Afzal Ahmed, Derek Holton and Honor Williams
Mathematical scientists typically address educational issues exclusively in terms of subject matter content and technical skills, with the 'solution' taking the form of new curriculum materials. Curriculum is, indeed, a crucial aspect of the problem, and one to which mathematically trained professionals have a great deal of value to offer. But taken alone it can, and often does, ignore issues of cognition and learning, of multiple strategies for active engagement of students with the mathematics, and of assessing their learning and understanding. (Hyman Bass, 1997)
In this chapter, we discuss ways of developing active learners of mathematics within the higher education context. This discussion is necessarily condensed but we have provided references to supplement our arguments. We believe that active learning enables a greater number of people to learn mathematics successfully as well as providing opportunities for more people to study mathematics at a deeper level. Hence active learning can help teachers to respond positively to the current Learning and Teaching and Widening Participation agendas within the higher education sector. Similarly, active learning may also help deal with some of the difficulties posed by the transition to higher education that were raised in Chapter 1. Further major outcomes of adopting this approach can be to engender excitement, enthusiasm, motivation and a sustained love of mathematics both for teachers and students.
Consider the following example. In order to understand later work related to Jordan canonical forms and generalized eigenvectors, students in advanced linear algebra courses need to know the concept of nilpotent matrices. Using experimentation, students can gain a good background for this material. Hillel (2001)