This book offers an up-to-date overview of the research on philosophy of mathematics education one of the most important and relevant areas of theory. The contributions analyse question challenge and critique the claims of mathematics education practice policy theory and research offering ways forward for new and better solutions. The book poses basic questions including: What are our aims of teaching and learning mathematics? What is mathematics anyway? How is mathematics related to society in the 21st century? How do students learn mathematics? What have we learnt about mathematics teaching? Applied philosophy can help to answer these and other fundamental questions and only through an in-depth analysis can the practice of the teaching and learning of mathematics be improved. The book addresses important themes such as critical mathematics education the traditional role of mathematics in schools during the current unprecedented political social and