Paul Ernest

This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical mathematics education, and the most relevant modern movements in the philosophy of mathematics. A case study is provided of an emerging research tradition in one country. This is the Hermeneutic strand of research in the philosophy of mathematics education in Brazil. This illustrates one orientation towards research inquiry in the philosophy of mathematics education. It is part of a broader practice of ‘philosophical archaeology’: the uncovering of hidden assumptions and buried ideologies within the concepts and methods of research and practice in mathematics education. An extensive bibliography is also included.

First published in 1991. What is mathematics, and how can we account for its nature? What philosophies of mathematics have been developed? What philosophical assumptions, possibly implicit, underpin the learning of mathematics? What are the aims of mathematics education and are they valid? What philosophical assumptions, possibly implicit, does mathematics teaching rest on? This study looks at these questions on the philosophy of mathematics.

Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.Proposing social constructivism as a novel philosophy of mathematics, this book is inspired by current work in sociology of knowledge and social studies of science. It extends the ideas of social constructivism to the philosophy of mathematics, developing a whole set of new notions. The outcome is a powerful critique of traditional absolutist conceptions of mathematics, as well as of the field of philosophy of mathematics itself. Proposed are a reconceptualization of the philosophy of mathematics and a new set of adequacy criteria.The book offers novel analyses of the important but under-recognized contributions of Wittgenstein and Lakatos to the philosophy of mathematics. Building on their ideas, it develops a theory of mathematical knowledge and its relation to the social context. It offers an original theory of mathematical knowledge based on the concept of conversation, and develops the rhetoric of mathematics to account for proof in mathematics. Another novel feature is the account of the social construction of subjective knowledge, which relates the learning of mathematics to philosophy of mathematics via the development of the individual mathematician. It concludes by considering the values of mathematics and its social responsibility.

First published in 1991. What is mathematics, and how can we account for its nature? What philosophies of mathematics have been developed? What philosophical assumptions, possibly implicit, underpin the learning of mathematics? What are the aims of mathematics education and are they valid? What philosophical assumptions, possibly implicit, does mathematics teaching rest on? This study looks at these questions on the philosophy of mathematics.