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.

Inhalt

PREFACE

Luis Radford

INTRODUCTION TO THE FIELD

Paul Ernest  The Philosophy of Mathematics Education: An Overview

THE NATURE OF MATHEMATICS

Jean Paul van Bendegem  Philosophy of Mathematical Practice: What is it All About?

Michael Otte  The Philosophy of Mathematical Education between Platonism and the Computer

Catarina Dutilh Novaes  A Dialogical Conception of Explanation in Mathematical Proofs

**Melissa Andrade-Molina, Paola Valero, **and Ole Ravn The amalgam of faith and reason: Euclid's Elements and the scientific thinker

CRITICAL MATHEMATICS EDUCATION

Ole Skovsmose  Students' Foregrounds and Politics of Meaning in Mathematics Education

Eric 'Rico' Gutstein  The Struggle is Pedagogical: Learning to Teach Critical Mathematics

Richard Barwell  Some Thoughts on a Mathematics Education for Environmental Sustainability

Margaret Walshaw  Epistemological Questions about School Mathematics

Brendan Larvor and Karen François  The Concept of Culture in Critical Mathematics Education

Paul Ernest The Ethics of Mathematics: Is Mathematics Harmful?

PHILOSOPHICAL THEORY IN MATHEMATICS EDUCATION RESEARCH

Anna Sfard  On the Need for Theory of Mathematics Learning and the Promise of 'Commognition'

Ladislav Kvasz  On the roles of Language in Mathematics Education

Uwe Schürmann  The Separation of Mathematics from Reality in Scientific and Educational Discourse

**Maria Aparecida Viggiani Bicudo  **Mathematics Education Actualized in the Cyberspace: a philosophical essay

PHILOSOPHY OF/IN TEACHING, LEARNING AND DOING MATHEMATICS

**John Mason  **Making Distinctions: A Phenomenological Exploration in Mathematics Education

**Michael Meyer  **Using Rules for Elaborating Mathematical Concepts

Nadia Stoyanova Kennedy  Towards a Wider Perspective: Opening a Philosophical Space in the Mathematics Curriculum

Bronislaw Czarnocha, William Baker and Olen Dias  Ockham Razor of Creativity Research in Mathematics Education

Regina Dorothea Möller  Teaching of Velocity in Mathematics Classes Chances for Philosophical Ideas

Hilary Povey, Gill Adams and Colin Jackson  Time for Work: Finding Worth-While-Ness in Making Mathematics

**Walther Paravicini, Jörn Schnieder and Ingrid Scharlau  **The Invisible Side of Mathematical Thinking: A Philosophical Approach

Jessica Kunsteller  Developing Rules Due to the Use of Family Resemblances in Classroom Communication****

BRIEF BIOGRAPHIES OF AUTHORS