SUMMARY
Background: Teachers’ knowledge of mathematical reasoning and how to foster it in pupils influence the way they plan and conduct their lessons. In geometry, it implies developing visualisation and spatial structuring. Objectives: This article addresses the knowledge of the preservice and in-service primary teachers about reasoning processes, namely the way they relate several reasoning processes when solving a didactical task involving geometry. Design: The study reported here followed a qualitative-interpretative approach, adopting a design-based research modality. Setting and Participants: The teacher education experiments were developed with 31 preservice primary teachers and 19 in-service teachers of grades 1 to 6. The participants were not selected since they were the unique classes of pre- and in-service primary teachers in the institution. Data collection and analysis: Data were collected by audio and video records of lessons, participant observation and the collection of written records of the preservice teachers. We used content analysis of the data using the framework we elaborated on before concerned with knowledge of reasoning processes. Results: The preservice teachers identified the process of generalising, relating it with comparing and exemplifying processes. Regarding the process of justifying, participants used the association to understand why a relationship works as a selection criterion for that process. On the contrary, the distinction between justifying and generalising appeared to be more difficult for in-service teachers. Conclusions: Collaborative work on didactical tasks that are supported by relevant mathematical tasks and real classroom episodes are promising scenarios to develop teachers’ knowledge about mathematical reasoning.