The aim of this study is to identify how the activity of proving is constituted in a Cypriot primary classroom for 12 year old students. Through Cultural-Historical Activity Theory (CHAT), the influence of research literature, curriculum prescriptions, the students and critically the teacher is documented. The evolution of objects, in particular the aims of the teacher, and other components in the activity systems is traced. Within the qualitative enquiry, this study employs CHAT alongside a collaborative design approach to explore the way the teacher is working with the students to foreground mathematical argumentation. The research is situated in a Cypriot primary school classroom with the researcher having the role of teacher researcher. The usual class teacher and researcher co-developed Dynamic Geometry Environment (DGE)-based tasks to be used with the children. As a result it was possible to track how the nature of the teacher’s objects changed and how contradictions emerged. Evidence from the curriculum documentation and from classroom observations was used to develop the activity systems of exploring and explaining. One important finding lies in how exploring and explaining were key sub-systems within the central activity system of proving as they provided a key pathway, which often included defining. Processes of explaining, defining and exploring appeared to create a fertile ground for the development of proving. I refer to these developments as pre-proving. However, it turns out that there are inherent contradictions within explaining and exploring that hinder the constitution of proving in the classroom. An emerging primary contradiction was apparent in the multifaceted nature of the object of both exploring and explaining to both facilitate mathematical argumentation and address a prescribed curriculum. Due to the tension between these objects, the teacher was often faced with dilemmas such as whether to open up playful activity or close it down to focus on the curriculum specifics. These led to a constant struggle in the teacher’s everyday practice. I report also on how primary contradictions led inevitably to higher-level contradictions between other components of the activity systems
