Olivia Fitzmaurice

The role of prior mathematical experience in predicting mathematics performance in higher education

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 students 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 1000 beginning undergraduates over a 3-year period, are detailed in this article along with the implications of such findings to educational policy and practice.

Mathematical thinking: challenging prospective teachers to do more than ‘talk the talk’

This paper reports on a research project which aims to improve prospective mathematics teachers’ relational understanding and pedagogical beliefs for teaching in second-level Irish classrooms. Prospective mathematics teachers complete their teacher education training with varying pedagogical beliefs, and often little relational understanding of the mathematics they are required to teach at second level. This paper describes a course designed by the authors to challenge such beliefs and encourage students to confront and possibly transform their ideas about teaching, while simultaneously improving their subject knowledge and relational understanding. Both content and pedagogical considerations for teaching second-level mathematics are integrated at all times. The course was originally optional and was piloted and implemented in a third-level Irish university. Apart from offering an insight into the design considerations when creating a course of this type, this paper also addresses some of the challenges faced when evaluating such a course. Overall participant feedback on the course is positive and both qualitative and quantitative results are provided to support this and also highlight the efficacy of the programme.

A Comparison of the Mathematical Performance of Mature Students and Traditional Students Over a 10-Year Period

Every student who enrols in a degree programme involving service mathematics in the University of Limerick in Ireland is given a mathematics diagnostic test. The diagnostic test was developed due to mathematics lecturers’ anxiety regarding students’ mathematical competency levels. Students receive the 40 question paper-based test in their first service mathematics lecture without prior notification. Initial analysis of students’ work revealed that many students were having difficulties with basic algebra and arithmetic in particular [Gill, O. 2006. “What Counts as Service Mathematics? An Investigation into the ‘Mathematics Problem’ in Ireland.” PhD diss., University of Limerick]. Further research highlighted the significant decline in diagnostic test performance and the changing profile of service mathematics students between 1998 and 2008 [Faulkner, Fiona, Ailish Hannigan, and Olivia Gill. 2010. “Trends in the Mathematical Competency of University Entrants in Ireland by Leaving Certificate Mathematics Grade.” Teaching Mathematics and Its Applications 29 (2): 76–93]. One of the most notable changes to the student profile over time was the increase in mature students (non-standard students) entering service mathematics programmes. Although non-standard students had a lower mean performance in the diagnostic test, they were found to have a higher mean performance in some cases in service mathematics compared to standard students. This paper explores some of the possible reasons for such findings.

Student perception of the impact of mathematics support in higher education

Mathematics support in higher education has become increasingly widespread over the past two decades, particularly in the UK, Ireland and Australia. Despite this, reliable evaluation of mathematics support continues to present challenges for those working in this area. One reason is because ideally, properly structured support should function as an integral part of the overall educational experience of the student, in tandem with lectures and tutorials. When this occurs, it makes it difficult to isolate the impact of mathematics support from these other entities. In this paper, the results of a large-scale nationwide survey conducted with first-year service mathematics students in nine higher education institutes in Ireland are considered, exploring students’ perceptions of the impact of mathematics support upon their retention, mathematical confidence, examination performance and overall ability to cope with the mathematical demands they face. Students were extremely positive about the effectiveness of mathematics support in all of these areas, providing valuable insights into the value of learning support in mathematics.

Ours Is Not to Reason Why, Just Invert and Multiply: An Insight into Irish Prospective Secondary Teachers' Conceptual Understanding of the Division of Fractions.

This paper reports on an investigation into the conceptual knowledge, through the domain of fraction division, of prospective secondary mathematics teachers in their final/fourth year of undergraduate initial teacher education. The aim of the study is to assess if levels of conceptual knowledge in this domain are sufficient in order for these prospective teachers to teach for understanding. Some impact of conceptual understanding on teaching approaches is also explored. The content of the teacher education program and its suitability for preparing prospective mathematics teachers is also considered. The results indicate that in spite of four years of mathematics teacher education, these prospective mathematics teachers hold a fragmented and limited conceptual understanding of dividing fractions. To address this issue and to ensure the effective implementation of Project Maths, it is argued that initial teacher education programs need to be revised to include an emphasis on school mathematics.

What Subject Matter Knowledge do second-level teachers need to know to teach trigonometry? An exploration and case study

This study reports on the level of trigonometry Subject Matter Knowledge (SMK) of third and final-year pre-service second-level mathematics teachers () at an Irish third-level institution. The aim of the study was to determine if this sample of prospective teachers has an appropriate level of SMK to teach second-level trigonometric concepts. The development of an instrument to measure teachers’ SMK of trigonometry with respect to teaching trigonometric concepts at second level is detailed in this report, and the subsequent findings from its administration to the sample are discussed. The findings indicate that the sample has gaps in their SMK of trigonometric concepts that are on second-level syllabi and are underprepared to teach those concepts for understanding. This study reveals that the majority of the sample has enough SMK to teach the early years of second-level trigonometry but does not have enough SMK to teach the later years. The strengths and shortcomings of the sample in relation to their SMK of trigonometry are presented. The authors conclude that second-level trigonometry content should be taught in initial mathematics teacher education in order to combat this issue.

An Investigation into the Statistics Education of Preservice Mathematics Teachers in an Irish University

This chapter investigates how well second-level preservice mathematics teachers at one Irish third-level teacher education college are prepared to teach statistics. An empirical study on the conceptual understanding of core statistical concepts of these preservice teachers as they prepare to graduate is presented. This issue is pertinent internationally (Shaughnessy, 1992; Zieffler et al., 2008) but particularly in Ireland currently as a new mathematics curriculum at second level, entitled “Project Maths,” was rolled out to all schools nationally in September, 2010. This new curriculum included a move from a situation where Statistics and Probability was previously an optional component of the exit-level school state examinations to a situation where it forms a compulsory one-fifth of the new curriculum. A study was carried out on 115 (86 % of the total 134) preservice mathematics teachers in the institution to assess how well prepared these preservice teachers are to teach statistics when they qualify. The chapter concludes with a discussion of the implications of these findings and the potential impact on their future students.