On the Use of Realistic Fermi Problems in Introducing Mathematical Modelling in Upper Secondary Mathematics
This paper reports a study investigating potential uses of Fermi problems to introduce mathematical modelling to Swedish upper secondary school students. The work of three groups of students’ is analysed using an analytic tool referred to as the “modellin
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On the Use of Realistic Fermi Problems in Introducing Mathematical Modelling in Upper Secondary Mathematics Jonas Bergman Ärlebäck and Christer Bergsten
Abstract This paper reports a study investigating potential uses of Fermi problems to introduce mathematical modelling to Swedish upper secondary school students. The work of three groups of students’ is analysed using an analytic tool referred to as the “modelling activity diagram”, adapted and developed by the author. It was observed that the processes involved in a mathematical modelling cycle were richly represented in groups’ solution. The students also frequently used their personal extra-mathematical knowledge in the solving process in three different ways: a creative, a verifying and a social way.
52.1 Introduction From the curriculum documents governing mathematics education in Swedish upper secondary school, one can identify an increased emphasis on mathematical modelling. However, as Lingefjärd (2006) states, “it seems that the more mathematical modeling is pointed out as an important competence to obtain for each student in the Swedish school system, the vaguer the label becomes” (p. 96). It is natural to ask why this is the case and what one can do about it. Research in this area is lacking in Sweden, but challenges and barriers to overcome are likely to be similar to those reported by Burkhardt (2006). Some support for this assumption is found in research reports on the dominant role of the use of traditional textbooks in Swedish mathematics classrooms, greatly influencing class organisation as well as content (Skolverket, 2003).
J.B. Ärlebäck (B) Linköpings Universitet, Linköping, Sweden e-mail: [email protected] C. Bergsten (B) Linköpings Universitet, Linköping, Sweden e-mail: [email protected] R. Lesh et al. (eds.), Modeling Students’ Mathematical Modeling Competencies, International Perspectives on the Teaching and Learning of Mathematical Modelling, DOI 10.1007/978-94-007-6271-8_52, © Springer Science+Business Media Dordrecht 2013
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J.B. Ärlebäck and C. Bergsten
The study reported here is part of a bigger research project aiming both to get an overall picture of the past and present state and status of mathematical modelling in the Swedish upper secondary school, and to design, implement and evaluate small lesson sequences on mathematical modelling, in line with the Swedish national curriculum. The aim of the pilot study which this paper reports is to investigate the potential of using Fermi problems to introduce mathematical modelling at the Swedish upper secondary level. More specifically the research question can be stated as follows. What mathematical modelling sub-activities do realistic Fermi problems activate? To answer this question, we first briefly discuss Fermi problems and mathematical modelling, before looking at the previous research done in connection with this area. Then, we describe the methodology, the definition of realistic Fermi Problems, and the concept of mathematical modelling sub-activities, be
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