logo logo European Journal of Mathematics and Science Education

EJMSE is is a, peer reviewed, online academic research journal.

Subscribe to

Receive Email Alerts

for special events, calls for papers, and professional development opportunities.


Publisher (HQ)

Eurasian Society of Educational Research
7321 Parkway Drive South, Hanover, MD 21076, USA
7321 Parkway Drive South, Hanover, MD 21076, USA
out of field teachers professional development mathematics teacher education mathematical knowledge for teaching

A Critical Examination of the Impacts and Lessons Learned from a Professional Development Program for Out-of-Field Mathematics Teachers

Catherine Paolucci , Máire Ní Ríordáin , Laura O’Dwyer

As international concerns about the prevalence of out-of-field teaching have grown, so have discussions about how to support out-of-field teachers. In.


As international concerns about the prevalence of out-of-field teaching have grown, so have discussions about how to support out-of-field teachers. In Ireland, the Professional Diploma in Mathematics for Teaching, a two-year professional development program, was created for out-of-field mathematics teachers. A pre-test, post-test, and final survey examined the program’s impact on participating teachers’ mathematical knowledge, confidence in teaching curricular content, and classroom practice. Findings offer evidence of development in participating teachers’ mathematical knowledge and self-efficacy after completing the program. They also raise important concerns about persistent weaknesses in participating teachers’ mathematical knowledge, particularly related to key areas of the curriculum.

Keywords: Out-of-field teachers, professional development, mathematics teacher education, mathematical knowledge for teaching.

cloud_download PDF
Article Metrics


Adler, J., & Venkat, H. (2014). Mathematical knowledge for teaching. In S. Leman (Ed.), Encyclopaedia of Mathematics Education (pp. 385-388). Springer Science + Business Media Dordrecht. 

Akiba, M., LeTendre, G. K., & Scribner, J. P. (2007). Teacher quality, opportunity gap, and national achievement in 46 countries. Educational Researcher, 36(7), 369-387. https://doi.org/10.3102%2F0013189X07308739.

Andrews, P. (2011). The cultural location of teachers' mathematical knowledge: Another hidden variable in mathematics education research? In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching (pp. 99-118). Springer.

Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177%2F0022487108324554.

Bandura, A. (1997). Self-efficacy: The exercise of control. W. H. Freeman.

Bitto, L., & Butler, S. (2010). Math teacher self-efficacy and its relationship to teacher effectiveness. Journal of Cross-Disciplinary Perspectives in Education, 3(1), 40-45.

Carney, M. B., Brendefur, J. L., Thiede, K., Hughes, G., & Sutton, J. (2016). Statewide mathematics professional development: Teacher knowledge, self-efficacy and beliefs. Educational Policy, 30(4), 539-572. https://doi.org/10.1177/0895904814550075.

Chapman, O. (2013). Investigating teachers’ knowledge for teaching mathematics. Journal of Mathematics Teacher Education, 16(4), 237-243. https://doi.org/10.1007/s10857-013-9247-2.

Clarke, D., & Hollingsworth, H. (2002). Elaborating a model of teacher professional growth. Teaching and Teacher Education, 18(8), 947-967. https://doi.org/10.1016/S0742-051X(02)00053-7

Davis, B., & Renert, M. (2013). Profound understanding of emergent mathematics: Broadening the construct of teachers’ disciplinary knowledge. Educational Studies in Mathematics, 82(2), 245-265. https://doi.org/10.1007/s10649-012-9424-8

Desimone, L. M. (2009). Improving impact studies of teachers’ professional development: Toward better conceptualizations and measures. Educational Researcher, 38(3), 181-199. https://doi.org/10.3102%2F0013189X08331140

Fauskanger, J. (2015). Challenges in measuring teachers’ knowledge. Educational Studies in Mathematics, 90(1), 57-73. https://doi.org/10.1007/s10649-015-9612-4

Gabriele, A. J., & Joram, E. (2007). Teachers’ reflections on their reform-based teaching in mathematics: Implications for the development of teacher self-efficacy. Action in Teacher Education, 29(3), 60-74. https://doi.org/10.1080/01626620.2007.10463461

Goddard, R. D., Hoy, W. K., & Hoy, A. W. (2000). Collective teacher efficacy: Its meaning, measure and impact on student achievement. American Educational Research Journal, 37, 479-507.

Goldsmith, L. T., Doerr, H. M., & Lewis, C. C. (2014). Mathematics teachers’ learning: A conceptual framework and synthesis of research. Journal of Mathematics Teacher Education, 17(1), 5–36. https://doi.org/10.1007/s10857-013-9245-4

Goos, M., O’Donoghue, J., Ní Ríordáin, M., Faulkner, F., Hall, T., & O’Meara, M. (2020). Designing a national blended learning program for “out-of-field” mathematics teacher professional development. ZDM Mathematics Education, 52, 893–905. https://doi.org/10.1007/s11858-020-01136-y

Hattie, J. (2012). Visible learning for teachers: Maximising impact on learning. Routledge.

Hill, H. C., & Ball, D. L. (2004). Learning mathematics for teaching: Results from California’s mathematics professional development institutes. Journal for Research in Mathematics Education, 35(5), 330-351. https://doi.org/10.2307/30034819

Hobbs, L. (2012). Teaching out-of-field: Factors shaping identities of secondary science and mathematics. Teaching Science, 58(1), 21-29.  

Hobbs, L. (2013). Teaching ‘out-of-field’ as a boundary-crossing event: Factors shaping teacher identity. International Journal of Science and Mathematics Education, 11(2), 109-132. https://doi.org/10.1007/s10763-012-9333-4.

Hobbs, L., & Törner, G. (Eds.) (2019). Examining the phenomenon of “teaching out-of-field”: International perspectives on teaching as a non-specialist. Springer.

Hollebrands, K. F., & Lee, H. S. (2020). Effective design of massive open online courses for mathematics teachers to support their professional learning. ZDM Mathematics Education, 52, 859–875. https://doi.org/10.1007/s11858-020-01142-0.

Ingersoll, R. M. (2001). The realities of out-of-field teaching. Educational Leadership, 5, 42-45.

Ingersoll, R. M. (2002). Out-of-field teaching, educational inequality and the organisation of schools: An exploratory analysis. University of Washington: Center for the Study of Teaching and Policy.

Kirwan, L. (2017). Mathematics curriculum in Ireland: The ınfluence of PISA on the development of project maths. International Electronic Journal of Elementary Education8(2), 317–332.

Krauss, S., Baumert, J., & Blum, W. (2008). Secondary mathematics teachers’ pedagogical content knowledge and content knowledge: validation of the COACTIVE constructs. ZDM: The International Journal on Mathematics Education, 40(5), 873-892. https://doi.org/10.1007/s11858-008-0141-9

Lampert, M. (2001). Teaching problems and the problems of teaching. Yale University Press.

Lane, C., & Ní Ríordáin, M. (2020). Out-of-Field Mathematics Teachers’ Beliefs and Practices: an Examination of Change and Tensions Using Zone Theory. International Journal of Science and Mathematics Education, 18, 337-355. https://doi.org/10.1007/s10763-019-09964-5.

Lowrie, T., & Jorgensen, R. (2016). Pre-service teachers’ mathematical content knowledge: implications for how mathematics is taught in higher education. Teaching Mathematics and Its Applications, 35, 202-215. https://doi.org/10.1093/teamat/hrv008

Merriman, B., Shiel, G., Perkins, R., & Cosgrove, J. (2014). Project Maths and PISA: Comparing the coverage of PISA mathematics items by the Project Maths and pre-Project Maths curricula. In E. McLoughlin & O. Finlayson (Eds.),  Proceeding of SMEC2014 - Science and Mathematics Education Conference (pp. 155-161). Dublin City University & St. Patrick’s College.

Ní Ríordáin, M., & Hannigan, A. (2011). Who teaches our students mathematics at post-primary education in Ireland? Irish Educational Studies, 30(3), 289-304. https://doi.org/10.1080/03323315.2011.569117

Ní Ríordáin, M., Paolucci, C., & O' Dwyer, L. M. (2017). An examination of the professional development needs of out-of-field mathematics teachers. Teaching and Teacher Education, 64, 162-174. https://doi.org/10.1016/j.tate.2017.02.001

Nixon, R. S., Campbell, B. K., & Luft, J. A. (2016). Effects of subject-area degree and classroom experience on new chemistry teachers’ subject matter knowledge. International Journal of Science Education, 38(10), 1636-1654. https://doi.org/10.1080/09500693.2016.1204482

Nixon, R. S., Luft, J. A., & Ross, R. J. (2017). Prevalence and predictors of out‐of‐field teaching in the first five years. Journal of Research in Science Teaching, 54(9), 1197-1218. https://doi.org/10.1002/tea.21402.

O'Meara, N., & Faulkner, F. (2021). Professional development for out-of-field post-primary teachers of mathematics: an analysis of the impact of mathematics specific pedagogy training. Irish Educational Studies, 40(2), 1-20. https://doi.org/10.1080/03323315.2021.1899026

Paolucci, C. (2015). Changing perspectives: Examining the potential for advanced mathematical studies to influence pre-service teachers' beliefs about mathematics. Teaching and Teacher Education, 49, 97-107. https://doi.org/10.1016/j.tate.2015.03.002

Rowland, T., & Ruthven, K. (2011). Mathematical knowledge in teaching. Springer. 

Schmidt, W. H., Houang, R., Cogan, L., Blömeke, S., Tatto, M. T., Hsieh, F. J., Santillan, M., Bankov, K., Han, S., Cedillo, T., Schwille, J., & Paine, L. (2008). Opportunity to learn in the preparation of mathematics teachers: its structure and how it varies across six countries. ZDM: The International Journal on Mathematics Education, 40(5), 735-747. https://doi.org/10.1007/s11858-008-0115-y

Shah, L., Jannuzzo, C., Hassan, T., Gadidov, B., Ray, H. E., & Rushton, G. T. (2019). Diagnosing the current state of out-of-field teaching in high school science and mathematics. PLoS ONE, 14(9), 1-12. https://doi.org/10.1371/journal.pone.0223186

Sharplin, E. D. (2014). Reconceptualising out-of-field teaching: Experiences of rural teachers in Western Australia. Educational Research, 56(1), 97-110. https://doi.org/10.1080/00131881.2013.874160

Shaughnessy, M. F. (2004). An interview with Anita Woolfolk: The educational psychology of teacher efficacy. Educational Psychology Review, 16(2), 153-175. https://doi.org/10.1023/B:EDPR.0000026711.15152.1f

Silverman, J., & Thompson, P. W. (2008). Toward a framework for the development of mathematical knowledge for teaching. Journal of Mathematics Teacher Education, 11(6), 499-511. https://doi.org/10.1007/s10857-008-9089-5

Tatto, M. T., Schwille, J., Senk, S., Ingvarson, L., Peck, R., & Rowley, G. (2008). Teacher Education and Development Study in Mathematics (TEDS-M): Policy, practice, and readiness to teach primary and secondary mathematics: Conceptual framework. Teacher Education and Development International Study Center, College of Education, Michigan State University.

Tatto, M. T., Schwille, J., Senk, S. L., Ingvarson, L., Rowley, G., Peck, R., Bankov, K., Rodriguez, M., & Reckase, M. (2012). The Teacher Education Study in Mathematics (TEDS-M): Policy, practice and readiness to teach primary and secondary mathematics (Findings from the IEA study of the mathematics preparation of future teachers). International Association for the Evaluation of Educational Achievement.