Moving Closer to Solving the 'Mathematics Problem' Where it Arises: The Influence of the 'Typical' Irish Pre-tertiary Mathematics Experience on Under-preparedness among Numerate Entrants

摘要

The contribution of mathematics proficiency to the numerate (e.g. science, engineering) disciplines is well-documented. Internationally concern exists that graduates of these disciplines are persistently demonstrating mathematical deficiencies i.e. the ‘Mathematics problem’. A connection has been made between this problem and the worldwide reportage of numerate entrants to numerate courses demonstrating insufficient and incomplete mathematical knowledge. While the characteristics of ’at risk’ students are more or less equivalent internationally, the same consensus does not exist in relation to the causes of this phenomenon. There is growing consensus however that ‘under-preparedness’ is caused by the apparent mismatch between the nature of the pre-tertiary and subsequent Tertiary level mathematics experience. This study focuses the ‘Mathematics problem’ from an Irish perspective, exploring the nature of the ‘typical’ pre-tertiary mathematics experience, which in turn provides insight into the nature of the transition required of Irish students entering the numerate disciplines. Brousseau’s ‘didactical contract’ is used as an intellectual tool to uncover the features of the mathematics experience in two case classrooms in Irish upper secondary schools (Senior Cycle). While the authors are both professional mathematics educators and therefore acutely aware of prevalent classroom practice, the restrictive nature of contract and its implications for students’ future mathematics education left all concerned astounded.