High Achievement in Mathematics and Science among Students in Ireland: An In-Depth Analysis of International Large-Scale Assessment Data Since 2000

ABSTRACT

National policy initiatives in Ireland, such as Project Maths and the Science, Technology, Engineering, and Mathematics (STEM) Education Policy Statement have sought to increase the engagement and performance of students in mathematics and science. The current study investigated the performance of students in Ireland in these areas and in reading in international large-scale assessments (Programme for International Student Assessment [PISA], Trends in International Mathematics and Science Study [TIMSS], and Progress in International Reading Literacy Study [PIRLS]), with a view to better understand the performance of high-achieving students, relative to their counterparts in other countries in general, and in countries with similar average performance. Lower than expected proportions of high achievers were noted and a pattern of relative underachievement was observed among high achievers – those performing at the highest levels of proficiency, and those performing at key benchmarks, including the 75th and 90th percentiles – in mathematics and science to a greater extent than in reading. These issues were found to be consistent over time, and more prevalent at post-primary level, compared with primary level. The findings of this study are discussed with reference to individual and societal costs, and specific issues that need to be investigated further are identified.

KEYWORDS:

• High achievement
• mathematics
• science
• PISA
• TIMSS
• PIRLS

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 An important distinction that needs to be made is that between high achievement and giftedness. While a group of high-achieving students may or may not include gifted students, the two groups are generally distinct. Usually, proportions of high-achieving students (ranging between 5% and 15% across the Organisation for Economic Co-operation and Development [OECD] countries in PISA) are higher than proportions of gifted students, who are often identified as the top 1% or 2% of students in their cohort and those students who often participate in national and international competitions such as the International Mathematical Olympiad.

2 PIRLS data are analysed so that performance among high-achieving students at primary level on reading can be compared with performance on mathematics and science, as assessed by TIMSS.

3 The PISA, TIMSS, and PIRLS databases are publicly available on the relevant websites.

4 PISA, TIMSS, and PIRLS are sample-based assessments that involve complex designs and sampling strategies. As a result, each student does not have the same chances of being selected to participate in these assessments. To control for this, each student is assigned a different weight, which needs to be taken into account in any analysis of data coming from these assessments as ignoring weights can lead to biased results that may be considerably influenced by responses coming from certain groups of students (e.g. students attending large schools). Also, due to time restrictions, each student is administered a subset of test items from the total item pool for each domain, with different groups of students answering different, although overlapping, sets of items. Given this method of assessing students, and the fact that PISA, TIMSS, and PIRLS are designed to make population-level estimations, rather than accurately describe individual students’ proficiencies based on their test scores, the imputation methodology of plausible values is often used. Plausible values constitute random draws from the distribution of scores that could be reasonably assigned to each individual (Wu 2005) and should be used in any analysis of data coming from these assessments.

5 The decline in performance in PISA 2009 in both reading and mathematics in Ireland has been investigated in several studies (e.g. Sachse, Mahler, and Pohl 2019). It has been partly attributed to limited student engagement with PISA tests, and the treatment of skipped and not reached items by the OECD’s contractors in the scaling process.

6 In TIMSS and PIRLS, medians rather than means are used for the comparisons of percentages of students at each international benchmark in international and national reports.

7 Reading data are not presented here; PIRLS assesses the reading literacy of fourth-grade students without an equivalent assessment at eighth grade.

8 Results for PISA are only presented for the major assessment domain in each cycle.

9 Results for PISA are only presented for the major assessment domain in each cycle.

10 Τhe bonus points scheme was introduced in 2012 for students who take the mathematics test of the Leaving Certificate examination at higher level. Based on the scheme, students who achieve grades D3 or 6 and above in the old and new grading system, respectively, are awarded 25 extra points in the subject (Central Applications Office 2012). This scheme was introduced as an incentive for students, seeking to increase the numbers of those taking the mathematics tests of the Junior and Leaving Certificate examinations at higher level. The bonus points scheme along with the implementation of other initiatives (e.g. Project Maths) intended to support the achievement of the national targets that were set in the 2011 National Strategy to Improve Literacy and Numeracy.

11 A potential overlap in the knowledge and skills measured by these assessments should be acknowledged (see Eivers 2010).

12 The targets for the increase of the proportions of high-achieving students in NAMER set in the 2011 Strategy were met as per the results of NAMER 2014. Consequently, the interim review report of the Strategy, published in 2017, updated these targets; however, data from a more recent administration of NAMER that could be used to gauge progress towards the achievement of the updated targets are not available at the time of writing.

Additional information

Funding

This work was supported by the Irish Research Council (grant number: GOIPG/2018/3368).

Notes on contributors

Vasiliki Pitsia

Vasiliki Pitsia is a research assistant at the Educational Research Centre, Ireland. She holds a BEd from the University of Ioannina, Greece, an MSc in Quantitative Methods and Statistical Analysis in Education from Queen’s University Belfast, UK, and a PhD in Assessment from Dublin City University, Ireland. Vasiliki has worked as a researcher, data analyst, and psychometrician on various projects in Ireland and Greece and as a consultant at the World Bank. She has also given lectures on research methodology, measurement, assessment, and statistics to postgraduate students and academic staff in academic institutions across Europe. Vasiliki’s research has attracted grants, such as the Irish Research Council Government of Ireland Postgraduate Scholarship, and it has been published in peer-reviewed academic journals and presented at national and international conferences. Her research interests include research methodology, statistical analysis, psychometrics, measurement, and assessment.

Zita Lysaght

Zita Lysaght is a member of the School of Policy and Practice and a Research Associate and member of the Advisory Board and Advisory Panel of CARPE at DCU. She coordinates and teaches classroom assessment and research methodology modules on undergraduate, masters and doctoral programmes and directs and supervises a range of research and doctoral projects.

Michael O'Leary

Michael O’Leary holds the Prometric Chair in Assessment at Dublin City University and is the Director of CARPE. He is a graduate of the BEd Programme at St Patrick’s College and holds an M.Ed. from Trinity College, Dublin. He gained his PhD in Educational Research and Measurement at Boston College in 1999. Michael has provided statistical analysis of data for the national surveys of reading and mathematics achievement in Ireland and collaborated over many years with colleagues on a variety of research projects ranging from the introduction of calculators at Junior Cycle to the Leaving Certificate programme as a preparation for college. In June 2020 he was appointed by the Minister for Education to the Independent Steering Committee on the implementation of Calculated Grades. He leads an extensive programme of research at CARPE focused on assessment and measurement at all levels of the educational system and in the workplace.

Gerry Shiel

Gerry Shiel worked as a Research Fellow at the Educational Research Centre prior to retirement in 2020. He coordinated implementation of the Programme for International Student Assessment (PISA) in Ireland across its first seven cycles (from 2000 to 2018). He also worked on national assessments of English reading and mathematics, and on the Progress in International Reading Literacy Study, as well as on the development of standardised tests at primary and post-primary levels. He holds a PhD in curriculum and assessment from the University of Texas (Austin).