What makes for effective learning and teaching in mathematics and its applications? We only need to consider some of the concerns about learning and teaching that have been raised in recent years to realize that this is an important question. Within higher education, there have been difficulties with recruiting and retaining sufficient numbers of students (see, for example, Thomas, 2000; Quality Assurance Agency for Higher Education, 2000). Various reports have pointed to the inadequate mathematical preparation of students for existing degree programmes (London Mathematical Society, 1996; Engineering Council, 2000). At the same time there is in many places a shortage of mathematically qualified teachers in schools (Tikly and Wolf, 2000). Concerns over such issues are closely linked to the recognition that modern economies need a large number of individuals with understanding of mathematics and its applications if they are to thrive. And while making learning and teaching in higher education more effective is only likely to provide one element in any moves to improve mathematical education more widely, it remains an important element.