Over the last 20 years, the authors have utilised Bronfenbrenner's ecological and bioecological models as a basis for their work investigating children's transition to school, including the place of mathematics learning in this transition. The later bioecological model gave increased emphasis to the role of the individual within contexts, the processes that characterised interactions within and across contexts (proximal processes), and the influence of time. This bioecological model outlined four elements--person, process, context and time--which, together, were described as influencing the development of individuals. While the mathematical learning of young children influences, and is influenced by, all four elements of the model, the critical role of proximal processes in this learning is highlighted in this paper. Our aim is to identify how the four elements of the bioecological model, particularly proximal processes, provide a framework to analyse the experiences of the adults--early childhood educators and parents--involved in an early childhood mathematics education intervention designed to promote engagement with mathematics in playful situations. Data are drawn from 35 early childhood educators and 37 parents over 2 consecutive years (2013, 2014) with generally different participants in each year.