Mathematics Education of Pre-Service Teachers

As Reflected in Methods Course Syllabus


  • Leslie-Anne Unsworth Waterloo Region District School Board, Ontario, Canada
  • Immaculate K. Namukasa Western University, Ontario, Canada
  • Kinful Aryee University of Western, Ontario, Canada
  • Donna Kotsopoulos Western University, Ontario, Canada



This study seeks to contribute a better understanding of what future pre-service teachers of mathematics learn in their mathematics methodology courses at the universities. Course syllabi from six countries were analyzed using the Mathematics Teacher Educator (MTEd) Instrument to examine the “ideal” curriculum trends in mathematics education courses of pre-service teachers. The MTEd identifies 11 research areas and these were our guiding theoretical and analytical frameworks. Each of the syllabi contained in the final syllabus data set (n = 31) were coded using the MTEd Instrument. Correlation analysis was conducted to examine the relationship between category levels and overall levels assigned to each syllabus in elementary-only and secondary-only syllabi. Mann-Whitney U test was conducted between the elementary and secondary data sets. Findings from the study indicated that research related to the mathematics education of pre-service teachers was moderately represented in the course syllabi analyzed. Technology and assessment were the only two categories that were correlated to overall score. Recommendations for mathematics teacher education courses are offered.

Author Biographies

Leslie-Anne Unsworth , Waterloo Region District School Board, Ontario, Canada

Leslie-Anne Unsworth (formerly, Purdy) is an educator with the Waterloo Region District School Board in Ontario, Canada. She obtained her Bachelor’s of Arts and Business from the University of Waterloo, her Bachelor’s of Education from Wilfrid Laurier University, and her Master’s of Education from the University of Western Ontario.

Immaculate K. Namukasa, Western University, Ontario, Canada

Dr. Namukasa is an associate professor of the Faculty of education and distinguished teaching fellow with the Center for Teaching and Learning, 2017 to 2020 at Western University in Ontario, Canada. She obtained her Doctorate in Secondary Education at the University of Alberta.

Kinful Aryee, University of Western, Ontario, Canada

Dr. Kinful Aryee is an international school teaching educator and a research associate at Western University in Ontario, Canada. She obtained her Bachelor’s of Education in Science from the University of Cape Coast, Ghana, West Africa, her Master’s and Doctorate in Curriculum Development and Pedagogy at Western University, Canada.

Donna Kotsopoulos, Western University, Ontario, Canada

Dean & Professor, Faculty of Education, Western University since January 2021.


Adler, J., & Davis, Z. (2006). Opening another black box: Researching mathematics for teaching in mathematics teacher education. Journal for Research in Mathematics Education, 37(2), 270–296.

Apple, M. W. (1992). Do the standards go far enough? Power, policy, and practice in mathematics education. Journal for Research in Mathematics Education, 23(5), 412-431.

Artzt, A. F., & Armour-Thomas, E. (2002). Becoming a reflective mathematics teacher: A guide for observations and self-assessment. Mahwah, NJ: Lawrence Erlbaum Associates.

Ball, D. L. (2000). Bridging practices: Intertwining content and pedagogy in teaching and learning to teach. Journal of Teacher Education, 51(3), 241-247.

Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 83-104). Westport, CT: Ablex Publishing.

Ball, D. L., Hill, H. C, & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29(1), 14-17, 20-22, 43-46.

Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389–407. DOI:10.1177/0022487108324554

Ball, D., & Grevholm, B. (2008). The professional formation of mathematics teachers. In M. Menghini, F. Furinghetti, L. Giacardi, & A. Arzarello. (Eds.), The First Century of the International Commission on Mathematical Instruction (1908-2008). Reflecting and Shaping the World of Mathematics Education. Proceedings of the Symposium held in Rome, 5th-8th March 2008. International Commission on Mathematics Instruction. Rome, Italy.

Bartolo, P., Smyth, G., Swennen, A., & Klink, M. (2008). Teacher education for diversity. In M. van der Klink & A. Swennen (Eds.), Becoming a teacher educator (pp. 117-132). Netherlands: Springer.

Blömeke, S. (2014). Framing the enterprise: Benefits and challenges of international studies on teacher knowledge and teacher beliefs--modeling missing links. In S. Blömeke, F-J. Hsieh, G. Kaiser & W. H. Schmidt (Eds.), International perspectives on teacher knowledge, beliefs and opportunities to learn, Advances in mathematics education (pp 1 - 10). Dordrecht: Springer.

Blömeke, S., Suhl, U., Kaiser, G., & Döhrmann, M. (2012). Family background, entry selectivity and opportunities to learn: What matters in primary teacher education? An international comparison of fifteen countries. Teaching and Teacher Education, 28(1), 44-55.

Blubaugh, W. L. (2009). A course for pre-service mathematics teachers that focuses on mathematics and the integration of technology. Mathematics and Computer Education, 43(1), 41-47.

Burkhardt, H. Fraser, R. & Ridgway, J. (1990). The dynamics of curriculum change. In I. Wirszup & R. Streit (Eds.), Developments in school mathematics around the world (Vol. 2, pp. 3-30). Reston, VA: National Council of Teachers of Mathematics.

Burton, L. D. (2003). The formal, the planned, and the learned curriculum in an elementary education course for mathematics: Three perspectives on course content. A paper presented at the 2nd Annual General Meeting of the American association for the Advancement of Curriculum Studies. Chicago: Illinois.

Canãdas M. C., Gómez, P. & Rico, L. (2013). Structure of primary mathematics teacher education programs in Spain. International Journal of Science and Mathematics Education, 11, 879 - 894.

Chai, C. S., Koh, J. H. L., & Tsai, C-C. (2010). Facilitating preservice teachers' development of technological, pedagogical, and content knowledge (TPACK). Educational Technology & Society, 13 (4), 63-73.

Chapman, O. (2007). Facilitating preservice teachers’ development of mathematics knowledge for teaching arithmetic operations. Journal of Mathematics Teacher Education, 10(4), 341-349.

Ching-Shu, C. (2006). Perspective of prospective pedagogy in early Algebra: US-Russian forum on elementary mathematics and measure up. Taiwan Mathematical Teacher Electronic Journal, Issue 6.

Clark-Wilson, A., Robutti, O., & Sinclair, N. (2014). The mathematics teacher in the digital era: An international perspective on technology focused professional development. Mathematics Education in the Digital Era, v. 2. Dordrecht: Springer.

CMEC. (2010). Teacher Education and development study in mathematics 2008: A Canadian Report. Toronto: CMEC.

Corlu, M. S. (2013). Insights into STEM education praxis: As assessment scheme for course syllabi. Educational Science, Theory and Practice, 13(4), 2477-2485.

Cunningham, A. C., & Bennett, K. (2009). Teaching formative assessment strategies to preservice teachers: Exploring the use of handheld computing to facilitate the action research process. Journal of Computing in Teacher Education, 25(3), 99-105.

da Ponte, J. P., Oliveira, H., & Varandas, J. M. (2002). Development of pre-service mathematics teachers' professional knowledge and identity in working with information and communication technology. Journal of Mathematics Teacher Education, 5(2), 93-115.

D'Ambrosio, U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the Learning of Mathematics, 5(1), 44-48.

Deng, Z. (2011). Revisiting curriculum potential. Curriculum Inquiry, 41(5), 538-559.

Doyle, W. (1992). Curriculum and pedagogy. In P. W. Jackson (Ed.), Handbook of Research on Curriculum. (pp. 486-516). New York: Macmillan.

Dumma C. M. & Mojeed K. A. (2015). Preparation of mathematics teachers: Lessons from review of literature on teachers’ knowledge, beliefs, and teacher education. American Journal of Educational Research, 3(4), 505-513. doi: 10.12691/education-3-4-18.

Ernest, P. (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13-33.

Esmonde, I. (2009). Ideas and identities: Supporting equity in cooperative mathematics learning. Review of Educational Research, 79(2), 1008-1043.

Freiman V. (2014). Technology design in mathematics education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education. Springer, Dordrecht.

García, M., Sánchez, V. & Escudero, I. (2007). Learning through reflection in mathematics teacher education. Educational Studies in Mathematics, 64(1), 1-17.

Goldin, G. (2002). Affect, meta-affect, and mathematical belief structures. In G. Leder, E. Pehkonen & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 59-72). Dordrecht: Kluwer.

Greenhow, C., Robelia, B., & Hughes, J. E. (2009). Learning, teaching, and scholarship in a digital age. Educational Researcher, 38(4), 246-259.

Gutiérrez, R. (2013). Why (Urban) mathematics teachers need political knowledge. Journal of Urban Mathematics Education, 6(2), 7–19.

Hill, C. H., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.

Hora, M. T., & Ferrare, J. J. (2013). Instructional system of practice: A multidimensional analysis of math and science undergraduate course planning and classroom teaching. International Journal of Learning Sciences, 22(2), 212-257.

Hsieh, F-J. (2013). Strengthening the conceptualization of mathematics pedagogical content knowledge for international studies: A Taiwanese perspective. International Journal of Science and Mathematics Education, 11(4), 923-947.

Hsieh, F-J., Law, C-K., Shy, H-W., Wang, T-Y., Hsieh, C-J., & Tang, S-J. (2011). Mathematics teacher education quality in TEDS-M: Globalizing the views of future teachers and teacher educators. Journal of Teacher Education, 12(1), 172 - 187.

Hurrell, D. P. (2013). What teachers need to know to teach mathematics: An argument for a reconceptualized model. Australian Journal of Teacher Education, 38(11), 54-64.

Johnston, R. (2007). Dominant discourses and teacher education: Current curriculum or curriculum remembered? Asia-Pacific Journal of Teacher Education, 35(4), 351-365.

Jonassen, D., Howland, J., Marra, R., & Crismond, D. (2008). Meaningful learning with technology (3rd ed.). Upper Sandle River, NJ: Pearson.

Jonker, L. (2008). A mathematics course for prospective elementary school teachers. Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 18(4), 325-336.

Ketterlin-Geller, L., & Yovanoff, P. (2009). Diagnostic assessments in mathematics to support instructional decision making. Practical Assessment, Research, & Evaluation, 14(16).

Kotsopoulos, D., Morselli, F., & Purdy, L. (2011). The impact of mathematics teacher education research on pre-service teacher education. In Wiest, L. R., & Lamberg, T. (Eds.). proceedings of the 33rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1424-1431). Reno, NV: University of Nevada, Reno.

Lerman, S. (2014). (Ed.), Encyclopedia of Mathematics Education (pp. 295-299). Dordrecht, Netherlands: Springer.

Lin, J. M-C. (2008). ICT education: To integrate or not to integrate? British Journal of Educational Technology, 39(6), 1121-1123.

Little, M.E. (2009). Teaching mathematics: Issues and solutions. Teaching Exceptional Children Plus, 6(1).

Matejka, K., & Kurke, L. B. (1994). Designing a great syllabus. College Teaching, 42(3), 115-117.

McDonnough, J. T., & Matkins, J. J. (2010). The role of field experience in elementary preservice teachers' self-efficacy and ability to connect research to practice. School Science & Mathematics, 110(1), 13-23.

Mistretta, R. M. (2005). Integrating technology into the mathematics classroom: The role of teacher preparation programs. Journal of The Mathematics Educator, 15(1), 18–24.

Monoranjan, B. (2015). Constructivism approach in mathematics teaching and assessment of mathematical understanding. Basic Research Journal of Education Research and Review, 4(1), 8-12.

Monroe, E. E. (1984). The development of a mathematics methods course from pre-service elementary teachers: some considerations. Technical Report. Western Kentucky University.

NCATE. (2008). Professional standards for the accreditation of teacher preparation institutions [Electronic Version]. National Council for Accreditation of Teacher Education (NCATE). Retrieved June 11, 2019, from

NCTM. (2012). Council of the Accreditation of Educator Preparation (CAEP) Standards for Mathematics Teacher Preparations. Reston, VA: NCTM.

NCTM. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics (NCTM). Reston, VA: NCTM.

Niess, M. L. (2001). A model for integrating technology in preservice science and mathematics content-specific teacher preparation. School Science & Mathematics, 101(2), 102-110.

Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. In J. F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 257-315). Charlotte, NC: Information Age.

Picha, G. (2018). Effective technology use in math class: Ensuring that the technology we bring into math classes fosters active engagement is key. Edutopia.Retrieved July 23, 2020, from

Post, G. & Varoz, S. (2008). Lesson-study groups with prospective and practicing teachers. Teaching Children Mathematics, 14(8), 472-478.

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.

Sinay, E., & Nahornick, A. (2016). Teaching and learning mathematics research series l: Effective instructional strategies. (Research Report No. 16/17-08). Toronto, Ontario, Canada: Toronto District School Board.

Skovsmose, O. (1990). Mathematical education and democracy. Educational Studies in Mathematics, 21, 109-128.

Sleeter, C. E. (2001). Epistemological diversity in research on preservice teacher preparation for historically underserved children. In W. G. Secada (Ed.), Review of Research in Education 25, 2000-2001 (pp. 209-250). Washington, D.C.: American Educational Research Association.

Stigler, J., & Hiebert, J. (1999). The Teaching Gap. New York: The Free Press.

Sturdivant, R., Dunham, P., & Jardine, R. (2009). Preparing mathematics teachers for technology-rich environments. PRIMUS, 19, 161 - 173. DOI:10.1080/10511970802409180

Stylianides, G. J., & Stylianides, A. J. (2009). Mathematics for teaching: A form of applied mathematics. Teaching and Teacher Education, 26(2), 161-172.

Tatto, M. T. (2013). The Teacher Education and development study in mathematics (TEDS-M): policy, practice, and readiness to teach primary and secondary mathematics in 17 countries. Technical Report. Amsterdam: International Association for the Evaluation of Student Achievement.

Tatto, M. T., Lerman, S. & Novotna, J. (2010). The organization of the mathematics preparation and development of teachers: a report from the ICMI Study 15. Journal of Mathematics Teacher Education, 13(4), 313–324.

Tatto, M. T., & Senk, S. (2011). The mathematics education of future primary and secondary teachers: Methods and findings from the teacher education and development study in mathematics. Journal of Teacher Education, 62(2),121-137.

Tatto, M. T., Rodriguez, M., Ingvarson, L., Rowley, G., Maeda, Y., & Byun, S-Y, (2013). Development of the TEDS-M survey questionnaires. In M. T. Tatto (Ed.), The Teacher Education and Development Study in Mathematics (TEDS-M): policy, practice, and readiness to teach primary and secondary mathematics in 17 countries (pp. 47-70). IEA technical report. Netherlands: Amsterdam.

Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grows (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 127-146). New York: Macmillan.

Tsafos, V. (2010). Developing a practice-theory model in pre-service teacher education in Greece. Action Research, 8(2), 153-170.

Tsai, P. S., & Tsai, C. C. (2019). Preservice teachers' conceptions of teaching using mobile devices and the quality of technology integration in lesson plans. British Journal of Educational Technology, 50(2), 614-625.

Wang, T., & Tang, S. (2013). Profiles of opportunities to learn for TEDS-M future secondary mathematics teachers. International Journal of Science and Mathematics Education, 11(4), 847 - 877.

Watson, A., & Sullivan, P. (2008). Teachers learning about tasks and lessons. In D. Tirosh & T. Wood (Eds.), The international handbook of mathematics teacher education (Vol. 2: Tools and processes in mathematics teacher education, pp. 109-134). AW Rotterdam, The Netherlands: Sense Publishers.

Xiao, L., & Carroll, J. M. (2007). Fostering an informal learning community of computer technologies at school. Behavior & Information Technology, 26(1), 23-36.

Xu, Y. T., & Liu, Y. C. (2009). Teacher assessment knowledge and practice: A narrative inquiry of a Chinese college EFL teacher's experience. Tesol Quarterly, 43(3), 493-513.

Zaslavsky, O. (2007). Mathematics-related tasks, teacher education, and teacher educators. The dynamics associated with tasks in mathematics teacher education. Journal of Mathematics Teacher Education, 10(4-6), 433-440.