ZIZO: a history-based approach to mathematics teacher education

In this paper, we discuss the zoom in and zoom out approach to mathematics teacher education (ZIZO), which is intentionally designed to foster commognitive conflicts through the exploration of historical sources and the engagement with collective discussions. ZIZO is structured in three interconnected moments: firstly, participants are invited to immerse in primary sources, as a means of shaking their comfort zones regarding legitimate mathematical procedures and criteria; secondly, they engage in plenary discussions on the historical contextualisation of mathematical ideas, supported by the study of secondary sources; finally, they return to the source to unveil specific aspects of historical practices. This approach is part of a broader proposal, which builds upon participants’ collective experiences to stimulate the development of a problematising stance toward knowledge production and teaching of mathematics. We exemplify ZIZO by a case in which the study of books I and II of Euclid’s Elements was used to problematise usual approaches to the teaching of Pythagoras’ theorem and areas in Brazilian secondary school. Our findings suggest that the engagement with Euclidean practices led teachers to problematise their views on the teaching of areas as geometrical magnitudes and as measurements, as well as the pedagogical uses of manipulable materials. These results highlight ZIZO’s potential for teacher education, especially regarding the problematisation of views on what mathematics is and how it is learned and taught.