Mathematics Communication within the Frame of Supplemental Instruction : Identifying Learning Conditions

In the Swedish context teaching at primary and secondary school is combined with collaborative exercises in a variety of subjects. These collaborative moments can be in the form of mini projects that groups of students are supposed to present to the classmates when fulfilled. A collaborative moment may also be an exercise that the students solve together. The main idea is thus that the students learn together. One method for students’ learning together is Supplemental instruction or SI. SI is a complement to regular teaching where students are provided peer collaborative learning exercises. The method is being used at university level in many countries, e.g. Canada, USA, Australia and Great Britain. To strengthen students’ knowledge in mathematics, a couple of schools in Sweden have introduced SI. Such an extra effort with problem solving and mathematics communication is in line with the new Swedish mathematics curriculum. Collaborative exercises in school may lead to enhanced learning among the students, but collaborative work may also lead in the opposite direction. As collaboration is widely used in schools in Sweden it is important to investigate what conditions in the classroom can lead to learning during collaborative work. Thus, this study examined five SI-groups at two Swedish upper secondary schools. The groups were observed and videotaped repeatedly. The analyses of the observations aimed at identifying conditions leading to observable learning outcome at students’ mathematics discussions. In order to achieve this an analysis strategy was needed which led to a second aim, i.e. formulating a useful analysis strategy that built on existing theoretical frameworks. Two well tested frameworks were used: the SOLO-taxonomy (Structure of the Observed Learning Outcome) and the ATD-praxeology (Anthropological Theory of Didactics). The analysis showed that learning outcomes in the discussions were indeed facilitated by the SI-leaders’ guidance. In addition the results indicate that 6 carefully chosen exercises, as well as careful organisation of the SI-sessions, can lead to a higher level learning outcome. The study also showed that the chosen analysis strategy with well tested frameworks was successful. The findings can be used both for future research and for development of collaborative learning