This work gives a new argument for ‘Empirical Philosophy of Mathematical Practice’. It analyses different modalities on how empirical information can influence philosophical endeavours. We evoke the classical dichotomy between “armchair” philosophy and empirical/experimental philosophy, and claim that the latter should in turn be subdivided in three distinct styles: Apostate speculator, Informed analyst, and Freeway explorer. This is a shift of focus from the source of the information towards its use by philosophers. We present several examples from philosophy of mind/science (...) and ethics on one side and a case study from philosophy of mathematics on the other. We argue that empirically informed philosophy of mathematics is different from the rest in a way that encourages a Freeway explorer approach, because intuitions about mathematical objects are often unavailable for non-mathematicians. This consideration is supported by a case study in set theory. (shrink)

This paper claims that the awareness of crucial philosophical questions and controversies, which have arisen during the historical evolution of fundamental concepts, ideas and processes in mathematics, should be an essential component of the professional knowledge of student teachers who intend to teach children mathematics.

The 1990s could be called The Decade of Sociology in mathematics education. It was during those years that the sociology of mathematics became a core ingredient of discourse in mathematics education and the philosophy of mathematics and mathematics education. Unresolved questions and uncertainties have emerged out of this discourse that hinge on the key concept of social construction. More generally, what is at issue is the very idea of “the social”. Within the framework of the general problem of “the social”, (...) we want to open a discussion of boundaries and margins in mathematics and mathematics education. By theorizing the divisions of purity and danger, we will be able to better understand the intersection of logic, mathematics, and thinking with gender, race, and class, and morals, ethics, and values in the classroom. The process of transforming the sociology of mathematics and the sociology of mind into pedagogical tools for mathematics educators and philosophers of education has already begun. One of the tasks before us is the development of a more profound and at the same time more practical grasp of “the social”. Our objective in this paper is to move ourselves and our readers in the direction of just such a grasp of the social. (shrink)

Ethnomathematics is a relatively new discipline that investigates mathematical knowl edge in small-scale, indigenous cultures. This essay locates ethnomathematics as one of five distinct subfields within a general anthropology of mathematics and describes interactions between cultural and epistemological features that have created these divisions. It reviews the political and pedagogical issues in which ethnomathematics research and practice is immersed and examines the possibilities for both conflict and collaboration with the goals, theories, and methods of social constructivism.

Kitcher and Aspray distinguish a mainstream tradition in the philosophy of mathematics concerned with foundationalist epistemology, and a ‘maverick’ or naturalistic tradition, originating with Lakatos. My claim is that if the consequences of Lakatos's contribution are fully worked out, no less than a radical reconceptualization of the philosophy of mathematics is necessitated, including history, methodology and a fallibilist epistemology as central to the field. In the paper an interpretation of Lakatos's philosophy of mathematics is offered, followed by some critical discussion, (...) and an extension to a social constructivist position (which might well have been unacceptable to Lakatos). (shrink)