detailed examination of the causes of these performance differences, by looking closely at each lab implementation (e.g. problems chosen for the lab, tutor personal performance, time schedule, number of participants...).