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Proponents of robust research design and methodology (particularly, although not exclusively, in more positivist-leaning epistemology) have often suggested that the role of the researcher should be as invisible, or distanced, as possible in the research process. Many of the case studies presented in this book take a more qualitative, interpretative approach, reflecting the often complex, situated, local and dynamic contexts in which out-of-school learning occurs. This raises particular challenges relating to the researcher role, especially when the researcher's presence materially changes the context and phenomena that are being researched. Some of the case studies describe the tensions and affordances of the researcher as insider/outsider and demonstrate how this role can develop and change as a project progresses and the implications this has for research practice, research quality and research governance.

Ethics work in research is often conceived of as a process of research governance. The case study chapters, however, provide evidence of a much more sophisticated engagement with ethical dilemmas arising in research and an enactment of ‘everyday ethics’, in other words, a concern with our relationships with, and responsibilities to, other people (Banks, 2016). This emphasis on relationality can often lead to what Cook (2009) describes as ‘mess’ in research, which needs to be made sense of. This is in contrast to the notion of ‘well-ordered’ research, which underpins many of the ethical frameworks, principles and guidelines that are produced for research. The chapters also indicate the opening up of new spaces for research that raise new challenges in respect of ethical practice, including, for example, digital spaces (Case Study 4 – Minecraft Club). Case Study 8 – Democratic Engagement also demonstrates that both researchers and participants in the research process find ways in which to challenge conformity and research norms in order to access knowledge, and this is not always a harmonious process. The following sections try to make sense of the implications of these issues for the ethical practice of research. This chapter pulls together three key themes emerging from the case studies of research governance, ethical relationality and ethical spaces, presenting an analytical overview of all three areas using the concept of ‘willful subjects’.

This chapter reflects on the concept of knowledge – or perhaps, more accurately, the multiple knowledges – generated in this field of study. We consider, through drawing on some of the examples of ways in which knowledge about out-of-school learning is constructed in the case studies, issues such as the authenticity and value of knowledges pertinent to this field, the power structures and knowledge hierarchies involved and the localised sites of such knowledge production. We conclude with some thoughts about how researchers can manage the tensions involved in making decisions about whether to try to integrate or to keep separate such multiple forms of knowledge.

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.