Conservative and transformative changes in algebra in Swedish lower secondary textbooks 1995–2015

Authors

  • Kristina Palm Kaplan
  • Johan Prytz

Abstract

The present study examines textbook algebra tasks in an attempt to understand how textbooks change in a reform of lower secondary school algebra. Changes in 1557 textbook tasks for year 8 are described in terms of algebraic activities and school algebra discourses. The tasks were taken from textbooks published before and after a new syllabus was introduced in Sweden in 2011. The results show that the new syllabus’ focus on mathematical competences was not stressed in the textbooks and that the greatest change was an increase in word problems connected to everyday situations. It is suggested that, in this reform, textbooks have been conservative and transformative in relation to the syllabus.

References

Alshwaikh, J. (2016). Investigating the geometry curriculum in Palestinian textbooks: towards multimodal analysis of Arabic mathematics discourse. Research in Mathematics Education, 18 (2), 165-181. https://doi.org/10.1080/14794802.2016.1177580

Apple, M. W. (2004). Ideology and curriculum (3rd ed.). Taylor & Francis. https://doi.org/10.4324/9780203487563

Apple, M. W. & Aasen, P. (2003). The state and the politics of knowledge. Taylor & Francis. https://doi.org/10.4324/9780203441190

Blanton, M., Brizuela, B. M., Stephens, A., Knuth, E., Isler, I. et al. (2018). Implementing a framework for early algebra. In C. Kieran (Ed.), Teaching and learning algebraic thinking with 5- to 12-year-olds (pp. 27-49). Springer International. https://doi.org/10.1007/978-3-319-68351-5_2

Blanton, M., Stephens, A., Knuth, E., Gardiner, A. M., Isler, I. & Jee-Seon, K. (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 (1), 39-87. https://doi.org/10.5951/jresematheduc.46.1.0039

Bloedy-Vinner, H. (2001). Beyond unknowns and variables - parameters and dummy variables in high school algebra. In R. Sutherland, T. Rojano, A. Bell & R. Lins (Eds.), Perspectives on school algebra (pp. 177-189). Kluwer. https://doi.org/10.1007/0-306-47223-6_10

Boesen, J., Helenius, O., Bergqvist, E., Bergqvist, T., Lithner, J. et al. (2014). Developing mathematical competence: from the intended to the enacted curriculum. The Journal of Mathematical Behavior, 33, 72-87. https://doi.org/10.1016/j.jmathb.2013.10.001

Bråting, K., Madej, L. & Hemmi, K. (2019). Development of algebraic thinking: opportunities offered by the Swedish curriculum and elementary mathematics textbooks. Nordic Studies in Mathematics Education, 24 (1), 27-49.

Cramer, K. & Post, T. (1993). Proportional reasoning. The Mathematics Teacher, 86 (5), 404-407. https://doi.org/10.5951/MT.86.5.0404

Eddy, C. M., Quebec Fuentes, S., Ward, E. K., Parker, Y. A., Cooper, S. et al. (2015). Unifying the algebra for all movement. Journal of Advanced Academics, 26 (1), 59-92. https://doi.org/10.1177/1932202X14562393

Häggström, J. (2008). Teaching systems of linear equations in Sweden and China: What is made possible to learn? (Doctoral thesis). Acta Universitatis Gothoburgensis.

Halliday, M. A. K. & Hasan, R. (1989). Language, context, and text: aspects of language in a social-semiotic perspective. Oxford University Press.

Hill, H. C. & Charalambous, C. Y. (2012). Teacher knowledge, curriculum materials, and quality of instruction: lessons learned and open issues. Journal of Curriculum Studies, 44 (4), 559-576. https://doi.org/10.1080/00220272.2012.716978

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). Luleå University of Technology.

Johansson, M. (2003). Textbooks in mathematics education: a study of textbooks as the potentially implemented curriculum (Licentiate thesis). Luleå University of Technology.

Johansson, M. (2006). Teaching mathematics with textbooks (Doctoral thesis). Luleå University of Technology.

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). Lawrence Erlbaum. https://doi.org/10.4324/9781315097435-2

Kaput, J. J., Blanton, M. L. & Moreno, L. (2008). Algebra from a symbolization point of view. In J. J. Kaput, D. W. Carraher & M. L. Blanton (Eds.), Algebra in the early grades (pp. 19-55). Lawrence Erlbaum. https://doi.org/10.4324/9781315097435-3

Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels. Building meaning for symbols and their manipulation. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 707-762). Information Age.

Kongelf, T. R. (2015). Introduksjon av algebra i matematikkbøker for ungdomstrinnet i Norge [Introduction of algebra in mathematics textbooks for lower secondary school in Norway]. Nordic Studies in Mathematics Education, 20 (3-4), 83-109.

Lindensjö, B. & Lundgren, U. P. (2014). Utbildningsreformer och politisk styrning [Educational reforms and political government]. Liber.

Luke, A. (1995). Text and discourse in education: an introduction to critical discourse analysis. Review of Research in Education, 21, 3-48. https://doi.org/10.2307/1167278

Lundberg, A. (2011). Proportionalitetsbegreppet i den svenska gymnasiematematiken: en studie om läromedel och nationella prov [The concept of proportionality in Swedish upper secondary mathematics: a study on textbooks and national tests] (Licentiate thesis). Linköping University.

Martin, J. R., Matthiessen, C. M. I. M. & Painter, C. (1997). Working with functional grammar. Arnold.

Morgan, C. (2016a). Mathematics education as a matter of discourse. In M. A. Peters (Ed.), Encyclopedia of educational philosophy and theory (pp. 1-6). Springer. https://doi.org/10.1007/978-981-287-532-7_514-1

Morgan, C. (2016b). Studying the role of human agency in school mathematics. Research in Mathematics Education, 18 (2), 120-141. https://doi.org/10.1080/14794802.2016.1176595

Morgan, C. & Sfard, A. (2016). Investigating changes in high-stakes mathematics examinations: a discursive approach. Research in Mathematics Education, 18 (2), 92-119. https://doi.org/10.1080/14794802.2016.1176596

Neumann, J., Hemmi, K., Ryve, A. & Wiberg, M. (2015). Mathematics textbooks' impact on classroom instruction: examining the views of 278 Swedish teachers. In H. Silfverberg, T. Kärki & M. Hannula (Eds.), Proceedings of NORMA 14 (pp. 215-224). University of Turku.

Palm Kaplan, K. (2018). Discourses in school algebra: the textbooks' different views on algebra and the positioning of students. Nordic Studies in Mathematics Education, 23 (1), 47-65.

Ponte, J. P. da & Guimarães, H. M. (2014). Notes for a history of the teaching of algebra. In A. Karp & G. Schubring (Eds.), Handbook on the history of mathematics education (pp. 459-472). Springer. https://doi.org/10.1007/978-1-4614-9155-2_22

Prytz, J. (2007). Speaking of geometry - a study of geometry textbooks and literature on geometry instruction for elementary and lower secondary levels in Sweden, 1905-1962, with a special focus on professional debates. (Doctoral thesis). Uppsala University.

Prytz, J. (2017). Governance of Swedish school mathematics - where and how did it happen? A study of different modes of governance in Swedish school mathematics, 1910-1980. Espacio, Tiempo y Educación, 4 (2), 43. https://doi.org/10.14516/ete.180

Prytz, J. (2018). The New math and school governance: an explanation of the decline of the New math in Sweden. In F. Furinghetti & A. Karp (Eds.), Researching the history of mathematics education (pp. 189-216). Springer. https://doi.org/10.1007/978-3-319-68294-5_10

Radford, L. (2011). Grade 2 students' non-symbolic algebraic thinking. In J. Cai & E. Knuth (Eds.), Early algebraization (pp. 303-322). Springer. https://doi.org/10.1007/978-3-642-17735-4_17

Sidenvall, J., Lithner, J. & Jäder, J. (2015). Students' reasoning in mathematics textbook task-solving. International Journal of Mathematical Education in Science and Technology, 46 (4), 533-552. https://doi.org/10.1080/0020739X.2014.992986

Skolverket. (1994). Kursplaner för grundskolan [Syllabuses for the compulsory school]. Fritzes offentliga publikationer.

Skolverket. (2011a). Kommentarmaterial till kursplanen i matematik [Commentary material to the syllabus in mathematics]. Fritzes offentliga publikationer.

Skolverket (2011b). Läroplan för grundskolan, förskoleklassen och fritidshemmet 2011 [Curriculum for the compulsory school, preschool class and the recreation centre 2011]. Fritzes offentliga publikationer.

Stein, M. K., Remillard, J. T. & Smith, M. S. (2007). How curriculum influences student learning. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319-369). Information Age.

Sundberg, D. & Wahlström, N. (2012). Standards-based curricula in a denationalised conception of education: the case of Sweden. European Educational Research Journal, 11 (3), 342-356. https://doi.org/10.2304/eerj.2012.11.3.342

Wetherell, M. (2001). Themes in discourse research: the case of Diana. In M. Wetherell, S. Taylor & S. J. Yates (Eds.), Discourse theory and practice. A reader (pp. 14-28). Sage.

Downloads

Published

2024-11-19

How to Cite

Palm Kaplan, K., & Prytz, J. (2024). Conservative and transformative changes in algebra in Swedish lower secondary textbooks 1995–2015. NOMAD Nordic Studies in Mathematics Education, 25(2), 49–70. Retrieved from https://tidsskrift.dk/NOMAD/article/view/149051

Issue

Section

Articles