Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

References

• Asiala, M., Brown, A., DeVries, D., Dubinsky, E., Mathews, D., & Thomas, K. (1996). A framework for research and curriculum development in undergraduate mathematics education. Research in Collegiate Mathematics Education, 6, 1–32.
   Google Scholar
• Ball, D. L. (2009, April 23). With an eye on the mathematical horizon: Knowing mathematics for teaching to learners' mathematical futures. Paper presented at the National Council of Teachers of Mathematics (NCTM) Annual Meeting, Washington, DC. Retrieved from http://www-personal.umich.edu/∼dball/presentations/index.html
   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.
   Google Scholar
• Carraher, D. W., & Schliemann, A. D. (2007). Early algebra and algebra reasoning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 669–705). Charlotte, NC: Information Age.
   Google Scholar
• Common Core State Standards in Mathematics (CCSS-M). (2010). Common Core State Standards in Mathematics. Retrieved from http://www.corestandards.org/the-standards/mathematics
   Google Scholar
• Conference Board of the Mathematical Sciences. (2001). The mathematical education of teachers (MET I). Retrieved from http://cbmsweb.org/MET_Document/
   Google Scholar
• Conference Board of the Mathematical Sciences. (2012). The mathematical education of teachers II (MET II). Retrieved from http://www.cbmsweb.org/MET2/MET2Draft.pdf
   Google Scholar
• Cuoco, A., & Rotman, J. (2013). Learning modern algebra: From modern attempts to prove Fermat's last theorem. Washington, DC: Mathematical Association of America.
   Google Scholar
• Darling-Hammond, L. (2000). Teacher quality and student achievement: A review of state policy evidence. Educational Policy Analysis Archives, 8(1). Retrieved from http://epaa.asu.edu/ojs/article/view/392
   Google Scholar
• Harry, B., Sturges, K., & Klingner, J. K. (2005). Mapping the process: An exemplar of process and challenge in grounded theory analysis. Educational Researcher, 34(2), 3–13.
   Google Scholar
• Hill, H. C., Sleep, L., Lewis, J. M., & Ball, D. L. (2007). Assessing teachers' mathematical knowledge: What knowledge matters and what evidence counts. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 111–155). Charlotte, NC: Information Age.
   Google Scholar
• Jakobsen, A., Thames, M. H., & Ribeiro, C. M. (2013, February 5–10). Delineating issues related to horizon content knowledge for mathematics teaching. Paper presented at the Eighth Congress of European Research in Mathematics Education (CERME-8), Manavgat-Side, Antalya-Turkey. Retrieved from http://cerme8.metu.edu.tr/wgpapers/WG17/WG17_Jakobsen_Thames_Ribeiro.pdf
   Google Scholar
• Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 5–17). New York, NY: Lawrence Erlbaum.
   Google Scholar
• Klein, F. (1932). Elementary mathematics from an advanced standpoint: Arithmetic, algebra, analysis (E. R. Hedrick & C. A. Noble, Trans.). Mineola, NY: Macmillan.
   Google Scholar
• McRory, R., Floden, R., Ferrini-Mundy, J., Reckase, M. D., & Senk, S. L. (2012). Knowledge of algebra for teaching: A framework of knowledge and practices. Journal for Research in Mathematics Education, 43(5), 584–615.
   Google Scholar
• Monk, D. H. (1994). Subject area preparation of secondary mathematics and science teachers and student achievement. Economics of Education Review, 13(2), 125–145.
   Google Scholar
• Morris, A. (1999). Developing concepts of mathematical structure: Pre-arithmetic reasoning versus extended arithmetic reasoning. Focus on Learning Problems in Mathematics, 21(1), 44–67.
   Google Scholar
• Nathan, M. J., & Petrosino, A. (2003). Expert blind spot among preservice teachers. American Educational Research Journal, 40(4), 905–928.
   Google Scholar
• Piaget, J. (1952). The origins of intelligence in children. New York, NY: International University Press.
   Google Scholar
• Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers' mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255–281.
   Google Scholar
• Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
   Google Scholar
• Silverman, J., & Thompson, P. W. (2008). Toward a framework for the development of mathematical knowledge for teaching. Journal of Mathematics Teacher Education, 11(6), 499–511.
   Google Scholar
• Simon, M. (2006). Key developmental understandings in mathematics: A direction for investigating and establishing learning goals. Mathematical Thinking and Learning, 8(4), 359–371.
   Google Scholar
• Strauss, A., & Corbin, J. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Newbury Park, CA: Sage.
   Google Scholar
• Wasserman, N. (2014). Introducing algebraic structures through solving equations: Vertical content knowledge for K-12 mathematics teachers. PRIMUS, 24(3), 191–214.
   Google Scholar
• Wasserman, N., & Stockton, J. (2013). Horizon content knowledge in the work of teaching: A focus on planning. For the Learning of Mathematics, 33(3), 20–22.
   Google Scholar
• Zazkis, R., & Leikin, R. (2010). Advanced mathematical knowledge in teaching practice: Perceptions of secondary mathematics teachers. Mathematical Thinking and Learning, 12(4), 263–281.
   Google Scholar
• Zazkis, R., & Mamolo, A. (2011). Reconceptualizing knowledge at the mathematical horizon. For the Learning of Mathematics, 31(2), 8–13.
   Google Scholar