Aspects of Democracy in Different Contexts of Mathematics Classes

This chapter aims to discuss relations between aspects of democracy and different mathematics classrooms with the potential to become landscapes of investigation. The theoretical framework is based on the concepts of mathemacy, dialogue, representativeness, equity, inclusion, collaboration and criticism, which are essential for the maintenance and promotion of democracy. Three episodes of different mathematics classrooms are reflected upon: a class on functions in Brazilian higher education, high-school students visiting a quilombola community, and a mathematics class with Colombian adolescents. The likelihood for the three episodes to move into landscapes of investigation is discussed. Aspects that could have led these classes away from the path of landscapes of investigation are highlighted: these include the demand of the school institutions for teachers to follow a specific teaching material and/or regulate class time, students’ movements to reinforce the culture of exercises, and the failure of education managers to legitimise work aimed at the development of democracy. The analysis of the episodes showed the presence of aspects that could contribute to the promotion and maintenance of democracy: the dialogical posture of the teacher, and both teachers and students’ opportunities to discuss social, cultural, political and ethnic issues in mathematics classes.