What University Curriculum Best Helps Students to Become Mathematicians?

Abstract

In this chapter we draw on our research with mathematics students and recent graduates to investigate the tertiary mathematics curriculum. We present an argument for a particular vision of such a curriculum, which we refer to as a ‘broad’ as opposed to a ‘narrow’ curriculum. A narrow curriculum looks inwards and focuses primarily on the mathematics itself – the mathematical techniques that will be used by students of mathematics in specific situation. Traditional courses in mathematics have relied on such a curriculum for a long time. A broad curriculum looks outwards and focuses on the uses of mathematics as a way of investigating, understanding, and even changing the world. Such a curriculum positions students as citizens of the world first, future professionals in a variety of areas second, and mathematicians or users of mathematics third. Fewer mathematics courses are built on such an approach. Our arguments are based firmly on our students’ and recent graduates’ voices, as shown in transcripts of research interviews, and are consistent with ideas advocated by mathematics educators, in groups such as critical mathematics education and calculus reform, and with more general views of curriculum. Research into graduates’ early professional experiences and their views of their previous mathematics education reinforces these ideas and grounds them in the reality of the professional workplace. Such research indicates that a curriculum acknowledging and incorporating students’ and graduates’ ideas can assist in increasing their effectiveness as future professionals – as mathematicians or expert users of mathematics. Further, a curriculum that incorporates such views can include important aspects of professional formation such as communication and interpersonal skills, appreciation of a creative approach to problems, awareness of issues of sustainability and ethical considerations.