How and why is mathematics taught? These can be problematic questions. This book seeks to improve on our modern answers, finding better and more truthful explanations that are supported by evidence. The contributors to the book have various perspectives, but their chapters are cross-referenced and commented on, to create a stimulating discourse. Agreement is found on particular matters, such as the need for non-hierarchical approaches, and the contributions are all written to be relevant to policy-makers and practitioners, as well as researchers.