The relationship between the mathematics taught in teacher training and the mathematics demanded in teaching practices is an issue that has been problematized for many years in the field of Mathematics Education. Nonetheless, recent studies show it is still a focus of interest in the field. In this study, we have identified different connections that teacher educators are able to establish between the mathematics they teach and that which their students, prospective mathematics teachers, will have to teach eventually. We have conducted an in-depth case study and have identified that teacher educators establish content connections, modeled instruction connections, and disciplinary practice connections. Furthermore, we have reported the main difficulties that arise in establishing these connections. Additionally, we have identified a new type of connection, which we call professional practice connections.

• 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. https://doi.org/10.1007/s10857-017-9388-9
• Marshman, M. (2021) Learning to teach mathematics: How secondary prospective teachers describe the different beliefs and practices of their mathematics teacher educators. In M. Goos & K. Beswick (Eds.), The learning and development of mathematics teacher educators (pp. 123-144). Springer. https://doi.org/10.1007/978-3-030-62408-8_7
• Rojas, F., & Deulofeu, J. (2015). El formador de profesores de matemática: Un análisis de las percepciones de sus prácticas instruccionales desde la «tensión» estudiante-formador [The teacher educator of mathematics: An analysis of the perceptions of their instructional practices from the student-teacher “tension”]. Enseñanza de las Ciencias [Science Teaching], 33(1), 47-61. http://dx.doi.org/10.5565/rev/ensciencias.1322
• Rojas, F., Montenegro, H., Goizueta, M., & Martínez, S. (2021) Researching modelling by mathematics teacher educators: Shifting the focus onto teaching practices. In M. Goos & K. Beswick (Eds.), The learning and development of mathematics teacher educators (pp. 367-382). Springer. https://doi-org.proxy.timbo.org.uy/10.1007/978-3-030-62408-8_19
• Suominen, A. (2018). Abstract algebra and secondary school mathematics connections as discussed by mathematicians and mathematics educators. In N. Wasserman (Ed.), Connecting abstract algebra to secondary mathematics, for secondary mathematics teachers (pp. 149-173). Springer. https://doi.org/10.1007/978-3-319-99214-3_8
• Ticknor, C. S. (2012). Situated learning in an abstract algebra classroom. Educational Studies in Mathematics, 81, 307-323. https://doi.org/10.1007/s10649-012-9405-y
• Wasserman, N. (2018). Exploring advanced mathematics courses and content for secondary mathematics teachers. In N. Wasserman (Ed.), Connecting abstract algebra to secondary mathematics, for secondary mathematics teachers (pp. 1-15). Springer. https://doi.org/10.1007/978-3-319-99214-3_1
• Weber, K., Mejía-Ramos, J., Fukawa-Connelly, T., & Wasserman, N. (2020). Connecting the learning of advanced mathematics with the teaching of secondary mathematics: Inverse functions, domain restrictions, and the arcsine function. The Journal of Mathematical Behavior, 57, 1-21. https://doi.org/10.1016/j.jmathb.2019.100752
• Winsløw, C., & Grønbæk, N. (2014). The ecological Klein’s double discontinuity revisited: Contemporary challenges for universities preparing teachers to teach calculus. Recherches in Didactique des Mathématiques [Research in Mathematics Didactics], 34(1), 59-86.
• Yan, X., Marmur, O., & Zazkis, R. (2021). Advanced mathematics for secondary school teachers: Mathematicians’ perspective. International Journal of Science and Mathematics Education. https://doi.org/10.1007/s10763-020-10146-x

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