This paper addresses the issue of teaching and learning engineering mathematics in order to support a future of life-long learning in the knowledge society, based on a form of understanding that goes beyond facts, theorems and algorithms. Drawing on three research studies, the importance is shown of students' experience of reflection on study, integration of mathematics into other aspects of an educational programme and into the world at large, and autonomy as a learner. Attention is then moved to implications for the processes of teaching, in order to support such understanding as a capability that students take with them from the university to the workplace. (Contains 2 figures and 2 tables.)