Conclusion: Becoming a Mathematician – Revisited

Abstract

In this concluding chapter we summarise the main ideas and arguments of the previous chapters, based on the research that we have carried out with many students and graduates of the mathematical sciences. Here we allow two students to present their context, goals and ideas about their mathematical studies in a more extensive way – one is an engineer studying mathematics as a professional component, the other is an honours student majoring in statistics. We use their stories to illuminate the important aspects of becoming and being that have been central themes throughout the book:

• Becoming a mathematician involves not only learning mathematics, but also becoming aware of the mathematical way of looking at the world, and the role mathematics plays in life.

• Students see mathematics and learning mathematics in a small number of qualitatively different ways. The narrowest views are based on techniques and components; broader views are based on the notion of models, applied or abstract; the broadest view is a strong connection between mathematics and personal and professional life.

• Some students can have very sophisticated insight into their own ideas, learning and future professional use of mathematics: others need some help and encouragement to get there. Graduates have corresponding narrow to broad conceptions of various aspects of their professional work. These could be addressed more explicitly in undergraduate courses.

• Mathematics curriculum can be aimed at the broadest conceptions of mathematics and learning, inclusive of a range of graduate skills and dispositions, and mathematics teachers can usefully direct their own learning to the broadest conceptions of mathematics, learning and teaching.