This is a book about teaching mathematics in schools. There are many excellent books about teaching mathematics that are driven by pedagogy, psychology or research. This book is different. It is driven by the mathematics that underpins the school mathematics curriculum, informed by the authors' experiences and opinions. In the field of pedagogy, there are very few fixed "knowns". Mathematics, on the other hand, is a well-founded rock. So, the thoughts and advice provided by Keith Parramore and Joan Stephens are anchored to that rock. Lessons Learned from Maths Lessons is based on observations in secondary schools, and many sections are relevant to primary school mathematics. The authors are a husband-and-wife team of practising mathematicians, with a wealth of experience in supporting trainee teachers. They have learned something new and/or interesting from every mathematics lesson they have observed. One objective of this book is to share some of that learning with the reader. A second objective is to promote an approach to teaching mathematics that empowers pupils and promotes understanding. Trainee teachers often identify specific topic areas that they perceive they need to develop. Parramore and Stephens argue that the greater need is for them to develop depth rather than breadth, to truly explore the mathematical foundations of what they are teaching.