Changing mathematics curricula and their emphases have provoked some international concern about the ability of students entering university with regard to their apparently decreasing levels of competence (Smith, 2004). This has been particularly apparent with regard to essential technical facility, analytical powers, and perceptions of the place of precision and proof in mathematics. Such mathematical under-preparedness of students entering university has been seen as an issue (Hourigan & O’Donoghue, 2007; Kajander & Lovric, 2005; Luk, 2005; Selden, 2005), andone that may impact on students’ success in university mathematics (Anthony, 2000; D’Souza & Wood, 2003), although not all studies agree on the extent of the problem (Engelbrecht & Harding, 2008).Further, concern has been expressed about the levels of student enrolments in undergraduate mathematics programmes (Barton & Sheryn, 2009; the ICMI Pipeline Project) and the implications for the future of the subject.

Whilerecent research has specifically addressed these issues with regard to the transition from school (Brandell, Hemmi & Thunberg, 2008; Engelbrecht & Harding, 2008; James, Montelle & Williams, 2008; Jennings, 2009), overall the volume of research in tertiary mathematics education has, until recently, been relatively modest (Selden & Selden, 2001).

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