In this article and part 2, the author focuses on how an individual appropriates notions from the socially-sanctioned body of knowledge called mathematics. Specifically, the author is concerned with how students, to a greater or lesser extent, internalise mathematical ideas that exist in the social world (on the chalkboard, in textbooks, in the activities of their lecturers and fellow students) and make them their own. The motivation for focusing on the individual is that, at university level, mathematical learning largely takes place in a context which consists of an individual reading definitions and theorems and engaging in exercises or tasks suggested by a textbook or lecturer. [Part 2 is published in volume 24 number 3 2004.]