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Algebra Teaching and Learning

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References

  • Arcavi A, Drijvers P, Stacey K (2017) The learning and teaching of algebra: ideas, insights, and activities. Routledge, London

    Google Scholar 

  • Artigue M (2002) Learning mathematics in a CAS environment: the genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. Int J Comput Math Learn 7:245–274

    Article  Google Scholar 

  • Bednarz N, Kieran C, Lee L (eds) (1996) Approaches to algebra: perspectives for research and teaching. Kluwer, Dordrecht

    Google Scholar 

  • Bell A (1996) Problem-solving approaches to algebra: two aspects. In: Bednarz N, Kieran C, Lee L (eds) Approaches to algebra: perspectives for research and teaching. Kluwer, Dordrecht, pp 167–185

    Chapter  Google Scholar 

  • Cai J, Knuth E (eds) (2011) Early algebraization. Springer, New York

    Google Scholar 

  • Freudenthal H (1977) What is algebra and what has it been in history? Arch Hist Exact Sci 16(3):189–200

    Article  Google Scholar 

  • Hoch M, Dreyfus T (2006) Structure sense versus manipulation skills: an unexpected result. In: Novotná J, Moraová H, Krátká M, Stehliková N (eds) Proceedings of 30th conference of the international group for the psychology of mathematics education, vol 3. PME, Prague, pp 305–312

    Google Scholar 

  • Kaput JJ (1989) Linking representations in the symbol systems of algebra. In: Wagner S, Kieran C (eds) Research issues in the learning and teaching of algebra, Research agenda for mathematics education, vol 4. National Council of Teachers of Mathematics, Reston, pp 167–194

    Google Scholar 

  • Kaput JJ, Carraher DW, Blanton ML (eds) (2007) Algebra in the early grades. Routledge, New York

    Google Scholar 

  • Kieran C (1992) The learning and teaching of school algebra. In: Grouws DA (ed) Handbook of research on mathematics teaching and learning. Macmillan, New York, pp 390–419

    Google Scholar 

  • Kieran C (1996) The changing face of school algebra. In: Alsina C, Alvarez J, Hodgson B, Laborde C, Pérez A (eds) Eighth international congress on mathematical education: selected lectures. S.A.E.M. Thales, Seville, pp 271–290

    Google Scholar 

  • Kieran C (2006) Research on the learning and teaching of algebra. In: Gutiérrez A, Boero P (eds) Handbook of research on the psychology of mathematics education. Sense, Rotterdam, pp 11–50

    Google Scholar 

  • Kieran C (2007) Learning and teaching algebra at the middle school through college levels: building meaning for symbols and their manipulation. In: Lester FK Jr (ed) Second handbook of research on mathematics teaching and learning. Information Age Publishing, Greenwich, pp 707–762

    Google Scholar 

  • Kieran C (2013) The false dichotomy in mathematics education between conceptual understanding and procedural skills: an example from algebra. In: Leatham K (ed) Vital directions in mathematics education research. Springer, New York, pp 153–171

    Chapter  Google Scholar 

  • Kieran C (2017) Cognitive neuroscience and algebra: challenging some traditional beliefs. In: Stewart S (ed) And the rest is just algebra. Springer, New York, pp 157–172

    Chapter  Google Scholar 

  • Kieran C (ed) (2018) Teaching and learning algebraic thinking with 5- to 12-year-olds: the global evolution of an emerging field of research and practice. Springer, New York

    Google Scholar 

  • Kieran C, Pang JS, Schifter D, Ng SF (2016) Early algebra: research into its nature, its learning, its teaching. Springer Open eBooks, New York. http://www.springer.com/us/book/9783319322575. Accessed 3 Dec 2017

    Book  Google Scholar 

  • Kirshner D (2001) The structural algebra option revisited. In: Sutherland R, Rojano T, Bell A, Lins R (eds) Perspectives on school algebra. Kluwer, Dordrecht, pp 83–98

    Google Scholar 

  • Lee K, Lim ZY, Yeong SHM, Ng SF, Venkatraman V, Chee MWL (2007) Strategic differences in algebraic problem solving: neuroanatomical correlates. Brain Res 1155:163–171

    Article  Google Scholar 

  • Lee K, Yeong SHM, Ng SF, Venkatraman V, Graham S, Chee MWL (2010) Computing solutions to algebraic problems using a symbolic versus a schematic strategy. ZDM Int J Math Educ 42:591–605. https://doi.org/10.1007/s11858-010-0265-6

    Article  Google Scholar 

  • Lerman S (2000) The social turn in mathematics education research. In: Boaler J (ed) Multiple perspectives on mathematics teaching and learning. Ablex, Westport, pp 19–44

    Google Scholar 

  • Leung FKS, Clarke D, Holton D, Park K (2014) How is algebra taught around the world? In: Leung FKS, Park K, Holton D, Clarke D (eds) Algebra teaching around the world. Sense Publishers, Rotterdam, pp 1–15

    Google Scholar 

  • Linchevski L, Livneh D (1999) Structure sense: the relationship between algebraic and numerical contexts. Educ Stud Math 40:173–196

    Article  Google Scholar 

  • Mason J, Graham A, Johnston-Wilder S (2005) Developing thinking in algebra. Sage, London

    Google Scholar 

  • Mullis IVS, Martin MO, Foy P, Hooper M (2016) TIMSS 2015 international results in mathematics. Retrieved from Boston College. TIMSS & PIRLS International Study Center website: http://timssandpirls.bc.edu/timss2015/international-results/

  • Radford L (2006) The anthropology of meaning. Educ Stud Math 61:39–65

    Article  Google Scholar 

  • Radford L (2018) The emergence of symbolic algebraic thinking in primary school. In: Kieran C (ed) Teaching and learning algebraic thinking with 5- to 12-year-olds: the global evolution of an emerging field of research and practice. Springer, New York, pp 1–23

    Google Scholar 

  • Schwartz J, Yerushalmy M (1992) Getting students to function in and with algebra. In: Dubinsky E, Harel G (eds) The concept of function: aspects of epistemology and pedagogy, MAA notes, vol 25. Mathematical Association of America, Washington, DC, pp 261–289

    Google Scholar 

  • Sfard A (2008) Thinking as communicating. Cambridge University Press, New York

    Book  Google Scholar 

  • Stacey K, Chick H (2004) Solving the problem with algebra. In: Stacey K, Chick H, Kendal M (eds) The future of the teaching and learning of algebra: the 12th ICMI study. Kluwer, Boston, pp 1–20

    Google Scholar 

  • Stacey K, Chick H, Kendal M (eds) (2004) The future of the teaching and learning of algebra: the 12th ICMI study. Kluwer, Boston

    Google Scholar 

  • Star JR, Caronongan P, Foegen A, Furgeson J, Keating B, Larson MR, Lyskawa J, McCallum WG, Porath J, Zbiek RM (2015) Teaching strategies for improving algebra knowledge in middle and high school students (NCEE 2014-4333). National Center for Education Evaluation and Regional Assistance (NCEE)/Institute of Education Sciences/U.S. Department of Education, Washington, DC. Retrieved from the NCEE website http://whatworks.ed.gov

    Google Scholar 

  • Wagner S, Kieran C (eds) (1989) Research issues in the learning and teaching of algebra (Vol. 4 of Research agenda for mathematics education). National Council of Teachers of Mathematics, Reston

    Google Scholar 

  • Waisman I, Leikin M, Shaul S, Leikin R (2014) Brain activity associated with translation between graphical and symbolic representations of functions in generally gifted and excelling in mathematics adolescents. Int J Sci Math Educ 12:669–696

    Article  Google Scholar 

  • Warren E, Trigueros M, Ursini S (2016) Research on the learning and teaching of algebra. In: Gutiérrez A, Leder GC, Boero P (eds) The second handbook of research on the psychology of mathematics education: the journey continues. Sense, Rotterdam, pp 73–108

    Chapter  Google Scholar 

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Correspondence to Carolyn Kieran .

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Kieran, C. (2020). Algebra Teaching and Learning. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_6

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