Vol. 30 No. 1 (2021)

A Discussion of Programmatic Differences within Mathematics Content Courses for Prospective Elementary Teachers

Tuyin An
Georgia Southern University
Daniel Clark
Western Kentucky University
Hwa Young Lee
Texas State University
Emily K Miller
West Chester University
Travis Weiland
Appalachian State University

Published 2021-08-17


  • pre-service teachers,
  • program design


Prospective elementary teacher (PSET) education programs vary greatly in the courses and course sequences employed to prepare their students. This article explores potential tradeoffs that arise for mathematics teacher educators, PSETs, and their future students due to the choices PSET education programs make regarding their design. Specifically, the sequencing of content and pedagogy across courses, integration of content and pedagogy within courses, content coverage, mathematical rigor, and interactions between PSETs’ beliefs and experiences are explored from the perspective of mathematics teacher educators using vignettes. Based on the vignettes and literature, future directions for research regarding PSET education program design are suggested.


  1. Association of Mathematics Teacher Educators. (2017). Standards for preparing teachers of mathematics. http://www.amte.net/standards
  2. 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.
  3. Boaler, J. (with Dweck, C.). (2016). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. Jossey-Bass.
  4. Common Core State Standards Initiative. (n.d.). Key shifts in mathematics. http://www.corestandards.org/other-resources/key-shifts-in-mathematics/
  5. Common Core State Standards Initiative. (2010). Common core state standards for mathematics. http://www.corestandards.org/wp-content/uploads/Math_Standards1.pdf
  6. Conference Board of the Mathematical Sciences. (2012). The mathematical education of teachers II (Vol. 17). American Mathematical Society. https://doi.org/10.1090/cbmath/017
  7. Goertz, M. E. (2010). National standards: Lessons from the past, directions for the future. In B. Reys, R. Reys, & R. Rheta (Eds.), Mathematics Curriculum: Issues, Trends, and Future Direction, 72nd Yearbook (pp. 51–64). National Council of Teachers of Mathematics.
  8. Gojak, L. M. (2013, February 5). What’s all this talk about rigor? National Council of Teachers of Mathematics. https://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Linda-M_-Gojak/What_s-All-This-Talk-about-Rigor_/
  9. Gomez, C. N. (2018). Identity work of a prospective teacher: An argumentation perspective on identity. Mathematics Teacher Education and Development, 20(1), 43–61.
  10. Greenberg, J., & Walsh, K. (2008). No common denominator: The preparation of elementary teachers in mathematics by America’s education schools. National Council on Teacher Quality. https://www.nctq.org/publications/No-Common-Denominator:-The-Preparation-of-Elementary-Teachers-in-Mathematics-by-Americas-Education-Schools
  11. Hanna, G. (2007). The ongoing value of proof. In P. Boero (Ed.), Theorems in school: From history, epistemology and cognition to classroom practice (pp. 3–18). Sense Publishers.
  12. Harel, G. (2008). What is mathematics? A pedagogical answer to a philosophical question. In B. Gold & R. A. Simons (Eds.), Proof and other dilemmas: Mathematics and philosophy (pp. 265–290). Mathematical Association of America.
  13. Hart, L. C. (2002). Preservice teachers’ beliefs and practice after participating in an integrated content/pedagogy course. School Science and Mathematics, 102(1), 4–14.
  14. Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for Research in Mathematics Education, 21(1), 33–46. http://dx.doi.org/10.5951/jresematheduc.21.1.0033
  15. Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (Vol. 1, pp. 371–404). Information Age Publishing.
  16. 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.
  17. Hodgen, J., & Askew, M. (2007). Emotion, identity and teacher learning: Becoming a primary mathematics teacher. Oxford Review of Education, 33(4), 469–487. https://doi.org/10.1080/03054980701451090
  18. Hodgson, B. R. (2001). The mathematical education of school teachers: Role and responsibilities of university mathematicians. In D. Holton, M. Artigue, U. Kirchgräber, J. Hillel, M. Niss, & A. Schoenfeld (Eds.), The teaching and learning of mathematics at university level (New ICMI Study Series, Vol. 7, pp. 501–518). Springer, Dordrecht. http://dx.doi.org/10.1007/0-306-47231-7_43
  19. Howson, G., Keitel, C., & Kilpatrick, J. (1981). Curriculum development in mathematics. Cambridge University Press.
  20. Kitcher, P. (1984). The nature of mathematical knowledge. Oxford University Press.
  21. Kutaka, T. S., Smith, W. M., Albano, A. D., Edwards, C. P., Ren, L., Beattie, H. L., Lewis, W. J., Heaton, R. M., & Stroup, W. W. (2017). Connecting teacher professional development and student mathematics achievement: A 4-year study of an elementary mathematics specialist program. Journal of Teacher Education, 68(2), 140–154. https://doi.org/10.1177/0022487116687551
  22. Lakatos, I. (1976). Proofs and refutations: The logic of mathematical discovery. Cambridge University Press. http://dx.doi.org/10.1017/CBO9781139171472
  23. Loewenberg Ball, D., Hoover Thames, M., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407. http://dx.doi.org/10.1177/0022487108324554
  24. Masingila, J. O., Olanoff, D. E., & Kwaka, D. K. (2012). Who teaches mathematics content courses for prospective elementary teachers in the United States? Results of a national survey. Journal of Mathematics Teacher Education, 15(5), 347–358. http://dx.doi.org/10.1007/s10857-012-9215-2
  25. Matthews, M. E., & Seaman, W. I. (2007). The effects of different undergraduate mathematics courses on the content knowledge and attitude towards mathematics of preservice elementary teachers. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1, 1–16.
  26. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. https://www.nctm.org/standards/
  27. National Council of Teachers of Mathematics. (2012). NCTM CAEP mathematics content for elementary mathematics specialist: Addendum to the NCTM CAEP standards 2012. https://www.nctm.org/uploadedFiles/Standards_and_Positions/CAEP_Standards/NCTM%20CAEP%20Standards%202012%20Mathematics%20Content%20-%20Elementary%20Mathematics%20Specialist.pdf
  28. National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all.
  29. National Research Council. (2001). Adding it up: Helping children learn mathematics. The National Academies Press. https://doi.org/10.17226/9822
  30. Peace, H., Quebec Fuentes, S., & Bloom, M. (2018). Preservice teachers’ transforming perceptions of science and mathematics teacher knowledge. International Journal of Educational Methodology, 4(4), 227–241. https://doi.org/10.12973/ijem.4.4.227
  31. Philipp, R. A., Ambrose, R., Lamb, L. L. C., Sowder, J. T., Schappelle, B. P., Sowder, L., Thanheiser, E., & Chauvot, J. (2007). Effects of early field experiences on the mathematical content knowledge and beliefs of prospective elementary school teachers: An experimental study. Journal for Research in Mathematics Education, 38(5), 438–476.
  32. Schmidt, W. H., & McKnight, C. C. (2012). Inequality for all: The challenge of unequal opportunity in American schools. Teachers College Press.
  33. Schmidt, W. H., Wang, H. C., & McKnight, C. C. (2005). Curriculum coherence: An examination of US mathematics and science content standards from an international perspective. Journal of Curriculum Studies, 37(5), 525–559. http://dx.doi.org/10.1080/0022027042000294682
  34. Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114–145. https://doi.org/10.2307/749205
  35. Sosina, V. E. (2020). How does context matter? Segregation, inequality, and disparities in K-12 education (Publication No. 28103866) [Doctoral dissertation, Stanford University]. ProQuest Dissertations Publishing.
  36. Wittmann, E. C. (2020). When is a proof a proof? In E. C. Wittmann (Ed.). Connecting mathematics and mathematics education (pp. 61–76). Springer.