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Mathematical modelling in upper secondary mathematics education in Sweden
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
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: urn:nbn:se:liu:diva-54318ISBN: 978-91-7393-488-6 (print)OAI: oai:DiVA.org:liu-54318DiVA: diva2:302720
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
List of papers
1. Towards understanding teachers’ beliefs and affects about mathematical modelling
Open this publication in new window or tab >>Towards understanding teachers’ beliefs and affects about mathematical modelling
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.

National Category
Pedagogy
Identifiers
urn:nbn:se:liu:diva-54316 (URN)
Conference
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
2. On the use of realistic Fermi problems for introducingmathematical modelling in school
Open this publication in new window or tab >>On the use of realistic Fermi problems for introducingmathematical modelling in school
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
Keyword
Fermi problems, Fermi estimates, Modelling cycles, Mathematical modelling, Modelling activity diagram
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-54664 (URN)
Available from: 2010-03-30 Created: 2010-03-30 Last updated: 2014-06-23
3. First results from a study investigating Swedish upper secondary students’ mathematical modelling competencies
Open this publication in new window or tab >>First results from a study investigating Swedish upper secondary students’ mathematical modelling competencies
2009 (English)Conference 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.

National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-54317 (URN)
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
4. Matematisk modellering i svenska gymnasieskolans kursplaner i matematik 1965-2000
Open this publication in new window or tab >>Matematisk modellering i svenska gymnasieskolans kursplaner i matematik 1965-2000
2009 (Swedish)Report (Other academic)
Abstract [en]

Denna rapport studerar hur begreppen matematisk modell och matematisk modellering behandlats i kursplanerna i matematik för motsvarande svenska gymnasieskolans naturvetenskapliga program mellan åren 1965 och 2000. En översikt över sex kursplaners olika form och innehåll ges och tre olika analyser på tre olika nivåer genomförs; en innehållsanalys, en kvalitativ analys, och en analys som beaktar relationen mellan begreppen modellering, tillämpningar och problemlösning. Analysen visar att matematiska modeller och modellering förekommit implicit sedan kursplanen från 1965, men att begreppen främst i de två senaste kursplanerna lyfts fram explicit och fått en central position i kursplanerna. I den nuvarande kursplanen Gy2000 framgår att matematiska modeller kan tolkas både som ett undervisningsmål i sig och som ett didaktiskt hjälpmedel att lära matematik.

Place, publisher, year, edition, pages
Linköping University: Linköping Universtity Electronic Press, 2009. 93 p.
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2009:8
National Category
Mathematics Computational Mathematics
Identifiers
urn:nbn:se:liu:diva-54267 (URN)LiTH-MAT-R-2009-8 (ISRN)
Available from: 2010-03-05 Created: 2010-03-05 Last updated: 2014-06-23
5. Designing, implementing and evaluating mathematical modelling modules at the upper secondary level
Open this publication in new window or tab >>Designing, implementing and evaluating mathematical modelling modules at the upper secondary level
2009 (English)Report (Other academic)
Abstract [en]

This study provides an account of how it is possible to work with mathematical models and modelling at the Swedish upper secondary level. It shows how a researcher and two teachers, departing from what is written in the mathematics curriculum document about mathematical models and modelling and the teachers’ mathematics teaching practices, collaborate to design and develop two so called modelling modules. These two modules designed for, and integrated in, the Mathematics C and Mathematics D course respectively, were implemented in the teachers’ classes and the whole process was evaluated. The students’ experiences of working with the modules were also investigated.

The conceptual framework used to study this process of design, implementation, and evaluation is built up of design-based research methodology, cultural historical activity theory (CHAT), and co-learning agreement between the researcher and the participants.

The teachers as well as the students expressed that they enjoyed working on the modules and found the experience positive and rewarding. However, some doubt concerning the learning outcome on behalf of the students were raised among the teachers, and the wish to incorporate more scheduled time into the modules was expressed by the students.

It is concluded that the participating teachers could had difficulties in expressing a clear conception of the notions of mathematical models or modelling and no affirmative conclusions could be drawn that the participation of the teachers changed their attitudes towards mathematical models and modelling. The designing process was often was restrained by constraints originating from the local school context, and working with modelling highlights many systemic tensions in the established school practice. Also, meta-results in form of suggestions of how to resolve different kinds of tensions in order to improve the study design are reported.

Place, publisher, year, edition, pages
Linköping University: Linköping Universtiy Electronic Press, 2009. 219 p.
National Category
Mathematics Computational Mathematics
Identifiers
urn:nbn:se:liu:diva-54269 (URN)LiTH-MAT-R-2009-9 (Local ID)LiTH-MAT-R-2009-9 (Archive number)LiTH-MAT-R-2009-9 (OAI)
Available from: 2010-03-05 Created: 2010-03-05 Last updated: 2014-06-23

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