Blue Skies Above the Horizon

  • Ami M. Mamolo
  • Peter D. Taylor
Part of the Research in Mathematics Education book series (RME)


In this commentary chapter, we draw on ideas from Baldinger and Murray; Cuoco; Wasserman and Galarza; and Zazkis and Marmur to articulate our views on the importance of mathematical structure and its relevance in secondary mathematics teachers’ disciplinary knowledge. In particular, we organize our discussion around two related questions—about the connections between abstract algebra and secondary school mathematics, and about how these connections can support the development of teachers’ disciplinary knowledge.


Abstract algebra Approaches Connections Knowledge at the mathematical horizon Teacher education 


  1. Adler, J., & Ball, D. (Eds.). (2009). Knowing and using mathematics in teaching. For the Learning of Mathematics, 29(3), 1–56.Google Scholar
  2. Ball, D. L., & Bass, H. (2009). With an eye on the mathematical horizon: Knowing mathematics for teaching to learners’ mathematical futures. Paper presented at the 43rd Jahrestagung der Gelleschaft fur Didaktic der Mathematik. Oldenburg, .Germany. Retrieved May 15, 2011, from:
  3. Ball, D., Thames, H. M., & Phelps, G. (2008). Content knowledge for teaching. Journal of Teacher Education, 59(5), 389–407.CrossRefGoogle Scholar
  4. Barabe, G., & Proulx, J. (2017). Revolutionner l’enseignment des mathematiques: Le projet visionnaire de Seymour Papert. For the Learning of Mathematics, 37(2), 25–29.Google Scholar
  5. Boaler, J. (2016). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. San Francisco, CA: Jossey-Bass.Google Scholar
  6. Common Core State Standards in Mathematics (CCSS-M). (2010). Retrieved from:
  7. Conference Board of Mathematical Sciences (CBMS). (2012). The mathematical education of teachers II. Washington, DC: American Mathematical Society and Mathematical Association of America.CrossRefGoogle Scholar
  8. Davis, B., & Simmt, E. (2006). Mathematics-for-teaching: An ongoing investigation of the mathematics that teachers (need to) know. Educational Studies in Mathematics, 61(3), 293–319.CrossRefGoogle Scholar
  9. Department for Education. (2014). The national curriculum in England: Key stages 3 and 4 framework document. Retrieved from:
  10. Dewey, J. (1934). Art as experience. New York, NY: Putnam.Google Scholar
  11. Fernandez, S., & Figueiras, L. (2014). Horizon content knowledge: Shaping MKT for a continuous mathematical education. REDIMAT, 3(1), 7–29.Google Scholar
  12. Follesdal, D. (2003). Husserl, Edmund (1859-1938). In E. Craig (Ed.), Routledge encyclopaedia of philosophy (2nd ed.). London: Routledge. Retrieved July 19, 2010, from: Google Scholar
  13. Gadanidis, G., Borba, M., Hughes, J., & Lacerda, H. (2016). Designing aesthetic experiences for young mathematicians: A model for mathematics education reform. International Journal for Research in Mathematics Education, 6(2), 225–244.Google Scholar
  14. Jakobsen, A., Thames, M. H., Ribeiro, C. M., & Delaney, S. (2012). Delineating issues related to horizon content knowledge for mathematics teaching. Paper presented at the Eighth Congress of European Research in Mathematics Education (CERME-8). Retrieved from: Scholar
  15. Mamolo, A., & Pali, R. (2014). Factors influencing prospective teachers’ recommendations to students: Horizons, hexagons, and heed. Mathematical Thinking and Learning, 16(1), 32–50.CrossRefGoogle Scholar
  16. Mason, J. (2002). Researching your own practice: The discipline of noticing. London: Routledge Falmer.Google Scholar
  17. Mason, J. (2001). Mathematics as a constructive enterprise. In J. Winter (Ed.), Proceedings of the British Society for Research into Learning Mathematics (Vol. 21, Num. 3) (pp. 52–57). Southampton: British Society for Research into Learning Mathematics.Google Scholar
  18. Ministry of Education. (2007). The Ontario curriculum grades 11 and 12: Mathematics. Retrieved from:
  19. Papert, S. (1972). Teaching children to be mathematicians versus teaching about mathematics. International Journal of Mathematical Education in Science and Technology, 3(3), 249–262.CrossRefGoogle Scholar
  20. Raymond, K. (2018). M is not just for STEM: How myths about the purposes of mathematics education have narrowed mathematics curricula in the United States. Education Sciences, 8(2), 47.CrossRefGoogle Scholar
  21. Sinclair, N. (2006). Mathematics and beauty. New York, NY: Teachers College Press.Google Scholar
  22. Taylor, P. (2018). Teach the mathematics of mathematicians. Education Sciences, 8(2), 56.CrossRefGoogle Scholar
  23. Wasserman, N., Fukawa-Connelly, T., Villanueva, M., Mejia-Ramos, J. P., & Weber, K. (2017). Making real analysis relevant to secondary teachers: Building up from and stepping down to practice. PRIMUS, 27(6), 559–578.CrossRefGoogle Scholar
  24. Wasserman, N., Weber, K., & McGuffey, W. (2017). Leveraging real analysis to foster pedagogical practices. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro, & S. Brown (Eds.), Proceedings of the 20th annual conference on Research in Undergraduate Mathematics Education (RUME) (pp. 1–15). San Diego, CA: RUME.Google Scholar
  25. Wasserman, N. H., & Stockton, J. C. (2013). Horizon content knowledge in the work of teaching: A focus on planning. For the Learning of Mathematics, 33(3), 20–22.Google Scholar
  26. Whitehead, A. N. (1929). Aims of education. New York, NY: The Free Press.Google Scholar
  27. Zazkis, R., & Mamolo, A. (2011). Reconceptualizing knowledge at the mathematical horizon. For the Learning of Mathematics, 31(2), 8–13.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Faculty of EducationUniversity of Ontario Institute of TechnologyOshawaCanada
  2. 2.Department of Mathematics and StatisticsQueen’s UniversityKingstonCanada

Personalised recommendations