Mathematical under-preparedness: the influence of the pre-tertiary mathematics experience on students' ability to make a successful transition to tertiary level mathematics courses in Ireland

Internationally, the consequences of the 'Mathematics problem' are a source of concern for the education sector and governments alike. Growing consensus exists that the inability of students to successfully make the transition to tertiary level mathematics education lies in the substantial mismatch between the nature of entrants' pre-tertiary mathematical experiences and subsequent tertiary level mathematics-intensive courses. This paper reports on an Irish study that focuses on the pre-tertiary mathematics experience of entering students and examined its influence on students' ability to make a successful transition to tertiary level mathematics. Brousseau's 'didactical contract' is used as an intellectual tool to uncover and describe the contract that exists in two case mathematics classrooms in Irish upper secondary schools (Senior Cycle). Although the authors are professional mathematics educators and well informed about classroom practice in Ireland, they were genuinely surprised by the very restrictive nature of this contract and the damaging consequences for students' future mathematical education.