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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.

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Notes

  1. This can also be described as a process of recontextualisation by recontextualising fields (Bernstein, 2000; Dowling, 2014).

  2. The title of this paper alludes to Freudenthal (1973).

  3. Skovsmose (2005, pp. 140–143) makes a distinction between constructors, operators and consumers, recognising that people are affected by or involved in technology in different ways. Constructors develop the technology and are in a position to regard the technology as white boxes, whereas the operators are those that make their working decisions based on input and output values and relate to the technology, more or less, as black boxes (cf. Williams & Wake, 2007a).

  4. For references regarding the terms used, see Velten (2009).

  5. The distinction with the corresponding types of models was made in Velten (2009) by the terms phenomenological and mechanistic models, respectively; see Section 2 above.

  6. Chevallard (2006, p. 22) defines didactics as “the science of the diffusion of knowledge in any social group”.

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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.

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Authors and Affiliations

  1. Department of Mathematics, Linköping University, SE-581 83, Linköping, Sweden

    Peter Frejd & Christer Bergsten

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  1. Peter Frejd
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  2. Christer Bergsten
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Correspondence to Peter Frejd.

Appendix

Appendix

Interview questions

The main aim of the interview question is to find:

1. What is your academic background?

Background information

2. What are you working life experiences before you got here?

Background information

3. What is your profession and what role does mathematical modelling play in your profession?

Background information

4. What does mathematical modelling mean to you? Has your view on modelling changed during the years? (If yes) How?

Constructors’ conceptions

5. Make a general description of how you work with a modelling problem (from start to end).

Pre-construction, construction, post- construction

6. Who gives you the problems to work with? What type of problems do you work with? What are the aims with the problems you get?

Pre-construction

7. What will be the use of the model? Who sets the goal for the mathematical activity? Who defines the criteria?

Pre-construction

8. How do you work with mathematical modelling in your profession (by yourself, in groups)? If it is group work how/what communication takes place? What types of artefacts are used?

Construction

9. What kind of models do you develop (static/dynamic, deterministic/stochastic, discrete/continuous, analytic/simulations)?

Construction

10. What are the connections between input and output?

Construction

11. How was the necessary measurement data obtained? Is there a way to control the quality and the origin of the data? Can you give example of values and quantity of the data?

Construction

12. What factors may have affected the investigated phenomena (measuring instrument or its use)?

Construction

13. Is it possible to control the result? What types of assumptions have been made according to the context? Who decide what assumptions are important? What is the accuracy of the result?

Construction

14. How does the solution contribute to understanding and action?

Construction

15. What is an acceptable solution? Are there other solutions? (if yes) How do you decide which solution?

Construction

16. Are there any risks to use the result? If so, how is that considered? Are ethical issues discussed?

Post-construction

17. Is mathematical modelling something that was a part of your education in school or something you learned in your profession?

Background information

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Frejd, P., Bergsten, C. Mathematical modelling as a professional task. Educ Stud Math 91, 11–35 (2016). https://doi.org/10.1007/s10649-015-9654-7

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