Mathematics at work a study of mathematical organisations in Rwandan workplaces and educational settings

Abstract: To make mathematics more significant for the beneficiaries, the problem studied in this thesis is to investigate how to connect mathematical daily practices with educational contexts. The overarching aim is to investigate how to contextualise school mathematics within Rwandan cultural mathematics practices. The content of the thesis reports on the characteristics of mathematical organisations in three workplace settings (taxi driving, house construction and restaurant management) which in turn serve as source for the design of contextualised mathematical activities for student teachers in a teacher education programme. Three levels of mathematical practices are described: (1) mathematical practices that are performed by workers within their respective workplaces, (2) mathematical practices that are performed by student teachers while solving and posing contextualised mathematical tasks for secondary school students, (3) mathematical practices that are carried out by secondary school students. Data gathered from individual and group interviews, transcripts of group discussions and students’ written reports of mathematical work were analysed from the perspective of both activity theory and anthropological theory of didactics. Findings from workplace settings revealed that mathematical organisations performed by workers are characterised by techniques which are functional to the problem at hand, the cultural constraints and the educational background of the workers. As long as they are pragmatic towards the goals of the activity no further justification of the techniques used is needed, resulting in a mathematical organisation with undeveloped know-why (logos). On the contrary, at university and secondary school settings, students justified the used techniques throughout the related taught content of the subject mathematics. Also from each category of mathematical practice, it is shown that while connecting workplaces and educational settings the didactic transposition process was much influenced by the institutional conditions and constraints.