An analysis of mathematical modelling in Swedish textbooks in upper secondary school
DOI:
https://doi.org/10.7146/nomad.v18i3.148516Abstract
A new national curriculum has recently been implemented in the Swedish upper sec-ondary school where one of the goals to be taught is modelling ability. This paper presents a content analysis of 14 ”new” mathematical textbooks with the aim to investigate how the notion of mathematical modelling is presented. An analytic scheme is developed to identify mathematical modelling in the textbooks and to analyse modelling tasks and instructions. Results of the analysis show that there exist a variety of both explicit and implicit descriptions, which imply for teachers to be attentive to complement the textbooks with other material.
References
Alfredsson, L., Bråting, K., Erixon, P. & Heikne, H. (2011). Matematik 5000. Stockholm: Natur & Kultur.
Blomhøj, M. & Kjeldsen, T. H. (2006). Teaching mathematical modeling through project work. ZDM, 38 (2), 163-177. https://doi.org/10.1007/BF02655887
Blomhøj, M. & Højgaard Jensen, T. (2007). What's all the fuss about competencies? In W. Blum, P. L. Galbraith, H. Henn & M. Niss (Eds.), Modelling and applications in mathematics education. The 14th ICMI study (pp. 45-56). New York: Springer. https://doi.org/10.1007/978-0-387-29822-1_3
Blomhøj, M. & Højgaard Jensen, T. (2003). Developing mathematical modelling competence: conceptual clarification and educational planning. Teaching Mathematics and its Applications, 22 (3), 123-139. https://doi.org/10.1093/teamat/22.3.123
Blum, W., Galbraith, P.L., Henn, H. & Niss, M. (Eds.). (2007). Modelling and applications in mathematics education. The 14th ICMI study. New York: Springer. https://doi.org/10.1007/978-0-387-29822-1
Blum, W. & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects: state, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22 (1), 37-68. https://doi.org/10.1007/BF00302716
Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38 (2), 86-95. https://doi.org/10.1007/BF02655883
Cabassut, R. & Wagner, A. (2011). Modelling at primary school through a French-German comparison of curricula and textbooks. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 559-568) Springer: New York. https://doi.org/10.1007/978-94-007-0910-2_54
Charalambous, C.Y., Delaney, S., Hsu, H. & Mesa, V. (2010). A comparison analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning, 12, 117-151. https://doi.org/10.1080/10986060903460070
Chávez, O. (2003). From the textbook to the enacted curriculum: textbook use in the middle school mathematics classroom (Unpublished doctoral theses). University of Missouri, Columbia.
Dowling, P. (1996). A sociological analysis of school mathematics texts. Educational Studies in Mathematics, 31, 389-415. https://doi.org/10.1007/BF00369156
Fan, L. & Zhu, Y. (2007). Representation of problem-solving procedures: a comparative look at China, Singapore and US mathematics textbooks. Educational Studies in Mathematics, 66, 61-75. https://doi.org/10.1007/s10649-006-9069-6
Frejd, P. (2011). Mathematical modelling in upper secondary school in Sweden: an exploratory study (Licentiate thesis). Linköping University.
Garcia, F. Gascón, J. Higueras, L. & Bosch, M. (2006). Mathematical modelling as a tool for the connection of school mathematics. ZDM, 38 (3), 226-246. https://doi.org/10.1007/BF02652807
Gatabi, A., Stacey, K. & Gooya, Z. (2012). Investigating grade nine textbook problems for characteristics related to mathematical literacy. Mathematics Education Research Journal, 24 (4), 403-421. https://doi.org/10.1007/s13394-012-0052-5
Gennow, S., Gustafsson, I.-M. & Silborn, B. (2011). Exponent. Malmö: Gleerups utbildning.
Haggarty, L. & Pepin, B. (2002). An investigation of mathematics textbooks and their use in English, French and German classrooms: Who gets an opportunity to learn what? British Educational Research Journal, 28 (4), 567-590. https://doi.org/10.1080/0141192022000005832
Ikeda, T. (2007). Possibilities for, and obstacles to teaching and applications and modeling in lower secondary levels. In W. Blum, P. L. Galbraith, H. Henn & M. Niss (Eds.), Modelling and applications in mathematics education. The 14th ICMI study (pp. 457-462). New York: Springer. https://doi.org/10.1007/978-0-387-29822-1_51
Jablonka, E. (2010). Reflections on mathematical modelling. In H. Alrø, O. Ravn & P. Valero (Eds.), Critical mathematics education: past, present and future. Festschrift for Ole Skovsmose (pp. 89-100). Rotterdam: Sense Publishers. https://doi.org/10.1163/9789460911644_008
Jablonka, E. & Gellert, U. (2007). Mathematisation - demathematisation. In U. Gellert & E. Jablonka (Eds.), Mathematisation and demathematisation: social, philosophical and educational ramifications (pp. 1-18). Rotterdam: Sense Publishers. https://doi.org/10.1163/9789460911439_002
Jablonka, E. & Johanssson, M. (2010). Using texts and tasks: Swedish studies on mathematic textbooks. In B. Sriraman et al. (Eds.), The first sourcebook of Nordic research in mathematics education (pp. 269-282). Charlotte: Information Age Publishing.
Jakobsson-Åhl, T. (2008). Word problems in upper secondary algebra in Sweden over the years 1960-2000. Nordic Studies in Mathematics Education, 13 (1), 7-28.
Johansson, L.-G. & Olsson, T. (2011). Exponent. Malmö: Gleerups utbildning.
Johansson, M. (2005). The mathematics textbook. From artefact to instrument. Nordic Studies in Mathematics Education, 10 (3-4), 43-64.
Kaiser, G. & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38 (3), 302-310. https://doi.org/10.1007/BF02652813
Kongelf, T.R. (2011). What characterises the heuristic approaches in mathematics textbooks used in lower secondary schools in Norway? Nordic Studies in Mathematics Education, 16 (4), 5-44.
Lesh, R. & Zawojewski, J. S. (2007). Problem solving and modeling. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning: a project of the National Council of Teachers of Mathematics (Vol. 2, pp. 763-804). Charlotte: Information Age Pub.
Lester, F.K. (1994). Musings about mathematical problem-solving research 1970-1994. Journal for Research in Mathematics Education, 25, 660-675. https://doi.org/10.2307/749578
Lu, X. & Bao, J. (2012). Comparative study on mathematics applications in mathematics textbooks. In Pre-proceedings of ICME12, The 12th International congress on mathematics education, Seoul, Korea, July 8-15, 2012 (pp. 3451- 3460).
Mayer, R.E., Sims, V. & Tajika, H. (1995). A comparison of how textbooks teach mathematical problem solving in Japan and the United States. American Educational Research Journal, 32 (20), 443-460. https://doi.org/10.2307/1163438
Niss, M. (1993a). Assessment in mathematics education and its effects: an introduction. In M. Niss. (Ed.), Investigations into assessment in mathematics education: an ICMI Study (pp. 1-30). Dordrecht: Kluwer. https://doi.org/10.1007/978-94-017-1974-2_1
Niss, M., Blum, W. & Galbraith, P.L. (2007). Introduction. In W. Blum, P.L. Galbraith, H. Henn & M. Niss (Eds.), Modelling and applications in mathematics education. The 14th ICMI study (pp. 3-32). New York: Springer. https://doi.org/10.1007/978-0-387-29822-1_1
Oke, K.H. & Bajpai, A.C. (1986). Assessment in mathematical modelling. In Berry, J.S., Burghes, D.N., Huntley, I.D., James, D.J.G. & Moscardini, A.O. (Eds.), Mathematical modelling methodology, models and micros (pp. 48-60). Chichester: Ellis Horwood.
Perrenet, J. & Zwaneveld, B. (2012). The many faces of the mathematical modeling cycle. Journal of Mathematical Modelling and Application, 1 (6), 3-21.
Reys, B. J., Reys, R. R. & Chávez, O. (2004). Why mathematics textbooks matter. Educational Leadership, 61 (5), 61-66.
Robson, C. (2002). Real world research: a resource for social scientists and practitioner-researchers (2nd. ed.). Oxford: Blackwell.
Rowlands, S. (2003). Misunderstanding modelling in mechanics: a review of the A-level textbook literature. Research in Mathematics Education, 5 (1), 97-120. https://doi.org/10.1080/14794800008520117
Schoenfeld, A.H. (1992). Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334-370). New York: Macmillan Publishing Company.
Sjunnesson, J., Holmström, M. & Smedhamre, E. (2011). Matematik M. Stockholm: Liber.
Skolverket. (2010). Förordning om ämnesplaner för de gymnasiegemensamma ämnena. Retrieved October 2, 2013 from http://www.skolverket.se/ publikationer?id=2705
Skolverket. (2011). Curriculum for the compulsory school, preschool class and the leisure-time centre 2011. Retrieved October 2, 2013 from http://www. skolverket.se/publikationer?id=2687
Skolverket. (2012). The subject syllabus for mathematics. Retrieved October 2, 2013 from http://www.skolverket.se/polopoly_fs/1.174554!/Menu/article/attachment/Mathematics.pdf
Skovsmose, O. (2006). Travelling through education. Uncertainty, mathematics, responsibility. Rotterdam: Sense Publishers. https://doi.org/10.1163/9789087903626
Stanic, G. M. A. & Kilpatrick, J. (1989). Historical perspectives on problem solving in mathematics curriculum. In R. I. Charles & E. A. Silver (Eds.), The teaching and assessing of mathematical problem solving (pp. 1-22). Reston: NCTM.
Szabo, A., Larsson, N., Viklund, G., Dufåker, D. & Marklund, M. (2011). Matematik Origo. Stockholm: Bonnier utbildning.
Viklund, G., Gustafsson, B. & Norberg, A. (2011). Matematik 1a. Stockholm: Bonnier utbildning.
Ärlebäck, J. B. (2009). Mathematical modelling in upper secondary mathematics education in Sweden (Doctoral dissertation). Linköping University.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.