Definition
The learning and teaching of the area of mathematics known as school algebra – and the research base accompanying this branch of mathematics education – has typically involved the secondary school student and has focused on forming and operating on polynomial and rational expressions using properties and the field axioms, as well as representing word problems with algebraic expressions containing variables and unknowns. However, over the past several decades, changes in perspective as to what constitutes school algebra have occurred, in addition to its extension in various forms to the elementary school level. Thus, current definitions of school algebra can differ widely, all the more so because what one takes to be algebra depends on factors that vary across communities (see, e.g., Stacey et al. 2004). Decades ago, Freudenthal (1977) characterized school algebra as including not only the solving of linear and quadratic equations but also algebraic thinking, which includes...
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References
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
Bednarz N, Kieran C, Lee L (eds) (1996) Approaches to algebra: perspectives for research and teaching. Kluwer, Dordrecht
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
Doerr HM (2004) Teachers’ knowledge and the teaching of algebra. In: Stacey K, Chick H, Kendal M (eds) The future of the teaching and learning of algebra: The 12th ICMI Study. Kluwer, Dordrecht, pp 267–290
Freudenthal H (1977) What is algebra and what has it been in history? Arch Hist Exact Sci 16(3):189–200
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, vol 4, Research agenda for mathematics education. National Council of Teachers of Mathematics, Reston, pp 167–194
Kaput JJ, Carraher DW, Blanton ML (eds) (2007) Algebra in the early grades. Routledge, New York
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
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
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
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, Greenwich, pp 707–762
Kieran C, Krainer K, Shaughnessy JM (in press) Linking research to practice: teachers as key stakeholders in mathematics education research. In: Clements MA, Bishop A, Keitel C, Kilpatrick J, Leung F (eds) Third international handbook of mathematics education. Springer, Dordrecht
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
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
Mason J, Graham A, Johnston-Wilder S (2005) Developing thinking in algebra. Sage, London
Radford L (2006) The anthropology of meaning. Educ Stud Math 61:39–65
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, vol 25, MAA notes. Mathematical Association of America, Washington, DC, pp 261–289
Sfard A (2008) Thinking as communicating. Cambridge University Press, New York
Stacey K, Chick H, Kendal M (eds) (2004) The future of the teaching and learning of algebra: the 12th ICMI Study. Kluwer, Dordrecht
Stigler JW, Gonzales PA, Kawanaka T, Knoll S, Serrano A (1999) The TIMSS videotape classroom study: methods and findings from an exploratory research project on eighth-grade mathematics instruction in Germany, Japan, and the United States, NCES publication no 1999074. U.S. Government Printing Office, Washington, DC
Wagner S, Kieran C (eds) (1989) Research issues in the learning and teaching of algebra, vol 4, Research agenda for mathematics education. National Council of Teachers of Mathematics, Reston
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Kieran, C. (2014). Algebra Teaching and Learning. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4978-8_6
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