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This chapter discusses the relationships between researchers and parent participants in a project that aimed to empower parents to support their children's informal mathematics learning. The Everyday Maths project used a parent-centred approach to empower parents in supporting their children's maths learning at home, through a series of workshops that took place in primary schools. In particular, we focus on relational issues between us (as researchers), parents, and schools – specifically, the way in which those relationships enabled both researchers and participants to develop new ways of thinking about their roles and positions, as well as develop their understanding about mathematics and about research. Relational agency (Edwards, 2010, 2017a) is used to understand the way in which these relationships played out. We also consider the way in which schools, as hosts of the project, impacted on this thinking. We reflect on schools' positions in the dynamics: they welcomed and supported our project, but as the project evolved, we questioned the way that schools positioned parents in relation to supporting children's learning, and encouraged parents to rethink their role. The potential for such disruption of relationships will be considered from an ethical stance. As researchers, we explore the ways in which we came to recognise each other's perspectives and develop a set of common understandings that were fundamental to our methodological approaches in this study.

Over the course of a two-year project, we set out to investigate the mathematics in children's everyday lives. We recognised the fact that this was a challenging project and that gaining access to children's personal lives would take time and some careful research design. A particular challenge centred on the difficulty of ensuring that our participants shared our understanding of ‘mathematics in everyday life’ and were happy and confident in sharing examples with us. In this chapter, we describe the way that we gradually increased the depth of our understanding of children's experience of mathematics outside of school through a series of studies with groups of primary school children. A structured diary study, and parental survey, allowed us to start a conversation with our participants about the kinds of activities we were interested in. A photo elicitation study then encouraged participants to cross the home-school boundary and share representations of their lives outside of school. These studies enabled us to develop enough of a shared language to carry out small group interviews with children and explore the mathematical thinking and learning in their out-of-school lives.