Widening access to advanced mathematics: Teachers’ perspectives on the impact on secondary school teaching

Olivia Fitzmaurice 1 * , Patrick Johnson 1
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1 School of Education, University of Limerick, Limerick, IRELAND
* Corresponding Author
EUR J SCI MATH ED, Volume 13, Issue 4, pp. 304-320. https://doi.org/10.30935/scimath/17304
Published: 18 October 2025
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ABSTRACT

In Ireland, mathematics is a core subject at secondary school and is chosen as a subject by almost the entire school leaving population. It can be taken at two levels: ordinary level and higher level (HL). In 2012 an incentive to increase participation at HL was undertaken by the Irish government. This incentive came in the form of bonus points (towards gaining access to their chosen university programme) to anyone who achieved 40% or above in this examination. It is the only subject (out of 53 offered) in which bonus points are awarded. The incentive was successful in that it doubled participation within ten years. The impact of this incentive on teachers however is the focus of this research. The goal of this study is to demonstrate the extent of the demands placed on teachers of advanced mathematics, both in the quantity of material they are required to cover and the depth they are expected to reach, all while managing larger class sizes and greater diversity in students’ mathematical abilities. This study is highly relevant to an international readership, as it explores how incentivising participation in a secondary school subject, and the resulting rise in student numbers and broader range of ability levels, can profoundly affect the teaching of the subject. The teachers interviewed in this study reported difficulty balancing larger, more diverse classes with the demands of a challenging syllabus and described how lesson pacing slowed to accommodate students with lower prior attainment, limiting time for deeper learning opportunities.
Keywords: mathematics education, mathematics examinations, summative assessment, advanced mathematics, incentivisation

CITATION

Fitzmaurice, O., & Johnson, P. (2025). Widening access to advanced mathematics: Teachers’ perspectives on the impact on secondary school teaching. European Journal of Science and Mathematics Education, 13(4), 304-320. https://doi.org/10.30935/scimath/17304

REFERENCES

  • Arnoux, P., Duverney, D., & Holton, D. (2009). The rise and fall of mathematical enrolments in the French educational system: A case study. International Journal of Mathematical Education in Science and Technology, 40(1), 43–57. https://doi.org/10.1080/00207390802586145
  • Artigue, M., & Blomhøj, M. (2013). Conceptualizing inquiry-based education in mathematics. ZDM Mathematics Education, 45(6), 797–810. https://doi.org/10.1007/s11858-013-0506-6
  • Au, W. (2007). High-stakes testing and curricular control: A qualitative metasynthesis. Educational Researcher, 36(5), 258–267. https://doi.org/10.3102/0013189X07306523
  • Baker, D. P., Fabrega, R., Galindo, C., & Mishook, J. (2004). Instructional time and national achievement: Cross-national evidence. Prospects, 34(3), 311–334. https://doi.org/10.1007/s11125-004-5310-1
  • Beilock, S. L. (2008). Math performance in stressful situations. Current Directions in Psychological Science, 17(5), 339–343. https://doi.org/10.1111/j.1467-8721.2008.00602.x
  • Bennett, J., Braund, M., & Sharpe, R. (2014). Student attitudes, engagement and participation in STEM subjects [Project report]. The University of York.
  • Braun, V., & Clarke, V. (2021). Thematic analysis: A practical guide. SAGE. https://doi.org/10.1007/978-3-319-69909-7_3470-2
  • Clerkin, A. (2012). Personal development in secondary education: The Irish transition year. Education Policy Analysis Archives, 20(38), 1–18. https://doi.org/10.14507/epaa.v20n38.2012
  • Davidovitch, N., & Yavich, R. (2018). The effect of motivation and self-efficacy on math studies in the Israeli Ministry of Education’s program “give five”. International Journal of Higher Education, 7(6), 63–77. https://doi.org/10.5430/ijhe.v7n6p63
  • Department of Education and Skills. (2015). Leaving certificate mathematics syllabus: Foundation, ordinary and higher level. Department of Education and Skills. https://curriculumonline.ie/getmedia/f6f2e822-2b0c-461e-bcd4-dfcde6decc0c/SCSEC25_Maths_syllabus_examination-2015_English.pdf
  • Ermatova, A., & Sharipov, B. (2024). Advantages and disadvantages of summative and formative assessment in education. Modern Science and Research, 3(12), 65–68. https://doi.org/10.5281/zenodo.14278925
  • Expert Group on Future Skills Needs. (2008). Statement on raising national mathematical achievement. Raising Future Skills Ireland. https://www.egfsn.ie/latest-news/2008/raising-national-mathematical-achievement/
  • Farvis, J., & Hay, S. (2020). Undermining teaching: How education consultants view the impact of high-stakes test preparation on teaching. Policy Futures in Education, 18(8), 1058–1074. https://doi.org/10.1177/1478210320919541
  • Findell, B., Swafford, J., & Kilpatrick, J. (Eds.). (2001). Adding it up: Helping children learn mathematics. National Academy Press.
  • Fitzmaurice, O., O’Meara, N., & Johnson, P. (2021). Highlighting the relevance of mathematics to secondary school students – Why and how. European Journal of STEM Education, 6(1), Article 07. https://doi.org/10.20897/ejsteme/10895
  • Freudenthal, H. (1973). Mathematical rigour. In Mathematics as an educational task (pp. 147–154). Springer. https://doi.org/10.1007/978-94-010-2903-2_8
  • Gill, O. (2006). What counts as service mathematics? An investigation into the ‘Mathematics Problem’ in Ireland [Unpublished doctoral thesis, University of Limerick].
  • Hattie, J. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge.
  • Hine, G. (2018). Exploring declining secondary student enrolments in higher-level mathematics courses. Issues in Educational Research, 28(3), 635–654.
  • Hine, G. (2023). Incentivising student enrolments in secondary mathematics courses: is a 10% bonus enough? International Journal of Mathematical Education in Science and Technology, 54(8), 1581–1597. https://doi.org/10.1080/0020739X.2023.2177895
  • Homer, M., Mathieson, R., Tasara, I., & Banner, I. (2018). Increasing post-16 mathematics participation in England: The early implementation and impact of core maths. In Proceedings of the BCME9 (pp. 88–95). BSRLM.
  • Johnson, P., & Fitzmaurice, O. (2025). Navigating mathematics curriculum reform: Teachers’ efforts and implementation challenges. Journal of Curriculum Studies, 1–25. https://doi.org/10.1080/00220272.2025.2495973
  • Johnson, P., Freemyer, J. V., & Fitzmaurice, O. (2019). The perceptions of Irish mathematics teachers toward a curriculum reform 5 years after its implementation. Frontiers in Education, 4. https://doi.org/10.3389/feduc.2019.00013
  • Krannich, M., Goetz, T., Lipnevich, A. A., Bieg, M., Roos, A. L., Becker, E. S., & Morger, V. (2019). Being over-or underchallenged in class: Effects on students’ career aspirations via academic self-concept and boredom. Learning and Individual Differences, 69, 206–218. https://doi.org/10.1016/j.lindif.2018.10.004
  • Maagan, D., & Zussman, N. (2019). Assessing the effectiveness of the “technological-scientific reserve” and “give five” programs. Bank of Israel. https://boi.org.il/media/g04p3loy/dp201910e.pdf
  • Mujtaba, T., Reiss, M. J., Rodd, M., & Simon, S. (2015). Methodological issues in mathematics education research when exploring issues around participation and engagement. In J. Middleton, J. Cai, & S. Hwang (Eds.), Large-scale studies in mathematics education (pp. 335–362). Springer. https://doi.org/10.1007/978-3-319-07716-1_15
  • Mujtaba, T., Reiss, M.J., & Hodgson, A. (2014). Motivating and supporting young people to study mathematics: A London perspective. London Review of Education, 12(1), 121–142. https://doi.org/10.18546/LRE.12.1.11
  • National Council for Curriculum and Assessment. (2015). Senior cycle mathematics specification: Examination. https://curriculumonline.ie/getmedia/f6f2e822-2b0c-461e-bcd4-dfcde6decc0c/SCSEC25_Maths_syllabus_examination-2015_English.pdf
  • O’Meara, N., & Prendergast, M. (2017). Time in mathematics education (TiME): A national study analysing the time allocated to mathematics at second level in Ireland. Epi*STEM: National Centre for STEM Education. https://core.ac.uk/download/pdf/296245499.pdf
  • O’Meara, N., Prendergast, M., & Treacy, P. (2020). What’s the point? Impact of Ireland’s bonus points initiative on student profile in mathematics classrooms. Issues in Educational Research, 30(4), 1418–1441. https://doi.org/10.34961/5555
  • O’Meara, N., Prendergast, M., & Treacy, P. (2023). Mathematics in Ireland’s upper secondary schools: Why do students choose higher-level maths? Issues in Educational Research, 33(1), 227–246. https://search.informit.org/doi/10.3316/informit.173498874602542
  • Phelps, G., Corey, D., DeMonte, J., Harrison, D., & Loewenberg Ball, D. (2012). How much English language arts and mathematics instruction do students receive? Investigating variation in instructional time. Educational Policy, 26(5), 631–662. https://doi.org/10.1177/0895904811417580
  • Prendergast, M., & O’Meara, N. (2016). A time profile of mathematics in a “gap year” in Irish secondary schools. European Journal of Science and Mathematics Education, 4(3), 293–304. https://doi.org/10.30935/scimath/9471
  • Prendergast, M., O’Meara, N., & Treacy, P. (2019). Incentivising the study of higher level mathematics. In A. Rogerson, & J. Morska (Eds.), Theory and practice: An interface or a great divide? the mathematics education for the future project–Proceedings of the 15th International Conference (pp. 479–484). https://doi.org/10.37626/GA9783959871129.0.90
  • Prendergast, M., O’Meara, N., & Treacy, P. (2020). Is there a point? Teachers’ perceptions of a policy incentivizing the study of advanced mathematics. Journal of Curriculum Studies, 52(6), 752–769. https://doi.org/10.1080/00220272.2020.1790666
  • Reiss, M. J., & Mujtaba, T. (2017). Should we embed careers education in STEM lessons? Curriculum Journal, 28(1), 137–150. https://doi.org/10.1080/09585176.2016.1261718
  • State Examinations Commission. (2024a). Leaving certificate examination 2024 – Mathematics – Paper 1 – Ordinary level. https://www.examinations.ie/archive/exampapers/2024/LC003GLP100EV.pdf
  • State Examinations Commission. (2024b). Leaving certificate examination 2024 – Mathematics – Paper 1 – Higher level. https://www.examinations.ie/archive/exampapers/2024/LC003ALP100EV.pdf
  • Stone, A. A., Schneider, S., Smyth, J. M., Junghaenel, D. U., Couper, M. P., Wen, C., Mendez, M., Velasco, S., & Goldstein, S. (2024). A population-based investigation of participation rate and self-selection bias in momentary data capture and survey studies. Current Psychology, 43(3), 2074–2090. https://doi.org/10.1007/s12144-023-04426-2
  • Suprayogi, M. N., Valcke, M., & Godwin, R. (2017). Teachers and their implementation of differentiated instruction in the classroom. Teaching and Teacher Education, 67, 291–301. https://doi.org/10.1016/j.tate.2017.06.020
  • TIMSS. (2019). TIMSS 2019 international results in mathematics and science–Instructional time in mathematics. TIMSS. https://timss2019.org/reports/instruction-time-mathematics/index.html
  • Tóth, E., & Csapó, B. (2022). Teachers’ beliefs about assessment and accountability. Educational Assessment, Evaluation and Accountability, 34(4), 459–481. https://doi.org/10.1007/s11092-022-09396-w
  • Treacy, P. T. (2017). Incentivizing advanced mathematics study at upper secondary level: The case of bonus points in Ireland. International Journal of Mathematical Education in Science and Technology, 49(3), 417–436. https://doi.org/10.1080/0020739X.2017.1366558
  • Treacy, P., Prendergast, M., & O’Meara, N. (2019). A “new normal”: Teachers’ experiences of the day-to-day impact of incentivising the study of advanced mathematics. Research in Mathematics Education, 22(3), 233–248. https://doi.org/10.1080/14794802.2019.1668832
  • Usman, A. I. (2015). Secondary school pre-service mathematics teachers’ content knowledge of algebraic word problem in Nigeria. European Journal of Science and Mathematics Education, 3(4), 350–363. https://doi.org/10.30935/scimath/9443
  • Zhao, M., Mu, B., & Lu, C. (2016). Teaching to the test: Approaches to teaching in senior secondary schools in the context of curriculum reform in China. Creative Education, 7(1), 32–43. https://doi.org/10.4236/ce.2016.71004