Mathematics education as a practice in pursuit of [intellectual] excellence

In this paper we argue that mathematics is a practice as described by MacIntyre (2007) in his seminal After Virtue. We explore the link between mathematics and virtue ethics, providing an account of how the social and moral life inherent in mathematics both exhibits and promotes excellence, not just in an intellectual sense but in an ethical sense as a contribution to flourishing. Conceiving of mathematics as a practice (in MacIntyre‘s sense) is necessary for identifying the core virtues as they are exercised in mathematics. We then argue that the practice of mathematics can foster intellectual (and derivatively moral) excellence, and investigate whether and how mathematics education, exhibits and promotes these same virtues, and hence the extent to which mathematics education is a practice properly so called.