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On the use of realistic Fermi problems for introducingmathematical modelling in school
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2009 (English)In: The Montana Mathematics Enthusiast, ISSN 1551-3440, Vol. 6, no 3, 331-364 p.Article in journal (Refereed) Published
Abstract [en]

In this paper an analytical tool referred to as the MAD (Modelling Activity Diagram) framework adapted from Schoenfeld’s parsing protocol coding scheme is used to address the issues of how to introduce mathematical modelling to upper secondary students. The work of three groups of students engaged in solving so called realistic Fermi problems were analysed using this framework, and it was observed that the processes involved in a typical mathematical modelling cycle were richly represented in the groups’ solving processes. The importance of the social interactions within the groups was noted, as well as the extensive use of extra-mathematical knowledge used by the students during the problem solving session.

Place, publisher, year, edition, pages
Montana Council of Teachers of Mathematics & Information Age Publishing , 2009. Vol. 6, no 3, 331-364 p.
Keyword [en]
Fermi problems, Fermi estimates, Modelling cycles, Mathematical modelling, Modelling activity diagram
National Category
URN: urn:nbn:se:liu:diva-54664OAI: diva2:306585
Available from: 2010-03-30 Created: 2010-03-30 Last updated: 2014-06-23
In thesis
1. Mathematical modelling in upper secondary mathematics education in Sweden
Open this publication in new window or tab >>Mathematical modelling in upper secondary mathematics education in Sweden
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The aim of this thesis is to investigate and enhance our understanding of the notions of mathematical models and modelling at the Swedish upper secondary school level. Focus is on how mathematical models and modelling are viewed by the different actors in the school system, and what characterises the collaborative process of a didactician and a group of teachers engaged in designing and developing, implementing and evaluating teaching modules (so called modelling modules) exposing students to mathematical modelling in line with the present mathematics curriculum. The thesis consists of five papers and reports, along with a summary introduction, addressing both theoretical and empirical aspects of mathematical modelling.

The thesis uses both qualitative and quantitative methods and draws partly on design-based research methodology and cultural-historical activity theory (CHAT). The results of the thesis are presented using the structure of the three curriculum levels of the intended, potentially implemented, and attained curriculum respectively.

The results show that since 1965 and to the present day, gradually more and more explicit emphasis has been put on mathematical models and modelling in the syllabuses at this school level. However, no explicit definitions of these notions are provided but described only implicitly, opening up for a diversity of interpretations.

From the collaborative work case study it is concluded that the participating teachers could not express a clear conception of the notions mathematical models or modelling, that the designing process often was restrained by constraints originating from the local school context, and that working with modelling highlights many systemic tensions in the established school practice. In addition, meta-results in form of suggestions of how to resolve different kinds of tensions in order to improve the study design are reported.

In a questionnaire study with 381 participating students it is concluded that only one out of four students stated that they had heard about or used mathematical models or modelling in their education before, and the expressed overall attitudes towards working with mathematical modelling as represented in the test items were negative. Students’ modelling proficiency was positively affected by the students’ grade, last taken mathematics course, and if they thought the problems in the tests were easy or interesting. In addition empirical findings indicate that so-called realistic Fermi problems given to students working in groups inherently evoke modelling activities.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2010. 75 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1289
National Category
urn:nbn:se:liu:diva-54318 (URN)978-91-7393-488-6 (ISBN)
Public defence
2010-03-12, C3, hus C, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Available from: 2010-03-30 Created: 2010-03-09 Last updated: 2010-03-30Bibliographically approved

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Bergman Ärlebäck, Jonas
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