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An analysis of mathematical modelling in Swedish textbooks in upper secondary school
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2013 (English)In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 18, no 3, 59-95 p.Article in journal (Refereed) Published
Abstract [en]

A new national curriculum has recently been implemented in the Swedish upper secondaryschool where one of the goals to be taught is modelling ability. This paperpresents a content analysis of 14 ”new” mathematical textbooks with the aim to investigatehow the notion of mathematical modelling is presented. An analytic scheme isdeveloped to identify mathematical modelling in the textbooks and to analyse modellingtasks and instructions. Results of the analysis show that there exist a variety ofboth explicit and implicit descriptions, which imply for teachers to be attentive tocomplement the textbooks with other material.

Place, publisher, year, edition, pages
2013. Vol. 18, no 3, 59-95 p.
National Category
URN: urn:nbn:se:liu:diva-103031OAI: diva2:685954
Available from: 2014-01-10 Created: 2014-01-10 Last updated: 2014-01-27Bibliographically approved
In thesis
1. Modes of Mathematical Modelling: An analysis of how modelling is used and interpreted in and out of school settings
Open this publication in new window or tab >>Modes of Mathematical Modelling: An analysis of how modelling is used and interpreted in and out of school settings
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The relevance of using mathematics in and for out-of-school activities is one main argument for teaching mathematics in education. Mathematical modelling is considered as a bridge between the mathematics learned and taught in schools and the mathematics used at the workplace and in society and it is also a central notion in the present Swedish mathematical syllabus for upper secondary school. This doctoral thesis reports on students’, teachers’ and modelling experts’ experiences of, learning, teaching and working with mathematical modelling in and out of school settings and their interpretations of the notion of mathematical modelling.

The thesis includes five papers and a preamble, where the papers are summarised, analysed, and discussed. Different methods are being used in the thesis such as video analysis of students’ collaboration working with modelling problem, interview investigations with teachers and expert modellers, content analysis of textbooks and literature review of modelling assessment. Theoretical aspects concerning mathematical modelling and the didactic transposition of modelling are examined.

The results presented in this thesis provide a fragmented picture of the didactic transposition of mathematical modelling in school mathematics in Sweden. There are significant differences in how modellers, teachers and students work with modelling in different practices in terms of the goal with the modelling activity, the risks involved in using the models, the use of technology, division of labour and the construction of mathematical models. However, there are also similarities identified described as important aspects of modelling work in the different practices, such as communication, collaboration, projects, and the use of applying and adapting pre-defined models. Students, teachers and modellers expressed a variety of descriptions of what modelling means. The variety of descriptions in the workplace is not surprising, since their working approaches are quite different, but it makes the notion difficult to transpose into school practise. Questions raised are if it is unrealistic to search for a general definition and if it is really necessary to have a general definition. The consequence, for anyone how uses the notion, is to always be explicit with the meaning.

An implication for teaching is that modelling as it shows in the workplace can never be fully ‘mapped’ in the mathematical classroom. However, it may be possible to ‘simulate’ such activity. Working with mathematical modelling in projects is suggested to simulate workplace activities, which include collaboration and communication between different participants. The modelling problems may for example involve economic and environmental decisions, to prepare students to be critically aware of the use of mathematics in private life and in society, where many decisions are based on mathematical models.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2014. 135 + 1 Appendix p.
Linköping Studies in Behavioural Science, ISSN 1654-2029 ; 181
National Category
Didactics Mathematics
urn:nbn:se:liu:diva-103689 (URN)10.3384/diss.diva-103689 (DOI)978-91-7519-414-1 (print) (ISBN)
Public defence
2014-02-14, C3, hus C, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Available from: 2014-01-23 Created: 2014-01-23 Last updated: 2014-01-23Bibliographically approved

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