Abstract
Historically, algebra in the U.S. has been viewed “as a gatekeeper to a college education and the careers such education affords” (Kilpatrick & Izsák, 2008, p. 11). As such, current curriculum documents emphasize the need to support all students in learning algebra (Common Core State Standards Initiative [CCSSI], 2010; National Council of Teachers of Mathematics [NCTM], 1989, 2000).
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References
APPA Group (led by Sutherland, R.). (2004). A toolkit for analyzing approaches to algebra. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra (pp. 73–96). Dordrecht: Kluwer.
Blanton, M. L. (2008). Algebra and the elementary classroom: Transforming thinking, transforming practice. Portsmouth, NH: Heinemann
Blanton, M. L., & Kaput, J. J. (2003). Developing elementary teachers’: “Algebra eyes and ears.” Teaching Children Mathematics, 10, 70–77.
Blanton, M., & Kaput, J. J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 36, 412–446.
Blanton, M., Stephens, A., Knuth, E. Gardiner, A. M., Isler, I., & Kim, J. S. (2015). The development of children’s algebraic thinking: The impact of a comprehensive early algebra intervention in third grade. Journal for Research in Mathematics Education, 46, 39–87.
Carraher, D. W., & Schliemann, A. D. (2007). Early algebra and algebraic reasoning. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 669–705). Reston, VA: National Council of Teachers of Mathematics.
Common Core State Standards Initiative. (2010). Common core state standards for mathematics. Washington, DC: National Governors Association Center for Best Practices and Council of Chief State School Officers. Retrieved from http://www.corestandards.org
Earnest, D. (2014). Exploring functions in elementary school: Leveraging the representational context. In K. Karp (Ed.), Annual perspectives in mathematics education: Using research to improve instruction (pp. 171–179). Reston, VA: National Council of Teachers of Mathematics.
Hunter, J. (2014). Developing learning environments which support early algebraic reasoning: A case from a New Zealand primary school. Mathematics Education Research Journal, 26, 659–682.
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). Reston, VA: National Council of Teachers of Mathematics.
Kazemi, E. (1998). Discourse that promotes conceptual understanding. Teaching Children Mathematics, 4, 410–414.
Kilpatrick, J., & Izsák, A. (2008). A history of algebra in the school curriculum. In C. E. Greenes (Ed.), Algebra and algebraic thinking in school mathematics: Seventieth yearbook (pp. 3–18). Reston, VA: National Council of Teachers of Mathematics.
Leung, A. (2012). Variation and mathematics pedagogy. In J. Dindyal, L. P. Cheng, & S. F. Ng (Eds.), Proceedings of the 35th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 433–440). Singapore: MERGA.
Ling, M. L. (2012). Variation theory and the improvement of teaching and learning. Gothenburg, Sweden: Acta Universitatis Gothoburgensis.
Lins, R., & Kaput, J. J. (2004). The early development of algebraic reasoning: The current state of the field. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of teaching and learning of algebra: The 12th ICMI study (pp. 45–70). Boston, MA: Kluwer Academic Publishers.
Lo, M. L., & Marton, F. (2012). Towards a science of the art of teaching: Using variation theory as a guiding principle of pedagogical design. International Journal for Lesson and Learning Studies, 1, 7–22.
Marton, F., & Pang, M. F. (2006). On some necessary conditions of learning. The Journal of the Learning Science, 15, 193–220.
Marton, F., Runesson, U., & Tsui, A. B. M. (2004). The space of learning. In F. Marton & A. B. M. Tsui (Eds.), Classroom discourse and the space of learning (pp. 3–36). Mahwah, NJ: Lawrence Erlbaum Associates.
Ministry of Education. (2007). The New Zealand curriculum. Wellington: Learning Media.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards. Reston, VA: Author.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
Ontario Ministry of Education. (2005). The Ontario curriculum: Grades 1–8 mathematics. Toronto, ON: Queen’s Printer for Ontario.
Ontario Ministry of Education. (n.d.). Paying attention to algebraic reasoning. Retrieved from http://edu.gov.on.ca/eng/literacynumeracy/PayingAttentiontoAlgebra.pdf
Soares, J., Blanton, M. L., & Kaput, J. J. (2005). Thinking algebraically across the elementary school curriculum. Teaching Children Mathematics, 12, 228–235.
Stacey, K., & Chick, H. (2004). Solving the problem with algebra. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra (pp. 1–20). Dordrecht: Kluwer.
Warren, E., & Cooper, T. (2008). Generalising the pattern rule for visual growth patterns: Actions that support 8 year olds’ thinking. Educational Studies in Mathematics, 67, 171–185.
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Barlow, A.T., Prince, K.M., Lischka, A.E., Duncan, M.D. (2017). Developing Algebraic Reasoning through Variation in the U.S.. In: Huang, R., Li, Y. (eds) Teaching and Learning Mathematics through Variation. Mathematics Teaching and Learning. SensePublishers, Rotterdam. https://doi.org/10.1007/978-94-6300-782-5_18
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DOI: https://doi.org/10.1007/978-94-6300-782-5_18
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