Peter Kahn and Joseph Kyle
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.
We therefore need to address the question of how to make learning and teaching in mathematics and its applications more effective. What is evident from the earlier chapters is that, while it is essential to consider the particular context, effective learning and teaching in mathematics and its applications are likely to be marked by a number of characteristics. Foremost among these characteristics is the recognition that the practice needs to be shaped by the nature of mathematics and its applications. And yet other features have also been seen as important. Learning and teaching clearly need to take into account the background of the students