Skip to main content

What Do Mathematics Teacher Educators Need to Know? Reflections Emerging from the Content of Mathematics Teacher Education

  • Chapter
  • First Online:
The Learning and Development of Mathematics Teacher Educators

Abstract

Mathematics teacher educators’ knowledge plays a central role in mathematics teacher education. Assuming the seminal orientations of Shulman’s work, as well as the last decades of discussion and research on the content of mathematics teacher education, we present a discussion of several domains of mathematics teacher educators’ knowledge. We start discussing the differences between the knowledge of teachers and MTEs, focusing on mathematical knowledge and pedagogical knowledge related to mathematics. We continue highlighting the complexity of the knowledge required for MTEs in order to foster the development of mathematics teaching practices and skills, as well as the knowledge needed to contribute to the building of a professional identity by (prospective) teachers. The prior elements conform to the content knowledge of the MTE, allowing us to elaborate on the elements that integrate MTEs’ pedagogical content knowledge. We finish sharing some reflections about different profiles of teacher educators related to their knowledge.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    This framework elaborates on Shulman’s (1986) and Ball et al.’s (2008) conceptualisations of teacher knowledge, proposing an intrinsic approach towards specialisation (Scheiner, Montes, Godino, Carrillo, & Pino-Fan, 2019). Carrillo et al.’s (2018) framework proposes a structuration of content knowledge in three subdomains – knowledge of topics, knowledge of the structure of mathematics and knowledge of the practice of mathematics – and PCK in another three subdomains, knowledge of mathematics teaching, knowledge of the features of the learning of mathematics and knowledge of mathematics learning standards.

References

  • Abell, S. K., Rogers, M. A. P., Hanuscin, D. L., Lee, M. H., & Gagnon, M. J. (2009). Preparing the next generation of science teacher educators: A model for developing PCK for teaching science teachers. Journal of Science Teacher Education, 20(1), 77–93.

    Article  Google Scholar 

  • Ball, D. L. (2017). Uncovering the special mathematical work of teaching. In G. Kaiser (Ed.), Proceedings from the 13th international congress of mathematics education (pp. 11–34). New York, NY: Springer.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Beswick, K., & Chapman, O. (2012). Mathematics teacher educators’ knowledge for teaching. In Paper presented at the12th international congress on mathematics education. Coex, Seoul: Korea.

    Google Scholar 

  • Beswick, K., & Chapman, O. (2013). Mathematics teacher educators’ knowledge. In A. M. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th conference of the international group for the psychology of mathematics education (p. 215). Kiel, Germany: PME.

    Google Scholar 

  • Carrillo, J., & Climent, N. (2011). The development of teachers’ expertise through their analyses of good practice in the mathematics classroom. ZDM Mathematics Education, 43(6–7), 915–926.

    Article  Google Scholar 

  • Carrillo, J., Climent, N., Montes, M., Contreras, L. C., Flores-Medrano, E., Escudero-Ávila, D., et al. (2018). The Mathematics Teacher’s Specialised Knowledge (MTSK) model. Research in Mathematics Education, 20(3), 236–253.

    Article  Google Scholar 

  • Coles, A. (2014). Mathematics teachers learning with video: The role, for the didactician, of a heightened listening. ZDM Mathematics Education, 46(2), 267–278.

    Article  Google Scholar 

  • Cooney, T. J., & Krainer, K. (1996). Inservice mathematics teacher education: The importance of listening. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 1155–1185). Dordrecht, The Netherlands: Kluwer Academic Publishers.

    Google Scholar 

  • Depaepe, F., Verschaffel, L., & Kelchtermans, G. (2013). Pedagogical content knowledge: A systematic review of the way in which the concept has pervaded mathematics educational research. Teaching and Teacher Education, 34, 12–25.

    Article  Google Scholar 

  • Douek, N. (2007). Some remarks about argumentation and proof. In P. Boero (Ed.), Theorems in school: From history, epistemology and cognition to classroom practice (pp. 163–181). Rotterdam, The Netherlands: Sense Publishers.

    Google Scholar 

  • Ernest, P. (1998). Social constructivism as a philosophy of mathematics. New York, NY: State University of NY Press.

    Google Scholar 

  • Goos, M. (2014). Researcher–teacher relationships and models for teaching development in mathematics education. ZDM Mathematics Education, 46, 189–200.

    Article  Google Scholar 

  • Grevholm, B., Millman, R., & Clarke, B. (2009). Function, form, and focus: The role of tasks in elementary mathematics teacher education. In B. Clarke, B. Grevholm, & R. Millman (Eds.), Tasks in primary mathematics education: Purpose, use and exemplars (pp. 1–5). New York, NY: Springer.

    Google Scholar 

  • Grossman, P., Wilson, S. M., & Shulman, L. S. (1989). Teachers of substance: Subject matter knowledge for teaching. In M. C. Reynolds (Ed.), Knowledge base for the beginning teacher (pp. 23–46). Oxford: Pergamon.

    Google Scholar 

  • Halai, A. (1998). Mentor, mentee, and mathematics: A story of professional development. Journal of Mathematics Teacher Education, 1, 295–315.

    Article  Google Scholar 

  • Harel, G., & Sowder, L. (2007). Toward a comprehensive perspective on proof. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 805–842). Charlotte, NC: NCTM and IAP.

    Google Scholar 

  • Ivars, P., & Fernández, C. (2018). The role of writing narratives in developing pre-service elementary teachers’ noticing. In G. Stylianides & K. Hino (Eds.), Research advances in the mathematical education of pre-service elementary teachers (pp. 245–259). London: Springer.

    Chapter  Google Scholar 

  • Jaworski, B. (2008). Development of the mathematics teacher educator and its relation to teaching development. In B. Jaworski & T. Wood (Eds.), The mathematics teacher educator as a developing professional (The international handbook of mathematics teacher education) (Vol. 4, pp. 335–361). Rotterdam, The Netherlands: Sense Publishers.

    Google Scholar 

  • Jaworski, B., & Huang, R. (2014). Teachers and didacticians: Key stakeholders in the processes of developing mathematics teaching. ZDM Mathematics Education, 46, 173–188.

    Article  Google Scholar 

  • Kelchtermans, G. (2009). Who I am in how I teach is the message: Self-understanding, vulnerability and reflection. Teachers and Teaching: Theory and Practice, 15(2), 257–272.

    Article  Google Scholar 

  • Kessels, J., & Korthagen, F. (1996). The relationship between theory and practice. Back to the classics. Educational Researcher, 25(3), 17–22.

    Article  Google Scholar 

  • Kilpatrick, J. (2008). A higher standpoint. In ICMI proceedings: Regular lectures (pp. 26–43). Retrieved from http://www.mathunion.org/icmi/publications/icme-proceedings/materials-from-icme-11-mexico/regular-lectures/

  • Kilpatrick, J., & Spangler, D. A. (2016). Educating future mathematics education professors. In L. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (3rd ed., pp. 297–309). London: Routledge.

    Google Scholar 

  • Kumaradivelu, B. (1999). Towards a postmethod pedagogy. TESOL Quarterly, 35(4), 537–560.

    Article  Google Scholar 

  • Leikin, R., Zazkis, R., & Meller, M. (2018). Research mathematicians as teacher educators: Focusing on mathematics for secondary mathematics teachers. Journal of Mathematics Teacher Education, 21, 451–473.

    Article  Google Scholar 

  • Leinhardt, G., Smith, D. A. (1985). Expertise in mathematics instruction: Subject matter knowledge. Journal of Educational Psychology, 99, 247–271.

    Google Scholar 

  • Lloyd, G. M. (2006). Preservice teachers’ stories of mathematics classrooms: Explorations of practice through fictional accounts. Educational Studies in Mathematics, 63(1), 57–87.

    Google Scholar 

  • Lynch-Davis, K., & Rider, R. L. (2006). The work of mathematics teacher educators. Charlotte, NC: Information Age Publishing.

    Google Scholar 

  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum.

    Book  Google Scholar 

  • Masingila, J., Olanoff, D., & Kimani, P. M. (2018). Mathematical knowledge for teaching teachers: Knowledge used and developed by mathematics teacher educators in learning to teach via problem solving. Journal of Mathematics Teacher Education, 21, 429–450.

    Article  Google Scholar 

  • Mason, J. (2002). Researching your own practice. The discipline of noticing. London: Routledge-Falmer.

    Book  Google Scholar 

  • Montes, M., Ribeiro, C., Carrillo, C., & Kilpatrick, J. (2016). Understanding mathematics from a higher standpoint as a teacher: An unpacked example. In C. Csikos, A. Rausch, & J. Szitányi (Eds.), Proceedings of the 40th conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 315–322). Szeged, Hungary: PME.

    Google Scholar 

  • NCTM (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: NCTM.

    Google Scholar 

  • Olanoff, D. (2011). Mathematical knowledge for teaching teachers: The case of multiplication and division of fractions. Mathematics Dissertations. Paper 64.

    Google Scholar 

  • Palhares, P., Gomes, A., Carvalho, P., & Cebolo, V. (2009). From teacher education to teacher practice: A gap affecting the implementation of tasks. In B. Clarke, B. Grevholm, & R. Millman (Eds.), Tasks in primary mathematics teacher education (pp. 275–284). New York, NY: Springer.

    Chapter  Google Scholar 

  • Perks, P., & Prestage, S. (1994). Planning for teaching. In B. Jaworski & A. Watson (Eds.), Mentoring in mathematics teaching (pp. 65–82). London: Falmer.

    Google Scholar 

  • Ponte, J. P. (2012). Mathematics teacher education programs: Practice and research. Journal of Mathematics Teacher Education, 15(5), 343–346.

    Article  Google Scholar 

  • Rowland, T., & Turner, F. (2009). How shall we talk about ‘subject knowledge’ for mathematics teaching? In M. Joubert (Ed.), Proceedings of the British Society for Research into Learning Mathematics (Vol. 28(2), pp. 91–96). University of Southampton, United Kingdom.

    Google Scholar 

  • Sánchez, M. V., & García, M. (2004). Formadores de profesores de matemáticas. Una aproximación teórica a su conocimiento profesional. Revista de educación, 333, 481–493.

    Google Scholar 

  • Sánchez-Matamoros, G., Fernández, C., & Llinares, S. (2015). Developing pre-service teachers’ noticing of students’ understanding of the derivative concept. International Journal of Science and Mathematics Education, 13(6), 1305–1329.

    Article  Google Scholar 

  • Scheiner, T., Montes, M. A., Godino, J. D., Carrillo, J., & Pino-Fan, L. R. (2019). What makes mathematics teacher knowledge specialized? Offering alternative views. International Journal of Science and Mathematics Education, 17(1), 153–172.

    Article  Google Scholar 

  • Schön, D. (1983). The reflective practitioner: How professionals think in action. New York, NY: Basic Books.

    Google Scholar 

  • Sherin, M. G., Linsenmeier, K., & van Es, E. A. (2009). Selecting video clips to promote mathematics teachers’ discussion of student thinking. Journal of Teacher Education, 60(3), 213–230.

    Article  Google Scholar 

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

    Google Scholar 

  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–22.

    Google Scholar 

  • Simon, M., & Tzur, R. (2009). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning, 6(2), 91–104.

    Article  Google Scholar 

  • Smith, K. (2005). Teacher educators’ expertise: What do novice teachers and teacher educators say. Teaching and Teacher Education, 21, 177–192.

    Article  Google Scholar 

  • Tzur, R. (2001). Becoming a mathematics teacher-educator: Conceptualizing the terrain through self-reflective analysis. Journal of Mathematics Teacher Education, 4, 259–283.

    Article  Google Scholar 

  • Van Putten, S., Stols, G., & Howie, S. (2014). Do prospective mathematics teachers teach who they say they are? Journal of Mathematics Teacher Education, 17(4), 369–392.

    Google Scholar 

  • Wenger, E. (1998). Communities of practice: Learning, meaning, and identity. New York, NY: Cambridge University Press.

    Book  Google Scholar 

  • Wu, H. (2011). The mis-education of mathematics teachers. Notices of the AMS, 58(3), 372–383.

    Google Scholar 

  • Zaslavsky, O., & Leikin, R. (2004). Professional development of mathematics teacher educators: Growth through practice. Journal of Mathematics Teacher Education, 7, 5–32.

    Article  Google Scholar 

  • Zaslavsky, O., & Peled, I. (2007). Professional development of mathematics educators. In B. Choksi & C. Natarajan (Eds.), epiSTEME reviews: Research trends in science, technology and mathematics education (pp. 211–225). Mumbai, India: Macmillan.

    Google Scholar 

  • Zopf, D. A. (2010). Mathematical knowledge for teaching teachers: The mathematical work of and knowledge entailed by teacher education (Unpublished doctoral dissertation). Michigan: University of Michigan.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Miguel Montes .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Escudero-Ávila, D., Montes, M., Contreras, L.C. (2021). What Do Mathematics Teacher Educators Need to Know? Reflections Emerging from the Content of Mathematics Teacher Education. In: Goos, M., Beswick, K. (eds) The Learning and Development of Mathematics Teacher Educators. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-62408-8_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-62408-8_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-62407-1

  • Online ISBN: 978-3-030-62408-8

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics