The early childhood education (ECE) sector has been subjected to increased governance, which has manifested in an increased focus on monitoring and steering the daily life of preschools. It is well documented that instruments of governance change teachers' priorities and practices. Changes are not always in line with the aims of the governing instrument. Empirical studies concerning governance in children's everyday lives have been rarer. Understanding the mechanisms of governance in the everyday lives of teachers and children requires theoretical tools which allow researchers to notice heterogeneous and situational elements that play a role in the act of governance. We explore governance in the contexts of ECE in two countries, Finland and Australia, with the help of ethnographic data and the concept of 'assemblage'. We propose an ontological foundation for governance research in ECE. We argue that taking socio-materiality as an ontological foundation of the research inquiry helps to see how the density of the socio-material elements of the situation may intensify the possibility of governing instruments interrupting meaningful interaction between children and adults.