In this Introduction, I distinguish between two a posteriori views with respect to mathematical knowledge. According to the epistemological a posteriori position, mathematical knowledge is acquired empirically. According to the methodological a posteriori approach, empirical research is important for understanding what mathematical knowledge is like. I emphasise the need for the latter in the epistemology of arithmetic, while also accepting the importance of a priori methodology. However, empirical researchers and philosophers of mathematics do not share a common conceptual framework, which makes successful interdisciplinary research difficult. After pointing out some of the key problems, I provide a coherent conceptual framework and consistent terminology.

Chapter 1 contextualises management strategies within a historical and conceptual framework. It introduces readers to a range of theorists who have been pivotal to the way classroom and behaviour management has been construed and applied over time; it therefore shows how modern management practices can be positioned. Throughout the text, references to the theorists introduced in this chapter and their approaches are linked to pedagogical practices – that is, other chapers show how the theories outlined in this chapter can be used in the classroom today to meet the needs of twenty-first century students. Therefore, this chapter can be used by readers to organise and connect the core concepts and principles of classroom and behaviour management as they proceed through the book and position their own management practices.