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 environmental crises, and the way in which the teaching and learning of mathematics can better serve social justice and make the world a better place for the future.

PREFACE.- INTRODUCTION TO THE FIELD.-The Philosophy of Mathematics Education: An Overview.-THE NATURE OF MATHEMATICS.- Philosophy of Mathematical Practice: What is it All About?.- The Philosophy of Mathematical Education between Platonism and the Computer.- A Dialogical Conception of Explanation in Mathematical Proofs.- The amalgam of faith and reason: Euclids Elements and the scientific thinker.-CRITICAL MATHEMATICS EDUCATION.- Students Foregrounds and Politics of Meaning in Mathematics Education.- The Struggle is Pedagogical: Learning to Teach Critical Mathematics.- Some Thoughts on a Mathematics Education for Environmental Sustainability.- Epistemological Questions about School Mathematics.- The Concept of Culture in Critical Mathematics Education.- The Ethics of Mathematics: Is Mathematics Harmful?.-PHILOSOPHICAL THEORY IN MATHEMATICS EDUCATION RESEARCH.- On the Need for Theory of Mathematics Learning and the Promise of Commognition.-On the roles of Language in Mathematics Education.- The Separation of Mathematics from Reality in Scientific and Educational Discourse.- Mathematics Education Actualized in the Cyberspace: a philosophical essay.-PHILOSOPHY OF/IN TEACHING, LEARNING AND DOING MATHEMATICS.- Making Distinctions: A Phenomenological Exploration in Mathematics Education.- Using Rules for Elaborating Mathematical Concepts.- Towards a Wider Perspective: Opening a Philosophical Space in the Mathematics Curriculum.- Ockham Razor of Creativity Research in Mathematics Education.- Teaching of Velocity in Mathematics Classes Chances for Philosophical Ideas.- Time for Work: Finding Worth-While-Ness in Making Mathematics.- The Invisible Side of Mathematical Thinking: A Philosophical Approach.- Developing Rules Due to the Use of Family Resemblances in Classroom Communication.-BRIEF BIOGRAPHIES OF AUTHORS.