Word problems in upper secondary algebra in Sweden over the years 1960–2000

Authors

  • Teresia Jakobsson-Åhl

DOI:

https://doi.org/10.7146/nomad.v13i1.148050

Abstract

This paper reports results from a study on school algebra at the upper secondary level. The study considered changes in the algebraic content as it was presented in mathematics textbooks in the second half of the twentieth century in Sweden. The paper describes the changes of word problems in terms of the way they are used for developing algebraic skills. It is shown in what ways the place of the problems, the context and the use of mathematical models changed in the period in question. The use of word problems is related to the curricular documents of the time and to different views on school algebra.

References

Bell, A. (1995). Purpose in school algebra. The Journal of Mathematical Behavior, 14, 41-73. https://doi.org/10.1016/0732-3123(95)90023-3

Bolea, P., Bosch, M. & Gascón, J. (2003). Why is modelling not included in the teaching of algebra at secondary school? In the proceeding to The third Conference of the European Society for Research in Mathematics Education. Retrieved May 6, 2006, from http://www.dm.unipi.it/~didattica/ CERME3/proceedings/Groups/TG6/TG6_bolea_cerme3.pdf

Burkhardt, H. (1989). Mathematical modelling in the curriculum. In W. Blum, J. S. Berry, R. Biehler, I. D. Huntley, G. Kaiser-Messmer et al. (Eds.), Applications and modelling in learning and teaching mathematics (pp. 1-11). New York: John Wiley & Sons.

Charbonneau, L. (1996). From Euclid to Descartes: algebra and its relation to geometry. In N. Bednarz, C. Kieran & L. Lee (Eds.), Approaches to algebra: perspectives for research and teaching (pp. 15-37). Dordrecht: Kluwer Academic. https://doi.org/10.1007/978-94-009-1732-3_2

Chevallard, Y. (1985). Le passage de l'arithmétique à l'algébrique dans l'enseignement des mathématique au collège - première partie: l'évolution de la transposition didactique. Petit x n o 5, 51-94.

Clements, M. A. (2003). An outsider's view of North American school mathematics curriculum trends. In G. Stanic & J. Kilpatrick (Eds.), A History of school mathematics (Vol. 2, pp. 1509-1580). Reston: National Council of Teachers of Mathematics.

Donoghue, E. F. (2003). Algebra and geometry textbooks in twentieth-century America. In G. Stanic & J. Kilpatrick (Eds.), A history of school mathematics (Vol. 1, pp. 329-398). Reston: National Council of Teachers of Mathematics.

Fey, J. T. & Graeber, A. O. (2003). From the New Math to the agenda for action. In G. Stanic & J. Kilpatrick (Eds), A history of school mathematics (Vol.1, pp. 521-558). Reston: National Council of Teachers of Mathematics.

Howson, K., Keitel, C. & Kilpatrick, J. (1981). Curriculum development in mathematics. Cambridge: University Press. https://doi.org/10.1017/CBO9780511569722

Håstad, M. (1978). Matematikutbildningen från grundskola till teknisk högskola, i går - i dag - i morgon. Stockholm: Reprocentrum, KTH.

Huntley, M. A., Rasmussen, C. L., Villarubi, R. S., Sangyong, J. & Fey, J. T. (2000). Effects of standards-based mathematics education: a study of the core-plus mathematics project algebra and functions strand. Journal for Research in Mathematics Education, 31 (3), 328-361. https://doi.org/10.2307/749810

Jakobsson-Åhl, T. (2006). Algebra in upper secondary mathematics: a study of a selection of textbooks used in the years 1960-2000 in Sweden (Licentiate thesis). Department of Mathematics, Luleå University of Technology.

Janvier, C. (1996). Modeling and initiation into algebra. In N. Bednarz, C. Kieran & L. Lee (Eds.), Approaches to algebra: perspectives for research and teaching (pp. 225-236). Dordrecht: Kluwer Academic.

Kendal, M. & Stacey, K. (2004). Algebra: a world of difference. In K. Stacey, H. Chick & M. Kendal (Eds.), The future of the teaching and learning of algebra (pp. 329-346). Dordrecht: Kluwer Academic. https://doi.org/10.1007/1-4020-8131-6_13

Kieran, C. & Yerushalmy, M. (2004). Research on the role of technological environments in algebra learning and teaching. In K. Stacey, H. Chick & M. Kendal (Eds.), The future of the teaching and learning of algebra, the 12th ICMI study (pp. 99-152). Dordrecht: Kluwer Academic.

Kissane, B. (2001). The algebra curriculum and personal technology: Exploring the links. In A. Rogerson (Ed.), Proceedings of the international conference: new ideas in mathematics education (pp. 127-132). Palm Cove Queensland, Australia: Programme Committee.

Kline, M. (1973). Why Johnny can't add: the failure of the New Math. New York: St. Martin's Press.

Kungliga Skolöverstyrelsen. (1960). Kursplaner och metodiska anvisningar för gymnasiet. Stockholm: Kungl. Skolöverstyrelsens skriftserie 36.

Marton, F. & Booth, S. (1997). Learning and awareness. Mahwah, N.J.: Erlbaum.

Schoen, H. L. (1988). Teaching elementary algebra with a world problem focus. In A. F. Coxford & A. P. Shulte (Eds.), The ideas of algebra, K-12; 1988 Yearbook (pp 119-126). Reston: National Council of Teachers of Mathematics.

Skolöverstyrelsen. (1965). Läroplan för gymnasiet. Stockholm: Kungliga Skolöverstyrelsen.

Skolöverstyrelsen. (1981). Läroplan för gymnasieskola. Matematik för treårig naturvetenskaplig linje och fyraårig teknisk linje: Supplement 75. (Lgy 70: II). Stockholm: Liber.

Skolverket. (1994). Naturvetenskapsprogrammet. Programmål, kursplaner, betygskriterier och kommentarer. Stockholm: Fritzes.

Stacey, K. & MacGregor, M. (2001). Curriculum reform and approaches to algebra. In R. Sutherland, T. Rojano, A. Bell & R. Lins (Eds.), Perspectives on school algebra (Vol. 22, pp. 141-153). Dordrecht: Kluwer Academic. https://doi.org/10.1007/0-306-47223-6_8

Sutherland, R. (2002). A comparative study of algebra curricula. London: Qualifications and Curriculum Authority.

Swan, M. (Ed.) (1985). Problems with patterns and numbers: an O-level module. Nottingham: Joint Matriculation Board

Usiskin, Z. (1997). Applications in the secondary school mathematics curriculum: a generation of change. American Journal of Education, 106 (November 1997), pp. 62-84. https://doi.org/10.1086/444176

Wheeler, D. (1996). Backwards and forwards: reflections on different approaches to algebra. In N. Bednarz, C. Kieran & L. Lee (Eds.), Approaches to algebra: perspectives for research and teaching (pp. 317-325). Dordrecht: Kluwer Academic. https://doi.org/10.1007/978-94-009-1732-3_21

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Published

2008-03-10

How to Cite

Jakobsson-Åhl, T. (2008). Word problems in upper secondary algebra in Sweden over the years 1960–2000. NOMAD Nordic Studies in Mathematics Education, 13(1), 7–27. https://doi.org/10.7146/nomad.v13i1.148050

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