Abstract
This chapter examines what might be the relevance of a unique abstract algebra course to teaching secondary school mathematics. The course was especially designed for experienced Israeli secondary school teachers of mathematics. One of its aims was to make the course relevant to the teachers’ work, for which we defined several modes of relevance. Analysis of didactical materials designed by the participating teachers, in which they connected the mathematics learned in the abstract algebra course to the school curriculum and teaching, exemplifies contribution of studies in the abstract algebra course at the level of specific content (i.e., algebra), and at the more general epistemological level of the nature of mathematics.
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References
Adler, J., Hossain, S., Stevenson, M., Clarke, J., Archer, R., & Grantham, B. (2014). Mathematics for teaching and deep subject knowledge: Voices of mathematics enhancement course students in England. Journal of Mathematics Teacher Education, 17(2), 129–148.
Baldinger, E. (2013). Connecting abstract algebra to high school algebra. In M. Martinez & A. Castro Superfine (Eds.), Proceedings of the 35th annual meeting of the North American chapter of the International Group for the Psychology of mathematics education (pp. 733–736). Chicago, IL: University of Illinois at Chicago.
Barton, B., & Paterson, J. (2009). Teachers learning mathematics: Professional development research. Report of a TLRI project. Wellington: NZ Council for Educational Research Retrieved from: http://tlri.org.nz/sites/default/files/projects/9256-FinalReport.pdf
Christy, D., & Sparks, R. (2015). Abstract algebra to secondary school algebra: Building bridges. Journal of Mathematics Education at Teachers College, 6(2), 37–42.
Dreher, A., Lindmeier, A., & Heinze, A. (2016). Conceptualizing professional content knowledge of secondary teachers taking into account the gap between academic and school mathematics. In C. CsĂkos, A. Rausch, & J. Szitányi (Eds.), Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education. PME: Szeged, Hungary.
Even, R. (2011). The relevance of advanced mathematics to teaching secondary school mathematics: Practitioners’ views. ZDM, 43(6-7), 941–950.
Even, R., Artstein, Z., & Elbaum-Cohen, A. (2018). The Rothschild-Weizmann master's program for practicing mathematics teachers. In N. Movshovitz-Hadar (Ed.), K-12 mathematics education in Israel: Issues and challenges (Vol. 13, pp. 235–242). Singapore: World Scientific Publication. isbn:978-981-3231-18-4.
Klein, F. (1932). Elementary mathematics from an advanced standpoint: Arithmetic, algebra, analysis (Vol. 1, E. R. Hedrick & C. A. Noble, trans.). New York: Macmillan. (Original work published 1908).
Murray, E., Baldinger, E., Wasserman, N., Broderick, S., White, D., Cofer, T., et al. (2015). Exploring connections between advanced and secondary mathematics. In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.), Proceedings of the 37th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1368–1376). East Lansing, MI: Michigan State University.
Steen, L. A. (1983). Developing mathematical maturity. In A. Ralston & G. S. Young (Eds.), The future of college mathematics (pp. 99–110). New York, NY: Springer.
Wasserman, N. (2016). Abstract algebra for algebra teaching: Influencing school mathematics instruction. Canadian Journal of Science Mathematics and Technology Education, 16(1), 28–47.
Wasserman, N. (2017). Making sense of abstract algebra: Exploring secondary teachers’ understanding of inverse functions in relation to its group structure. Mathematical Thinking and Learning, 19(3), 181–201.
Wu, H. (2011). The mis-education of mathematics teachers. Notices of the AMS, 58(3), 372–384.
Zazkis, R., & Leikin, R. (2010). Advanced mathematical knowledge in teaching practice: Perceptions of secondary mathematics teachers. Mathematical Thinking and Learning, 12(4), 263–281.
Ziegler, G. M., & Loos, A. (2014). Teaching and Learning “What is Mathematics.” Retrieved from: https://www.discretization.de/media/filer_public/2014/09/05/20140413icm-proceedings-ziegler.pdf
Zuo, H. & Leung, F. K. S. (2016). Senior secondary school teachers’ advanced mathematics knowledge and their teaching in china. Paper presented at the 13th International Congress on Mathematics Education.
Course Bibliography
Bergen, J. (2010). A concrete approach to abstract algebra: From the integers to the insolvability of the quintic. Burlington, MA: Elsevier, Academic Press.
Derbyshire, J. (2008). Unknown quantity: A real and imaginary history of algebra. London: Atlantic Books.
Gaal, L. (1973). Classical Galois theory. New York, NY: Chelsea Publishing.
Isaacs, I. M. (1994). Algebra: A graduate course (Graduate studies in mathematics, volume 100). Providence, Rhode Island: American Mathematical Society.
Jacobson, N. (1985). Basic Algebra I. Mineola, New York: Dover Publications.
Lang, S. (1985). Algebra (Graduate texts in mathematics). Boston MA: Addison Wesley Publishing Company.
Livio, M. (2006). The equation that couldn't be solved: How mathematical genius discovered the language of symmetry. New York, NY: Simon & Schuster Paperbacks.
Shamash, J. (2010). Algebra: From equations to structures (course file). Rehovot, Israel: Rothschild-Weizmann Programme for M.Sc. in Science Education, Department of Science Teaching, Weizmann Institute of Science.
Shamash, J. (2016). Algebra: From equations to structures (lecture notes). Rehovot, Israel: Rothschild-Weizmann Programme for M.Sc. in Science Education, Department of Science Teaching, Weizmann Institute of Science.
Singh, S. (1999). The code book: The science of secrecy from ancient Egypt to quantum cryptography. New York, NY: Anchor Books, Random House Inc..
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Shamash, J., Barabash, M., Even, R. (2018). From Equations to Structures: Modes of Relevance of Abstract Algebra to School Mathematics as Viewed by Teacher Educators and Teachers. 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_12
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