Encyclopedia of Mathematics Education

2014 Edition
| Editors: Stephen Lerman

Algebra Teaching and Learning

  • Carolyn KieranEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-94-007-4978-8_6

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...

Keywords

School algebra Research on the teaching and learning of algebra Widening perspectives on school algebra Relational thinking in algebra Technological tools in algebra learning Functions and multiple representations Algebraic reasoning Algebraic meaning Algebraic activity The technical-conceptual interface in algebra Teaching approaches Changing nature of research on algebra teaching and learning Role of teacher questioning in algebra learning Role of tasks in algebra teaching Teacher as key stakeholder in algebra research 
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References

  1. 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 7:245–274Google Scholar
  2. Bednarz N, Kieran C, Lee L (eds) (1996) Approaches to algebra: perspectives for research and teaching. Kluwer, DordrechtGoogle Scholar
  3. 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 167–185Google Scholar
  4. 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 267–290Google Scholar
  5. Freudenthal H (1977) What is algebra and what has it been in history? Arch Hist Exact Sci 16(3):189–200Google Scholar
  6. 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 167–194Google Scholar
  7. Kaput JJ, Carraher DW, Blanton ML (eds) (2007) Algebra in the early grades. Routledge, New YorkGoogle Scholar
  8. 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 390–419Google Scholar
  9. 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 271–290Google Scholar
  10. 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 11–50Google Scholar
  11. 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 707–762Google Scholar
  12. 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, DordrechtGoogle Scholar
  13. 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 83–98Google Scholar
  14. Lerman S (2000) The social turn in mathematics education research. In: Boaler J (ed) Multiple perspectives on mathematics teaching and learning. Ablex, Westport, pp 19–44Google Scholar
  15. Mason J, Graham A, Johnston-Wilder S (2005) Developing thinking in algebra. Sage, LondonGoogle Scholar
  16. Radford L (2006) The anthropology of meaning. Educ Stud Math 61:39–65Google Scholar
  17. 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 261–289Google Scholar
  18. Sfard A (2008) Thinking as communicating. Cambridge University Press, New YorkGoogle Scholar
  19. Stacey K, Chick H, Kendal M (eds) (2004) The future of the teaching and learning of algebra: the 12th ICMI Study. Kluwer, DordrechtGoogle Scholar
  20. 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, DCGoogle Scholar
  21. 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, RestonGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Quebec at MontrealMontrealCanada