### Abstract:

Declining standards in students’ mathematical competency levels has become a major issue in mathematics education both nationally and internationally (Smith 2004; Kajander and Lovric 2005; Gill et al 2010). This decline in standards, which has commonly become known as the ‘Mathematics Problem’, refers to issues such as poor numeracy skills in beginning undergraduates, difficulties with basic arithmetic and algebraic manipulations and an inability to cope with mathematics which is presented in unfamiliar formats (Hourigan and O’Donoghue 2007). Economists and educationalists agree that competent citizens in the area of mathematics and science are necessary for a successful economy (OECD 2006; Breen et al 2009; IBEC 2010). The need to try and overcome, or at least alleviate somewhat, the ‘Mathematics Problem’ has therefore been a priority of many third level institutions worldwide (Croft 2000; Tonkes et al 2005; Symonds et al 2008). Third level institutions have introduced a variety of different mathematical support structures in an attempt to support their mathematically less prepared students. One popular example of this is the introduction of diagnostic testing which aims to establish where students’ difficulties may lie and to identify the students within a particular cohort who are most ‘at risk’ of failing university mathematics courses. The University of Limerick (UL) introduced diagnostic testing in 1997. The same diagnostic test is still distributed today and so a large dataset has been created which currently consists of data on almost 8,000
students between 1997 and 2010. Diagnostic test data has been found to provide valuable
research opportunities such as the profiling of mathematics students over time (Kannemeyer 2005; Wilson and MacGillivary 2007; Faulkner et al 2010). Another popular use of diagnostic testing, which is prevalent in international education literature, is the prediction of students’ mathematical achievement (Simonite 2004; Barry and Chapman 2007; McDonald 2008). The wealth of data contained in the UL dataset and the examination of literature in the area of the ‘Mathematics Problem’ led the author to investigate the profile of third level mathematics students over time. An investigation into the profile of ‘at risk’ mathematics students over time enabled the author to create a predictive model of performance in mathematics. Finally the author used these research findings to inform a mathematics intervention which was implemented in UL. The intention of these investigations is to further quantify the ‘Mathematics Problem’ so as to inform and improve the teaching and learning of mathematics both nationally and internationally.