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Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers pp 431–450Cite as

Blue Skies Above the Horizon

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Part of the book series: Research in Mathematics Education ((RME))

Abstract

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.

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Notes

  1. 1.

    For those who might be interested in a more detailed discussion, the following link presents such an activity: http://www.mast.queensu.ca/~math9-12/musical%20magic%20of%2012.html.

References

  • Adler, J., & Ball, D. (Eds.). (2009). Knowing and using mathematics in teaching. For the Learning of Mathematics, 29(3), 1–56.

    Google Scholar 

  • Australian Curriculum. (2012). Retrieved from: https://www.australiancurriculum.edu.au/senior-secondary-curriculum/mathematics/

  • 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: www.mathematik.uni-dortmund.de/ieem/BzMU/BzMU2009/BzMU2009-Inhalt-fuer-Homepage.htm

  • Ball, D., Thames, H. M., & Phelps, G. (2008). Content knowledge for teaching. Journal of Teacher Education, 59(5), 389–407.

    Article  Google Scholar 

  • 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 

  • Boaler, J. (2016). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. San Francisco, CA: Jossey-Bass.

    Google Scholar 

  • Common Core State Standards in Mathematics (CCSS-M). (2010). Retrieved from: http://www.corestandards.org/the-standards/mathematics

  • Conference Board of Mathematical Sciences (CBMS). (2012). The mathematical education of teachers II. Washington, DC: American Mathematical Society and Mathematical Association of America.

    Book  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Department for Education. (2014). The national curriculum in England: Key stages 3 and 4 framework document. Retrieved from: https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/381754/SECONDARY_national_curriculum.pdf

  • Dewey, J. (1934). Art as experience. New York, NY: Putnam.

    Google Scholar 

  • Fernandez, S., & Figueiras, L. (2014). Horizon content knowledge: Shaping MKT for a continuous mathematical education. REDIMAT, 3(1), 7–29.

    Google Scholar 

  • Follesdal, D. (2003). Husserl, Edmund (1859-1938). In E. Craig (Ed.), Routledge encyclopaedia of philosophy (2nd ed.). London: Routledge. Retrieved July 19, 2010, from: www.rep.routledge.com/article/DD029

    Google Scholar 

  • 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 

  • 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: cerme8.metu.edu.tr/wgpapers/WG17/WG17_Jakobsen_Thames_Ribeiro.pdf

    Google Scholar 

  • Mamolo, A., & Pali, R. (2014). Factors influencing prospective teachers’ recommendations to students: Horizons, hexagons, and heed. Mathematical Thinking and Learning, 16(1), 32–50.

    Article  Google Scholar 

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

    Google Scholar 

  • 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 

  • Ministry of Education. (2007). The Ontario curriculum grades 11 and 12: Mathematics. Retrieved from: http://www.edu.gov.on.ca/eng/curriculum/secondary/math1112currb.pdf

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Sinclair, N. (2006). Mathematics and beauty. New York, NY: Teachers College Press.

    Google Scholar 

  • Taylor, P. (2018). Teach the mathematics of mathematicians. Education Sciences, 8(2), 56.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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 

  • Whitehead, A. N. (1929). Aims of education. New York, NY: The Free Press.

    Google Scholar 

  • Zazkis, R., & Mamolo, A. (2011). Reconceptualizing knowledge at the mathematical horizon. For the Learning of Mathematics, 31(2), 8–13.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Education, University of Ontario Institute of Technology, Oshawa, ON, Canada

    Ami M. Mamolo

  2. Department of Mathematics and Statistics, Queen’s University, Kingston, ON, Canada

    Peter D. Taylor

Authors
  1. Ami M. Mamolo
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  2. Peter D. Taylor
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Corresponding author

Correspondence to Ami M. Mamolo .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Science and Technology, Teachers College, Columbia University, New York, NY, USA

    Nicholas H. Wasserman

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Mamolo, A.M., Taylor, P.D. (2018). Blue Skies Above the Horizon. In: Wasserman, N. (eds) Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-99214-3_20

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  • DOI: https://doi.org/10.1007/978-3-319-99214-3_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99213-6

  • Online ISBN: 978-3-319-99214-3

  • eBook Packages: EducationEducation (R0)

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