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First results from a study investigating Swedish upper secondary students’ mathematical modelling competencies
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2009 (English)Conference paper, Published paper (Other academic)
Abstract [en]

This paper reports on the first results from a study investigating Swedish upper secondary students’ (11th – 12th grade) mathematical modelling competency. Using non-parametric statistical methods the data from 381 students are analysed and the students’ modelling competency is described in terms of seven subcompetencies. Possible factors affecting the students’ mathematical competency such as attitudes toward modelling, previous experiences, last taken mathematics course, grade, class and gender were also investigated.

Place, publisher, year, edition, pages
2009.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-54317OAI: oai:DiVA.org:liu-54317DiVA: diva2:302716
Conference
14th International Conference on the Teaching of Mathematical Modelling and Applications (ICTMA 14), University of Hamburg, 27th to 31st July, Germany
Available from: 2010-03-09 Created: 2010-03-09 Last updated: 2014-06-23Bibliographically approved
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.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1289
National Category
Mathematics
Identifiers
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)
Opponent
Supervisors
Available from: 2010-03-30 Created: 2010-03-09 Last updated: 2016-11-30Bibliographically approved
2. Mathematical modelling in upper secondary school in Sweden: An exploratory investigation
Open this publication in new window or tab >>Mathematical modelling in upper secondary school in Sweden: An exploratory investigation
2011 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

The official curriculum guidelines for upper secondary school in Sweden emphasise the use of mathematical models and mathematical modelling in mathematics education. However, no explicit definitions or descriptions of the notions are given in the curriculum. This licentiate thesis is an exploratory study which investigates teachers’ and students’ conceptions of the notion of mathematical modelling as well as their attitudes and experiences of working with mathematical modelling in mathematics classrooms. One experience of mathematical modelling that faces both students and teachers which is investigated is the national course tests in mathematics.

The thesis includes five papers and a preamble, where the papers are summarised, analysed, and discussed. Both quantitative and qualitative methods are being used in the thesis and theoretical aspects concerning mathematical modelling and conceptions are examined.

The results indicate that mathematical modelling plays a minor role in the investigated mathematics classrooms. The students as well as the teachers were not familiar with the notion of mathematical modelling. Only 23% of the 381 students and 50 % of the 18 teachers had heard the notion before participating in the study. Both teachers and students participating in this study expressed a variety of different interpretations of the notion of mathematical modelling. Negative attitudes were expressed by the students as well as by some of the teachers concerning mathematical modelling. These negative attitudes may present obstacles for implementing mathematical modelling in the upper secondary mathematics classroom. However, these negative attitudes are related to the used test items, which may have had a negative impact on the research, especially, as the test items only test parts of the modelling process. One dominant conception found among the teachers was that mathematical modelling is related to physics or chemistry. The conclusion made from the investigation about national course tests in mathematics course D, is that there is a lack of holistic assessment of mathematical modelling. Intra-mathematical aspects of mathematical modelling are put in favour for extra-mathematical aspects.

Researchers argue that if we want develop students’ modelling competency, than modelling has to be explicitly used and practised in the mathematics classrooms. However, for the Swedish upper secondary school this study concludes that this is not the case. A suggestion for future research is to focus on mathematical modelling in teacher education and design studies of incorporation of modelling activities into mathematics classrooms.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2011. 72 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1471Studies in Science and Technology Education, ISSN 1652-5051 ; 37
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-66304 (URN)978-91-7393-223-3 (ISBN)
Presentation
2011-03-22, 10:15 (Swedish)
Supervisors
Available from: 2011-03-11 Created: 2011-03-11 Last updated: 2016-11-30Bibliographically approved

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Frejd, PeterBergman Ärlebäck, Jonas

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