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Towards understanding teachers’ beliefs and affects about mathematical modelling
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2009 (English)Conference paper (Other academic)
Abstract [en]

Work in progress on a framework aiming at capturing teachers’ beliefs about mathematical models and modelling is presented. It is suggested that the belief structure of mathematical models and modelling as perceived by teachers fruitfully might be explored as partly constituted of the teachers’ beliefs about the real world, the nature of mathematics, school mathematics, and applying and applications of mathematics. Some aspects of the suggested framework are explored using two case study interviews. It is found that the two teachers do not have any well formed beliefs about mathematical models and modelling, and that the interpreted beliefs structure of the teachers contain inconsistencies which are made explicit within the framework. The empiric findings also suggest some modifications of the framework.

Place, publisher, year, edition, pages
National Category
URN: urn:nbn:se:liu:diva-54316OAI: diva2:302714
CERME 6 - Sixth Conference of European Research in Mathematics Education Lyon, France, January 28 - February1
Available from: 2010-03-09 Created: 2010-03-09 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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Mathematics and Applied MathematicsThe Institute of Technology

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