Evidence of deficiencies in basic mathematical skills of beginning undergraduates has been documented worldwide. Many different theories have been set out as to why these declines in mathematical competency levels have occurred over time. One such theory is the widening access to higher education which has resulted in a less mathematically prepared profile of beginning undergraduates than ever before. In response to this situation, the present study details the examination of a range of methods through which a student's mathematical performance in higher education could be predicted at the beginning of their third level studies. Several statistical prediction methods were examined and the most effective method in predicting students' mathematical performance was discriminant analysis. The discriminant analysis correctly classified 71.3% of students in terms of mathematics performance. An ability to carry out such a prediction in turn allows for appropriate mathematics remediation to be offered to students predicted to fail third level mathematics.The results of the prediction of mathematical performance, which was carried out using a database consisting of over 1,000 beginning undergraduates over a three year period, are detailed in this article along with the implications of such findings to educational policy and practice.

Deficiencies in beginning undergraduate students' basic mathematical skills has been an issue of concern in higher education, particularly in the past 15 years. This issue has been tracked and analysed in a number of universities in Ireland and internationally through student scores recorded in mathematics diagnostic tests. Students beginning their science-based and technology-based undergraduate courses in the University of Limerick have had their basic mathematics skills tested without any prior warning through a 40 question diagnostic test during their initial service mathematics lecture since 1998. Data gathered through this diagnostic test have been recorded in a database kept at the university and explored to track trends in mathematical competency of these beginning undergraduates. This paper details findings surrounding an analysis of the database between 2003 and 2013, outlining changes in mathematical competencies of these beginning undergraduates in an attempt to determine reasons for such changes. The analysis found that the proportion of students tested through this diagnostic test that are predicted to be at risk of failing their service mathematics end-of-semester examinations has increased significantly between 2003 and 2013. Furthermore, when students' performance in secondary level mathematics was controlled, it was determined that the performance of beginning undergraduates in 2013 was statistically significantly below that of the performance of the beginning undergraduates recorded 10 years previously.

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This article reports on the mathematical competency of students entering third-level education in the University of Limerick (UL). Data from diagnostic testing, gathered on 5,949 students between the years 1998 and 2008, are used to demonstrate the changes in competency levels of students entering UL. There has been a significant decline in the performance of students in the diagnostic test over time. The performance, on average, of students with the same leaving certificate mathematics grade on entry into university has not changed significantly over time. However, the profile of the entrants has changed considerably and this is contributing to the overall decline in mathematical competency.

In 2010 the Irish second level mathematics curriculum underwent a period of significant change when a new mathematics curriculum was introduced. Some preliminary research has been carried out into the impact, if any, that this mathematics curriculum is having on students mathematics performance which have suggested that students' procedural skills are declining year on year however their problem solving skills may have improved (Treacy and Faulkner 2015). Additional research in this area also highlighted that students willingness to engage in problem solving activities may have improved (Prendergast et al 2017). However preliminary analysis on the impact of the reformed mathematics curriculum, if any, on students' performance in higher education noted that further research was needed in this area to definitively establish what is happening. This research therefore aims to explicitly determine whether the procedural and problem solving skills of beginning undergraduates are changing over time as a result of the reformed mathematics curriculum introduced in second level education. A paper based diagnostic test designed and developed is used in an attempt to determine this. This paper will detail the piloting of this diagnostic test with a group of higher education students in the Irish context.