# Mathematical modelling as a professional task

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## Abstract

Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model constructors. The research question was: How can mathematical modelling by professional mathematical model constructors be characterised? The analysis of our interview data inspired by the coding procedure of grounded theory led us to the description of three main types of modelling activities as a characterisation of mathematical modelling as a professional task. In data-generated modelling the models are developed principally from quantitative data drawing on no or only some assumed knowledge of the system being modelled, while in theory-generated modelling the models are developed based on established theory. In the third activity, model-generated modelling, the development of new models is based on already established models. For all types, the use of computer support and communication between clients, constructors and other experts are central aspects. Finally, the three types of modelling activities are related to existing theoretical descriptions of mathematical modelling and the relevance of the study for mathematical modelling in education is discussed.

## Keywords

Mathematical modelling Workplace mathematics Computer support Didactic transposition## Notes

### Acknowledgments

We wish to thank the reviewers and the editor for valuable and constructive comments to earlier versions of this paper, as well as the participants in our study who so generously shared their experiences.

## References

- Ärlebäck, J. B. (2009).
*Mathematical modelling in upper secondary mathematics education in Sweden. A curricula and design study*. Dissertation. Linköping: Linköpings universitet.Google Scholar - Bernstein, B. (2000).
*Pedagogy, symbolic control and identity. Theory, research, critique*. New York: Rowman & Littlefield.Google Scholar - Bissell, C., & Dillon, C. (2000). Telling tales: Models, stories and meanings.
*For the Learning of Mathematics, 20*(3), 3–11.Google Scholar - Blomhøj, M., & Hoff Kjeldsen, T. (2006). Teaching mathematical modelling through project work.
*ZDM, 38*(2), 163–177.CrossRefGoogle Scholar - Blum, W., Galbraith, P. L., Henn, H., & Niss, M. (Eds.). (2007).
*Modelling and applications in mathematics education. The 14th ICMI study*. New York: Springer.Google Scholar - Blum, W., & Leiss, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. L. Galbraith, W. Blum, & S. Khan (Eds.),
*Mathematical Modelling (ICTMA12): Education, Engineering and Economics*(pp. 222–231). Chichester: Horwood Academic.Google Scholar - Boeije, H. (2010).
*Analysis in qualitative research*. Los Angeles and London: Sage.Google Scholar - Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process.
*ZDM, 38*(2), 86–95.CrossRefGoogle Scholar - Bosch, M., & Gascón, J. (2006). 25 years of the didactic transposition.
*ICMI Bulletin, 58*, 51–65.Google Scholar - Bryman, A. (2004).
*Social research methods*(2nd ed.). Oxford: Oxford University Press.Google Scholar - Chevallard, Y. (1991).
*La transposition didactique—Du savoir savant au savoir enseigné*. Grenoble: La Pensée sauvage.Google Scholar - Chevallard, Y. (2006). Steps towards a new epistemology in mathematics education. In M. Bosch (Ed.),
*Proceedings of Fourth Congress of the European Society for Research in Mathematics Education*(pp. 21–30). Barcelona, Spain: FUNDEMI IQS—Universitat Ramon Llull.Google Scholar - Dierdorp, A, Bakker, A., van Maanen, J. A., & Eijkelhof, H. (2014). Meaningful statistics in professional practices as a bridge between mathematics and science: an evaluation of a design research project.
*International Journal of STEM Education, 1*:9 (15 November 2014). Retrieved from: http://www.stemeducationjournal.com/content/1/1/9 - Dowling, P. (2014). Recontextualisation in mathematics education. In S. Lerman (Ed.),
*Encyclopedia of mathematics education*(pp. 525–529). Dordrecht: Springer Reference.Google Scholar - Drakes, C. I. (2012).
*Mathematical modelling: From novice to expert*. Dissertation. Simon Fraser University.Google Scholar - Frejd, P. (2011). An investigation of mathematical modelling in the Swedish national course tests in mathematics. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.),
*Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education*(pp. 947–956). Poland: University of Rzeszów.Google Scholar - Frejd, P. (2013). An analysis of mathematical modelling in Swedish textbooks in upper secondary school.
*Nordic Studies in Mathematics Education, 18*(3), 59–95.Google Scholar - Freudenthal, H. (1973).
*Mathematics as an educational task*. Dordrecht: Kluwer.Google Scholar - Gainsburg, J. (2003).
*The mathematical behavior of structural engineers*(Unpublished doctoral dissertation). Stanford University, USA. Google Scholar - Geiger, V., & Frejd, P. (2015). A reflection on mathematical modelling and applications as a field of research: Theoretical orientation and diversity. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.),
*Mathematical modelling in education research and practice: Cultural, Social and Cognitive Influences*(pp. 161–171). New York, NY: Springer.CrossRefGoogle Scholar - Greefrath, G. (2011). Using technologies: New possibilities of teaching and learning modelling—Overview. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.),
*Trends in teaching and learning of mathematical modelling, ICTMA 14*(pp. 301–304). Dordrecht: Springer.CrossRefGoogle Scholar - Harris, M. (1991). Looking for the maths in work. In M. Harris (Ed.),
*Schools, mathematics and work*. New York: Falmer Press.Google Scholar - Hoyles, C., Wolf, A., Molyneux-Hodgson, S., & Kent, P. (2002).
*Mathematical skills in the workplace: Final report to the Science, Technology and Mathematics Council*. London: Institute of Education, University of London, and Science, Technology and Mathematics Council. Retrieved from http://eprints.ioe.ac.uk/1565/. - Hunt, J. (2007). Communicating big themes in applied mathematics. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.),
*Mathematical modelling (ICTMA 12): Education, engineering and economics: Proceedings from the Twelfth International Conference on the Teaching of Mathematical Modelling and Applications*(pp. 2–24). Chichester: Horwood.Google Scholar - Jablonka, E. (1996).
*Meta-Analyse von Zugängen zur mathematischen Modellbildung und Konsequenzen für den Unterricht*[Analyses of approaches to mathematical modelling and educational consequences] (Doctoral dissertation). Retrieved from Transparent-Verlag Berlin. Google Scholar - Jablonka, E. (1997). What makes a model effective and useful (or not)? In S. K. Houston, W. Blum, I. D. Huntley, & N. T. Neill (Eds.),
*Teaching and learning mathematical modelling*(pp. 39–50). Chichester, UK: Albion Publishing.Google Scholar - Jablonka, E. (2007). The relevance of modelling and applications: Relevant to whom and for what purpose? In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.),
*Modelling and applications in mathematics education: The 14th ICMI Study*(pp. 193–200). New York, NY: Springer.Google Scholar - 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.Google Scholar - Kaiser, G., Blomhøj, M., & Sriraman, B. (2006). Towards a didactical theory for mathematical modelling.
*ZDM, 38*(2), 82–85.CrossRefGoogle Scholar - Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education.
*ZDM, 38*(3), 302–310.CrossRefGoogle Scholar - Lesh, R., & Doerr, H. M. (Eds.). (2003).
*Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching*. Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar - Morrison, M., & Morgan, M. (1999).
*Models as mediators*. Cambridge: Cambridge University Press.Google Scholar - NIBIB - National Institute of Biomedical Imaging and Bioengineering (2013).
*Computational modelling*. Retrieved from http://www.nibib.nih.gov/science-education/science-topics/computational-modeling. - Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.),
*Modelling and applications in mathematics education. The 14th ICMI Study*(pp. 3–32). New York, NY: Springer.CrossRefGoogle Scholar - Noss, R., Bakker, A., Hoyles, C., & Kent, P. (2007). Situating graphs as workplace knowledge.
*Educational Studies in Mathematics, 65*(3), 367–384.CrossRefGoogle Scholar - Noss, R., & Hoyles, C. (1996). The visibility of meanings: modelling the mathematics of banking.
*International Journal of Computers for Mathematical Learning, 1*(17), 3–31.Google Scholar - Oke, K. H., & Bajpai, A. C. (1986). Assessment in mathematical modelling. In J. S. Berry, D. N. Burghes, I. D. Huntley, D. J. G. James, & A. O. Moscardini (Eds.),
*Mathematical modelling methodology, models and micros*(pp. 48–60). Chichester: Ellis Horwood.Google Scholar - Perrenet, J., & Zwaneveld, B. (2012). The many faces of the mathematical modeling cycle.
*Journal of Mathematical Modelling and Application, 1*(6), 3–21.Google Scholar - Schmidt, B. (2012).
*Modelling in mathematics classrooms. Motives and obstacles from the teachers’ perspective*. Hildesheim: Franzbecker.Google Scholar - SIAM (Society for Industrial and Applied Mathematics). (2012).
*Report on Mathematics in Industry*. Philadelphia: SIAM. Retrieved from http://www.siam.org/reports/ - Siller, H.-S., & Greefrath, G. (2010). Mathematical modelling in class regarding to technology. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.),
*Proceedings of the Sixth Conference of the European Society for Research in Mathematics Education - CERME6*(pp. 2136–2145). Lyon, France: Institut National de Recherche Pédagogique.Google Scholar - Skovsmose, O. (2005).
*Travelling through education. Uncertainty, mathematics, responsibility*. Rotterdam: Sense Publishers.Google Scholar - Solomatine, D. P., & Ostfeld, A. (2008). Data-driven modelling: Some past experiences and new approaches.
*Journal of Hydroinformatics, 10*(1), 3–22.CrossRefGoogle Scholar - Sriraman, B., & Kaiser, G. (2006). Theory usage and theoretical trends in Europe: A survey and preliminary analysis of CERME4 research reports.
*ZDM, 38*(1), 22–51.CrossRefGoogle Scholar - Sträßer, R., Damlamian, A., & Rodrigues, J. F. (2012). Educational interfaces between mathematics and industry (ICMI-ICIAM-Study 20). In
*Pre-proceedings of ICME12, The 12th International congress on mathematics education, Seoul, Korea, July 8–15, 2012*(pp. 7863–7874). Retrieved from http://www.icme12.org/. - Strauss, A. L., & Corbin, J. M. (1998).
*Basics of qualitative research: techniques and procedures for developing grounded theory*(2nd ed.). Thousand Oaks, CA: Sage.Google Scholar - Triantafillou, C., & Potari, D. (2010). Mathematical practices in a technological workplace: The role of tools.
*Educational Studies in Mathematics, 74*, 275–294.CrossRefGoogle Scholar - Van der Valk, T., Van Driel, J. H., & De Vos, W. (2007). Common characteristics of models in present-day scientific practice.
*Research in Science Education, 37*(4), 469–488.CrossRefGoogle Scholar - Van der Velde, W. (2007). The world as computer. In P. T. Kidd (Ed.),
*European visions for the knowledge age: A quest for new horizons in the information society*(pp. 205–216). Macclesfield, UK: Cheshire Henbury.Google Scholar - Velten, K. (2009).
*Mathematical modeling and simulation. Introduction for scientists and engineers*. Weinheim, Germany: WILEY-VCH Verlag GmbH & Co. KGaA.Google Scholar - Wake, G. (2007). Considering workplace activity from a mathematical modelling perspective. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.),
*Modelling and applications in mathematics education*(pp. 395–402). New York, NY: Springer.CrossRefGoogle Scholar - Wake, G. (2012). Seeking principles of design for general mathematics curricula informed by research of use of mathematics in workplace contexts. In
*Pre-proceedings of ICME12, Seoul, Korea, July 8–15, 2012*(pp. 1679–1688). Retrieved from http://www.icme12.org/. - Wake, G. (2014). Making sense of and with mathematics: The interface between academic mathematics and mathematics in practice.
*Educational Studies in Mathematics, 86*, 271–290.Google Scholar - Wedege, T. (2010). Researching workers’ mathematics at work. In A. Araújo, A. Fernandes, A. Azevedo, & J. F. Rodrigues (Eds.),
*Educational interfaces between mathematics and industry. Proceedings of EIMI 2010 Lisbon conference*(pp. 565–574). Portugal: Centro International de Matemática.Google Scholar - Wikipedia (n.d.).
*Computational model*. Retrieved from en.wikipedia.org/wiki/Computational_model. - Williams, J., & Goos, M. (2013). Modelling with mathematics and technologies. In M. A. Clements, A. J. Bishop, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.),
*Third international handbook of mathematics education*(pp. 549–569). Berlin: Springer.Google Scholar - Williams, J., & Wake, G. (2007a). Black boxes in workplace mathematics.
*Educational Studies in Mathematics, 64*(3), 317–343.CrossRefGoogle Scholar - Williams, J., & Wake, G. (2007b). Metaphors and models in translation between college and workplace mathematics.
*Educational Studies in Mathematics, 64*(3), 345–371.CrossRefGoogle Scholar