# Old habits die hard: An uphill struggle against rules without reason in mathematics teacher education

More Detail

^{1}EPI•STEM, University of Limerick, Limerick, Ireland

^{2}Department of Mathematics and Statistics, University of Limerick, Limerick, Ireland

^{*}Corresponding Author

EUR J SCI MATH ED, Volume 5, Issue 1, pp. 91-109.
https://doi.org/10.30935/scimath/9500

OPEN ACCESS 1267 Views 829 Downloads

## ABSTRACT

Mathematics teacher educators in the University of Limerick became aware of a lack of conceptual understanding of key mathematics concepts of prospective secondary mathematics teachers through observation on teaching placement and in pedagogy lectures. A pilot study to enhance the conceptual understanding of prospective teachers was carried out with one undergraduate class in 2009/10 and a longer more in-depth programme was offered to all prospective mathematics teachers in the academic year 2011/12. The intervention was designed to get prospective mathematics teachers ‘thinking’ about mathematics topics they have so far taken for granted and hence better prepare them for classroom practice. This retrospective study divulges a number of observations which emerged, the main one being how rote learning and an emphasis on procedural skills at the expense of conceptual understanding results in a cycle of ineffective teaching which is difficult to break.

## CITATION

O’Meara, N., Fitzmaurice, O., & Johnson, P. (2017). Old habits die hard: An uphill struggle against rules without reason in mathematics teacher education.

*European Journal of Science and Mathematics Education, 5*(1), 91-109. https://doi.org/10.30935/scimath/9500## REFERENCES

- Ball, D.L., Hill, H.C. and Bass, H. (2005) Knowing Mathematics for Teaching: Who Knows Mathematics Well Enough to Teach Third Grade, and How Can We Decide.
*American Researcher,***29**(1), 14 - 46. - Ball, D.L. (1990) The Mathematical Understandings that Pre-service Teachers bring to Teacher Education.
*Elementary School Journal,***90***,*449 – 466. - Behr, M.J., Khoury, H.A., Harel, G., Post, T. and Lesh, R. (1997) Conceptual Units Analysis of Preservice Elementary School Teachers’ Strategies on a Rational Number as Operator Task.
*Journal for Research in Mathematics Education,***28**(1), 48 – 69. - Boaler, J. (1998) Open and Closed Mathematics: Student Experiences and Understandings.
*Journal for Research in Mathematics Education,***29**(1), 41 – 62. - Britzman, D.P. (1991)
*Practice Makes Practice: A Critical Stuy of Learning to Teach*. Albany, New York: SUNY - Brosnan, A. (2010)
*Project Maths Development Team: Supporting Good Practice.*Presentation at the 24th Annual Meeting of the Irish Mathematical Society, University of Limerick, 29 August - 30 August 2011 - Brousseau, G., (1984) The crucial role of the didactical contract. Proceedings of the TME 54.
- Brousseau, G., (1997) Theory of Didactical situations in Mathematics. In A.J. Bishop (Ed.)
*Mathematics Education Library*, Volume 19, Netherlands: Springer Netherlands. - Clarke, D. (2010) Speaking in and about mathematics classrooms internatinally: the technical vocabulary of students and teachers
*.*Proceedings of Australian Council for Educational Research (ACER) Research Conference, 3-7. - Commission on the Points System. (1998
*) Consultative process – Background Document*. Dublin, Ireland: The Stationary Office. - Conway, P. F. and Sloane, F. C. (2005)
*International Trends in Post-Primary Mathematics Education: Perspectives on Learning, Teaching and Assessment*. Dublin, Ireland: National Council for Curriculum and Assessment. - Daro, P. (2010) Standards, What’s the Difference? A View from Inside the Development of the Common Cord State Standards in the Ocassionally United States. Proceedings of Australian Council for Educational Research (ACER) Research Conference, 8 -16 .
- Crowther, K., Thompson, D. and Cullingford, C. (1997) Engineering degree students are deficient in mathematical expertise-Why?.
*International Journal Of Mathematical Education in Science and Technology,***28**(6)*,*785-792. - Da Ponte, J. P., & Chapman, O. (2008). Preservice mathematics teachers' knowledge and development. In L. English (Ed.), Handbook of international research in mathematics education (2nd ed., pp. 225-263). New York, NY: Routledge.
- Engineering Council (2000).
*Report on Measuring the Mathematics Problem*. London, England: Engineering Council. - Ernest, P. (2010) The social outcomes of school mathematics: Standard, unintended or visionary?. Proceedings of Australian Council for Educational Research (ACER) Research Conference, 21 - 26.
- Faulkner, F. (2012)
*An Analysis of Performance in Mathematics for Technology Undergraduates and an Investigation of Teaching Interventions for these Students*. PhD thesis, University of Limerick, Unpublished. - Gill, O. (2006)
*What Counts as Service Mathematics? An Investigation into the ‘Mathematics Problem’ in Ireland*. PhD thesis, University of Limerick, Unpublished - Gill, O., O’Donoghue, J., Hannigan, A., and Faulkner, F. (2010). Trends in Performance of Science and Technology Students (1997-2008) in Ireland.
*International Journal of Mathematical Education in Science and Technology,***41,**323-339. - Graeber, A. (1999) Forms of knowing mathematics: what preservice teachers should learm.
*Educational Studeis in Mathematics,***38**, 189-208. - Hopper, T. (1999) The Grid: reflecting from preservice teachers’ experiences of being taught.
*The Journal of Physical Education, Recreation and Dance,***70**(7), 53 - 59 - Hourigan, M., and O’Donoghue, J. (2007). Mathematical under-preparedness: the influence of the pre-tertiary mathematics experience on students’ ability to make a successful transition to tertiary level mathematics courses in Ireland.
*International Journal of Mathematical Education in Science and Technology,***38**, 461-476. - Institute of Mathematics and its Applications (1995) Mathematics Matters in Engineering. Southend-on-Sea, UK: I.M.A.
- Kennedy, M.K. (1999) The role of preservice teacher education, In Darling-Hammond and L Sykes (Eds).
*Teaching as the learning profession: Handbook of teaching and policy*(pp. 54-86). San Francisco, USA: Jossey Bass. - London Mathematics Society (1995). Report on Tackling the Mathematics Problem. Southend-on-Sea, UK: L.M.S.
- Lortie, D. (1975)
*Schoolteacher: A Sociological Study*. London: University of Chicago Press. - Ma, L. (1999).
*Knowing and teaching elementary mathematics : teachers' understanding of fundamental mathematics in China and the United States*. New York, USA: Routledge - Mirirai, C., Mutambara Lillias, H. N. and Chagwiza C.J, (2012) Teaching fractions at ordinary level: A case study of mathematics secondary school teachers in Zimbabwe.
*Educational Research and Review,***7**(4), 90-101. - Monk, D.H. (1994) Subject Area Preparation of Secondary Mathematics and Science Teachers and Student Achievement.
*Economics of Education Review,***13**(2)*,*125 – 145. - Murphy, M. (2002)
*An Investigation into the Mathematical Under-Preparedness Present Among Third Level Entrants: the Possible Contribution of the Second Level Mathematics Experience*. PhD thesis, University of Limerick, Unpublished - Nardi, E. & Steward,S. (2003) Is Mathematics T.I.R.E.D? A Profile of Quiet Disaffection in the Secondary Mathematics Classroom.
*British Educational Research Journal,***29**(3), 345 – 366. - Newton, K, Leonard, J., Evans, B. and Eastburn, J. (2012) Preservice Elementary Teachers’ Mathematics Content Knowledge and Teacher Efficacy.
*School Science and Mathematics,***112**(5), 289-299. - O’Donoghue, J. (1999).
*An intervention to assist at risk students in service mathematics courses at the University of Limerick*. University of Limerick, Limerick: University of Limerick teaching fellowship scheme. - O’ Meara, N., O’Donoghue, J. & Gill, O. (2011
*) Improving Mathematics Teaching at Second Level through**the Design of a Model of Teacher Knowledge and an**Intervention Aimed at Developing Teachers’ Knowledge.*PhD thesis, University of Limerick, Unpublished. - Pegg, J. (2010)
*Promoting the acquisition of higher order skills and understandings in primary and secondary mathematics*. Proceedings of Australian Council for Educational Research (ACER) Research Conference, 35 - 38. - Romberg, T.A., Carpenter, T.P. and Fennema, E. (1993) Towards a Common Research Perspective. In T. Romberg, E. Fennema & T. Carpenter (Eds.)
*Integrating Research on the Graphical Representation of Functions*(pp. 1 – 9), Hillsdale, New Jersey: Erlbaum - Sawx, G.B., Gearhart, M. and Nasir, N.S. (2001) Enhancing Students’ Understadning of Mathematics: A Study of Three Contrasting Approaches to Professional Support.
*Journal of Mathematics Teacher Education,***4***,*55 – 79. - Schoenfeld, A.H. (2009) Working with Schools: The story of a Mathematics Education Collaboration.
*The American Mathematical Monthly,***116***,*197 – 217. - Schoenfeld, A. H. (1988) When good teaching leads to bad results: The disasters of ‘well-taught’ mathematics courses.
*Educational Psychologist,***23**(2), 145-166. - Schwartz, J. E. (2008) Elementary Mathematics Pedagogical Content Knowledge: Powerful Ideas for Teacher, New York, USA: Pearson.
- Slattery, J. and Gill-Fitzmaurice, O. (2012)
*An Investigation into Preservice Teachers’ Conceptual Knowledge of the Division of Fractions*. Undergraduate Disertation Thesis , University of Limerick, Unpublished - Stacey, K. (2010) Mathematics teaching and learning to reach beyond the basics. Proceedings of Australian Council for Educational Research (ACER) Research Conference, 17 - 20.
- Star, J.R. (2000) On the Relationship Between Knowing and Doing in Procedural Learning. Proceedings of
*Fourth International Conference of the Learning Sciences*, 80-86. - State Examinations Commission (2001)
*Chief Examiner’s Report (Ordinary Level Mathematics)*http://www.examinations.ie/archive/examiners_reports/cer_2001/lcmaths_ol_01_er.pdf, (accessed June 2016) - State Examinations Commission (2005)
*Chief Examiner’s Report, 2005.*http://www.examinations.ie/archive/examiners_reports/cer_2005/LCMathematics.pdf (accessed June 2016) - Stylianides A.J. and Stylianides, G.J. (2007), Learning mathematics with understanding: A critical consideration of the learning principle in the Principals and Standards for School Mathematics.
*The Montana Mathematics Enthusiast,***4**(1), 103-114. - Thompson, A.G. (1992) Teachers’ Beliefs and Conceptions: A Synthesis of the Research. In D.A.Grouws (Ed)
*Handbook of Research on Mathematics Teaching and Learning*(pp. 127 – 146). New York, USA : Macmillan. - TIMSS (1995). Third International Mathematics and Science Study. Boston: International Association for the Evaluation of Educational Achievement.
- Toumasis, C. (1992) Problems in training secondary mathematics teachers: the Greek experience.
*International Journal of Mathematical Education in Science and Technology,***23**(2), 287-299. - Yin R (1994) Case study research: Design and methods (2nd Ed.).Beverly Hills, CA: Sage Publishing.