The Mathematical Education of Secondary Teachers

  • Maria Teresa TattoEmail author


This chapter explores the influence of pre-service teacher education on future secondary teachers’ mathematical knowledge for teaching across several of the countries/regions that participated in the Teacher Education and Development Study in Mathematics (TEDS-M) including Chile, Chinese Taipei, Germany, Malaysia, the Philippines, Poland, the Russian Federation, Singapore, Switzerland, and Thailand, and paying particular attention to the situation in the United States of America. This chapter uses survey and knowledge assessment data collected by TEDS-M from representative samples of teacher education programs and their future secondary teachers across these countries/regions. Multilevel analyses show wide variability in the knowledge for teaching mathematics future secondary teachers attain. Previous mathematics knowledge as a requirement for entry into teacher education and mathematics-rich opportunities to learn were associated with higher and deeper levels of mathematical and mathematical pedagogical knowledge, after controlling for individual characteristics. Beliefs espousing traditional orientations to learning mathematics were associated with lower levels of performance in the knowledge assessments. The discussion highlights the importance of self-study and self-regulation in teacher education.


  1. Adler, J. (2017). Mathematics in mathematics education. South African Journal of Science, 113(3/4). Retrieved from
  2. Association of Mathematics Teacher Educators (AMTE). (2015). Position: Equity in mathematics teacher education. Retrieved from
  3. Association of Mathematics Teacher Educators (AMTE). (2017). Standards for preparing teachers of mathematics. Retrieved from
  4. Ball, D. L. (1991). Research on teaching mathematics: Making subject matter knowledge part of the equation. In J. Brophy (Ed.), Advances in research on teaching, Volume 2: Teachers knowledge of subject matter as it relates to their teaching practice (pp. 1–48). Greenwich, CT: JAI Press.Google Scholar
  5. Ball, D.L. (Chair). (2003). Mathematical proficiency for all students: Toward a strategic research and development program in mathematics education, RAND mathematics study panel. Washington, DC.: U.S. Department of Education’s Office of Educational Research and Improvement Retrieved from
  6. 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.Google Scholar
  7. Ball, D. L., & Bass, H. (2003). Toward a practice-based theory of mathematical knowledge for teaching. In B. Davis & E. Simmt (Eds.), Proceedings of the 2002 annual meeting of the Canadian Mathematics Education Study Group (pp. 3–14). Edmonton, AB: CMESG/GDEDM.Google Scholar
  8. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389–407.CrossRefGoogle Scholar
  9. Bartell, T. G. (2013). Learning to teach mathematics for social justice: Negotiating social justice and mathematical goals. Journal for Research in Mathematics Education, 44(1), 129–163.CrossRefGoogle Scholar
  10. Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., et al. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133–180. Scholar
  11. Beswick, K. (2007). Teachers’ beliefs that matter in secondary mathematics classrooms. Educational Studies in Mathematics, 65(1), 95–120.CrossRefGoogle Scholar
  12. Beswick, K. (2009). School mathematics and mathematicians’ mathematics: Teachers’ beliefs about the nature of mathematics. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33 rd annual conference of the international group for the psychology of mathematics education (Vol. 2, pp. 153–160). Thessaloniki, Greece: IGPME.Google Scholar
  13. Boaler, J. (2002). Experiencing school mathematics: Traditional and reform approaches to teaching and their impact on student learning. Mahwah, NJ: Erlbaum.Google Scholar
  14. Bollen, K. A. (1989). A new incremental fit index for general structural equation models. Sociological Methods Research, 17(3), 303–316.CrossRefGoogle Scholar
  15. Boyd, D., Grossman, P. L., Lankford, H., Loeb, S., & Wyckoff, J. (2009). Teacher preparation and student achievement. Educational Evaluation and Policy Analysis, 31(4), 416–440.CrossRefGoogle Scholar
  16. Brese, F., & Tatto, M. T. (Eds.) (2012). User guide for the TEDS-M international database. Amsterdam, The Netherlands: International Association for the Evaluation of Educational Achievement (IEA).Google Scholar
  17. Carr, P. G. (2016). Highlights from TIMSS and TIMSS advanced 2015 (the Commissioner’s presentation). National Center for Education Statistics. Washinton, DC: Institute of Education Sciences. Retrieved from
  18. Casey, C., & Childs, R. (2011). Teacher education admission criteria as measure of preparedness for teaching. Canadian Journal of Education, 34(2), 3–20.Google Scholar
  19. Clift, R. T., & Brady, P. (2005). Research on methods courses and field experiences. In M. Cochran-Smith & K. Zeichner (Eds.), Studying teacher education: the report of the AERA panel on research and teacher education (pp. 309–424). Washington, DC: American Educational Research Association.Google Scholar
  20. Clotfelter, C. T., Ladd, H., & Vigdor, J. (2007). Teacher credentials and student achievement in high school: A cross-subject analysis with student fixed effects (CALDER Working Paper 11). Washington, DC: The Urban Institute.Google Scholar
  21. Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2002). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). New York, NY: Routledge.Google Scholar
  22. Common Core State Standards Initiative (CCSS-M). (2010). Common core state standards for mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.Google Scholar
  23. Constantine, J., Player, D., Silva, T., Hallgren, K., Grider, M., & Deke, J. (2009). An evaluation of teachers trained through different routes to certification, final report. (NCEE 2009–4043). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education..Google Scholar
  24. Croninger, R. G., Rice, J. K., Rathbun, A., & Nishio, M. (2007). Teacher qualifications and early learning: Effects of certification, degree, and experience on first-grade student achievement. Economics of Education Review, 26(3), 312–324.CrossRefGoogle Scholar
  25. Crowe, E. (2010). Measuring what matters: A stronger accountability model for teachers. Washington, DC: Center for American Progress.Google Scholar
  26. Darling-Hammond, L. (2000). Teacher quality and student achievement: A review of state policy evidence. Educational Policy Analysis Archives, 8(1).Google Scholar
  27. Darling-Hammond, L. (2013, June 18). Why the NCTQ teacher prep ratings are nonsense. Washington Post. Retrieved from
  28. Darling-Hammond, L., & Bransford, J. (Eds.). (2005). Preparing teachers for a changing world: What teachers should learn and be able to do. San Francisco, CA: Jossey-Bass.Google Scholar
  29. De Ayala, R. J. (2009). The theory and practice of item response theory. New York, NY: The Guilford Press.Google Scholar
  30. De Corte, E., Op’t Eynde, P., & Verschaffel, L. (2002). Knowing what to believe. In B. K. Hofer & P. R. Pintrich (Eds.), Personal epistemology: The psychology of beliefs about knowledge and knowing. Mahwah, NJ: Erlbaum.Google Scholar
  31. DOE (Department of Education). (2014). Teacher education issues. Proposed rule. Federal Register, 79, 232. Retrieved from
  32. Ferrini-Mundy, J., & Findell, B. (2000, October). The mathematical education of prospective teachers of secondary school mathematics: Old assumptions, new challenges. Paper prepared for the Mathematical Association of America Committee on the Undergraduate Program in Mathematics. Retrieved from
  33. Feuer, M. J., Floden, R. E., Chudowsky, N., & Ahn, J. (2013). Evaluation of teacher preparation programs: Purposes, methods, and policy options. Washington, DC: National Academy of Education Retrieved from Scholar
  34. Floden, R. E. (2012). Teacher value added as a measure of program quality: Interpret with caution. Journal of Teacher Education, 63(5), 356–360.CrossRefGoogle Scholar
  35. Floden, R., & Meniketti, M. (2005). Research on the effects of coursework in the arts and sciences and in the foundations of education. In M. Cochran-Smith & K. Zeichner (Eds.), Studying teacher education: the report of the AERA panel on research and teacher education (pp. 261–308). Washington, DC: American Educational Research Association.Google Scholar
  36. Floden, R. E., McDiarmid, G. W., & Jennings, N. (1996). Learning about mathematics in elementary methods courses. In D. J. McIntyre & D. M. Byrd (Eds.), Preparing tomorrow’s teachers: The field experience. Teacher education yearbook IV (pp. 225–241). Thousand Oaks, CA: Corwin.Google Scholar
  37. Goe, L. (2007). The link between teacher quality and student outcomes: A research synthesis. Washington, DC: National Comprehensive Center for Teacher Quality Retrieved from Scholar
  38. Goldhaber, D. D., & Brewer, D. J. (2000). Does teacher certification matter? High school certification status and student achievement. Educational Evaluation and Policy Analysis, 22, 129–146.CrossRefGoogle Scholar
  39. Goldhaber, D., Liddle, S., & Theobald, R. (2013). The gateway to the profession: Assessing teacher preparation programs based on student achievement. Economics of Education Review, 34, 29–44.CrossRefGoogle Scholar
  40. Graham, K. J., Portnoy, N., & Grundmeier, T. (2002). Making mathematical connections in programs for prospective teachers. Proceedings of the twenty-fourth annual meeting of the North American chapter of the international group for the psychology of mathematics education (Vol. 4), 1930–1932.Google Scholar
  41. Grossman, P., Hammerness, K., & McDonald, M. (2009). Redefining teacher: Re-imagining teacher education. Teachers and Teaching: Theory and Practice, 15(2), 273–290.CrossRefGoogle Scholar
  42. Handal, B. (2003). Teachers’ mathematical beliefs: A review. The Mathematics Educator, 13(2), 47–57.Google Scholar
  43. Hawkins, E. F., Stancavage, F. B., & Dossey, J. A. (1998). School policies and practices affecting instruction in mathematics (NCES 98–495). Washington, DC: National Center for Education Statistics Retrieved from Scholar
  44. Heafner, T., McIntyre, E., & Spooner, M. (2014). The CAEP standards and research on educator preparation programs: Linking clinical partnerships with program impact. Peabody Journal of Education, 89(4), 516–532.CrossRefGoogle Scholar
  45. Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.CrossRefGoogle Scholar
  46. Hill, H. C., Sleep, L., Lewis, J. M., & Ball, D. L. (2007). Assessing teachers’ mathematical knowledge: What matters and what evidence counts? In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning. Charlotte, NC: Information Age.Google Scholar
  47. Hill, H., Ball, D. L., & Schilling, S. G. (2009). Unpacking pedagogical content knowledge: Conceptualizing and measuring Teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400.Google Scholar
  48. Hu, L.-t., & Bentler, P. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1–55.CrossRefGoogle Scholar
  49. Ingvarson, L., Schwille, J., Tatto, M. T., Rowley, G., Peck, R., & Senk, S. (2013). An analysis of teacher education context, structure, and quality assurance arrangements in TEDS-M countries. Amsterdam, The Netherlands: International Association for the Evaluation of Educational Achievement.Google Scholar
  50. Kaplan, L., & Owings, W. A. (2001). Teacher quality and student achievement: Recommendations for principals. NASSP Bulletin, 85(628), 64–73.CrossRefGoogle Scholar
  51. Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. National Research Council, Mathematics Learning Study Committee. Washington, DC: National Academy Press. Retrieved from
  52. Krauss, S., Brunner, M., Kunter, M., Baumert, J., Blum, W., Neubrand, M., & Jordan, A. (2008). Pedagogical content knowledge and content knowledge of secondary mathematics teachers. Journal of Educational Psychology, 100(3), 716–725. Scholar
  53. Langrall, C. W., & Mooney, E. S. (2002). The development of a framework characterizing middle school students’ statistical thinking. Retrieved from
  54. Lerman, S. (2000). The social turn in mathematics education research. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 19–44). Westport, CT: Ablex Publishing.Google Scholar
  55. Levine, A. (2006). Educating school teachers. Retrieved from
  56. Lewis, L., Basmat, P., Carey, N., Bartfai, N., Farris, E., & Smerdon, B. (1999). Teacher quality: A report on the preparation and qualifications of public school teachers. Washington, DC: U.S. Department of Education, National Center for Education Statistics (NCES 1999-080).Google Scholar
  57. Marsh, H. W., Balla, J. R., & McDonald, R. P. (1988). Goodness-of-fit indices in confirmatory factor analysis: The effect of sample size. Psychological Bulletin, 102, 391–410.CrossRefGoogle Scholar
  58. Mazzeo, J., Lazer, S., & Zieky, M. J. (2006). Monitoring educational progress with group-score assessments. In R. L. Brennan (Ed.), Educational measurement (4th ed.). Westport, CT: Praeger.Google Scholar
  59. McCleod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning. Macmillan: New York, NY.Google Scholar
  60. Mewborn, D. S. (2000, April). Changing actions vs. changing beliefs: What is the goal of mathematics teacher education. Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans, LA.Google Scholar
  61. Meyer, J. P. (2011). jMetrik (Version 2.1) Computer software. Charlottesville, VA: University of Virginia Retrieved from
  62. Mikitovicsa, A., & Crehanb, K. D. (2002). Pre-professional skills test scores as college of education admission criteria. Journal of Educational Research, 95(4), 215–223.CrossRefGoogle Scholar
  63. Monk, D. H. (1994). Subject area preparation of secondary mathematics and science teachers and student achievement. Economics of Education Review, 13, 125–145.CrossRefGoogle Scholar
  64. Monk, D. H., & King, J. (1994). Multi-level teacher resource effects on pupil performance in secondary mathematics and science: The role of teacher subject matter preparation. In R. Ehrenberg (Ed.), Contemporary policy issues: Choices and consequences in education (pp. 29–58). Ithaca, NY: ILR Press.Google Scholar
  65. Mullens, J. E., Murnane, R. J., & Willett, J. B. (1996). The contribution of training and subject matter knowledge to teaching effectiveness: A multilevel analysis of longitudinal evidence from belize. Comparative Education Review, 40(2), 139–157.CrossRefGoogle Scholar
  66. Nardi, P. M. (2006). Interpreting data. Boston, MA: Pearson.Google Scholar
  67. National Commission on Mathematics and Science Teaching for the 21st Century. (2000). Before it’s too late: A report to the nation. Retrieved from
  68. National Council for Teacher Quality. (2013). Teacher prep review: A review of the nation’s teacher preparation programs. Retrieved from
  69. National Council of Teachers of Mathematics (NCTM). (2014). Principles to actions. Reston, VA: NCTM.Google Scholar
  70. NCSM & TODOS. (n.d.). Mathematics education through the lens of social justice. Retrieved from
  71. Provasnik, S., Kastberg, D., Ferraro, D., Lemanski, N., Roey, S., & Jenkins, F. (2012). Highlights from TIMSS 2011: Mathematics and science achievement of U.S. fourth- and eighth-grade students in an international context (NCES 2013-009). Washington, DC: National Center for Education Statistics, Institute of Education Sciences, U.S. Department of Education Retrieved from Scholar
  72. RAND Mathematics Study Panel. (2003). Mathematical proficiency for all students: Toward a strategic research and development program in mathematics education. RAND Mathematics Study Panel, Deborah Loewenberg Ball, Chair. Retrieved from
  73. Raudenbush Stephen, W., Bryk, A. S., Cheong, Y. F., & Congdon, R. (2004). HLM 6: Hierarchical Linear Modeling. Chicago, IL: Scientific Software International.Google Scholar
  74. Rowan, B., Correnti, R., & Miller, R. J. (2002, November). What large-scale, survey research tells us about teacher effects on student achievement: Insights from the prospects study of elementary schools. Philadelphia, PA: Consortium for Policy Research in Education, University of Pennsylvania.Google Scholar
  75. Rowland, T. (2012). Contrasting knowledge for elementary and secondary mathematics teaching. For the Learning of Mathematics, 32(1), 16–21.Google Scholar
  76. Rowland, T. & Turner, F. (2008). How shall we talk about ‘subject knowledge’ for mathematics teaching? In M. Joubert (Ed.) Proceedings of the British Society for Research into Learning Mathematics, 28(2), 91–96.Google Scholar
  77. Sawchuk, S. (2016, January 6). Law could spur changes in teacher requirements. Education Week, 35 (15), pp. 14–15.Google Scholar
  78. Schmidt, W. H., & Buchmann, M. (1983). Six teachers’ beliefs and attitudes and their curricular time allocations. The Elementary School Journal, 84(2), 162–172.CrossRefGoogle Scholar
  79. Speer, N., & King, K. (2009). Examining mathematical knowledge for teaching in secondary and post-secondary contexts. Retrieved from
  80. Staub, F. C., & Stern, E. (2002). The nature of teachers’ pedagogical content beliefs matters for students’ achievement gains: Quasi-experimental evidence from elementary mathematics. Journal of Educational Psychology, 94(2), 344–355.CrossRefGoogle Scholar
  81. Tatto, M. T. (1996). Examining values and beliefs about teaching diverse students: Understanding the challenges for teacher education. Educational Evaluation and Policy Analysis, 18, 155–180.CrossRefGoogle Scholar
  82. Tatto, M. T. (1998). The influence of teacher education on teachers’ beliefs about purposes of education, roles and practice. Journal of Teacher Education, 49, 66–77.CrossRefGoogle Scholar
  83. Tatto, M. T. (1999). The socializing influence of normative cohesive teacher education on teachers’ beliefs about instructional choice. Teachers and Teaching, 5, 111–134.CrossRefGoogle Scholar
  84. Tatto, M. T. (2011). Reimagining the education of teachers: The role of comparative and international research. Comparative Education Review, 55, 495–516.CrossRefGoogle Scholar
  85. Tatto, M. T. (Ed.). (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, The Netherlands: International Association for the Evaluation of Student Achievement.Google Scholar
  86. Tatto, M. T. & Hordern, J. (2017). The configuration of teacher education as a professional field of practice: A comparative study of mathematics education. In J. Furlong & G. Whitty (eds.), Knowledge and the study of education: An international exploration (pp. 255–274). Oxford, UK: Oxford Comparative Education Series, Symposium Books.Google Scholar
  87. Tatto, M. T., & Kularatna, N. G. (1993). The interpersonal dimension of teacher education: Comparing distance education with two other programs in Sri Lanka. International Journal of Educational Research, 19, 755–778.CrossRefGoogle Scholar
  88. Tatto, M. T., Nielsen, H. D., Cummings, W. C., Kularatna, N. G., & Dharmadasa, D. H. (1993). Comparing the effectiveness and costs of different approaches for educating primary school teachers in Sri Lanka. Teaching and Teacher Education, 9, 41–64.CrossRefGoogle Scholar
  89. Tatto, M. T., Schwille, J., Senk, S., Ingvarson, L., Peck, R., & Rowley, G. (2008). Teacher Education and Development Study in Mathematics (TEDS-M): Conceptual framework. Teacher Education and Development International Study Center, Michigan State University, East Lansing, MI, and IEA.Google Scholar
  90. Tatto, M. T., Schwille, J., Senk, S. L., Ingvarson, L., Rowley, G., Peck, R., … Reckase, M. (2012). Policy, practice, and readiness to teach primary and secondary mathematics in 17 countries. Findings from the IEA Teacher Education and Development Study in Mathematics (TEDS-M). Amsterdam, The Netherlands: International Association for the Evaluation of Student Achievement.Google Scholar
  91. Thomas, A. M., & Loadman, W. E. (2001). Evaluating teacher education programs using a national survey. The Journal of Educational Research, 94(4), 195–206.CrossRefGoogle Scholar
  92. Turner, E. E., Drake, C., Roth McDuffie, A., Aguirre, J. M., Bartell, T. G., & Foote, M. Q. (2012). Promoting equity in mathematics teacher preparation: A framework for advancing teacher learning of children’s multiple mathematics knowledge bases. Journal of Mathematics Teacher Education, 15(1), 67–82.CrossRefGoogle Scholar
  93. Usiskin, Z., Peressini, A., Marchisotto, E. A., & Stanley, D. (2003). Mathematics for high school teachers: An advanced perspective. Upper Saddle River, NJ: Prentice Hall.Google Scholar
  94. Van Dooren, W., Verschaffel, L., & Onghena, P. (2002). The impact of pre-service teachers’ content knowledge on their evaluation of students’ strategies for solving arithmetic and algebra word problems. Journal for Research in Mathematics Education, 33(5), 319–351.CrossRefGoogle Scholar
  95. Venkat, H., & Spaull, N. (2015). What do we know about primary teachers’ mathematical content knowledge in South Africa? An analysis of SACMEQ 2007. International Journal of Educational Development, 41, 121–130. Scholar
  96. Wayne, A. J., & Youngs, P. (2003). Teacher characteristics and student achievement gains: A review. Review of Educational Research, 73(1), 89–122.CrossRefGoogle Scholar
  97. Wu, M., Ray, A., Wilson, M., & Haldane, S. (2007). ACER conquest: Generalised item response modelling software (Version 2.0). Melbourne, VIC: ACER.Google Scholar
  98. Zeichner, K., & Conklin, H. (2005). Teacher education programs. In M. Cochran-Smith & K. Zeichner (Eds.), Studying teacher preparation: Report of the AERA Panel on Research and Teacher Education (pp. 645–735). Mahwah, NJ: Lawrence Erlbaum.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mary Lou Fulton Teachers CollegeArizona State UniversityTempeUSA

Personalised recommendations