The aim of this paper is to explore how a socio-political analysis can contribute to a deeper understanding of critical aspects for prospective primary mathematics teachers' identity construction during teacher training. The question we ask is: How may power relations in university settings affect prospective mathematics teachers' identity positioning? We elaborate on the elusive concepts of identity, positioning and power relations, seen as dynamic and changeable, as these represent three interconnected parts of research analysis in an ongoing larger project. In this paper we clarify the theoretical stance, ground the concepts historically and strive to connect them to research analysis. In this way we show that power relations and subject positioning in social settings are critical aspects and need to be taken into account if we aim at understanding prospective teachers' identities.