In this chapter we build on Chapter 1 and survey the previous research that has most strongly influenced our thinking in carrying out the projects that we discuss in this book. This chapter is divided into three main sections. First, we focus on what we know about children's mathematics learning out of school. We discuss what previous research tells us about how children's out-of-school mathematics learning might compare with their mathematics learning that takes place in classrooms, and about how children's out-of-school mathematics learning might vary among groups of children including ways that connect with culture and background. Second, we focus on what previous research has told us about parents' role in supporting learning in general, and mathematics learning in particular. And finally, we look at what previous research tells us about schools' efforts to improve parental engagement with children's learning, through programmes and interventions. These surveys of what previous research can tell us in these three areas will lead towards some discussion of where we identified some key gaps and open questions that we addressed in our own research.

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