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Modes of Mathematical Modelling: An analysis of how modelling is used and interpreted in and out of school settings
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
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.
Series
Linköping Studies in Behavioural Science, ISSN 1654-2029 ; 181
National Category
Didactics Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-103689DOI: 10.3384/diss.diva-103689ISBN: 978-91-7519-414-1 (print)OAI: oai:DiVA.org:liu-103689DiVA: diva2:690259
Public defence
2014-02-14, C3, hus C, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2014-01-23 Created: 2014-01-23 Last updated: 2016-11-30Bibliographically approved
List of papers
1. Mathematical modelling as a professional task: Implications for education
Open this publication in new window or tab >>Mathematical modelling as a professional task: Implications for education
(English)Manuscript (preprint) (Other academic)
Abstract [en]

From an explorative study on how professionals engage in mathematical modelling in their work, three main types of activities were identified, i.e. empirical, theoretical and applicational modelling. Based on the outcomes of the study, some issues related to mathematical modelling in education are discussed.

National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-103033 (URN)
Available from: 2014-01-10 Created: 2014-01-10 Last updated: 2014-01-23Bibliographically approved
2. An analysis of mathematical modelling in Swedish textbooks in upper secondary school
Open this publication in new window or tab >>An analysis of mathematical modelling in Swedish textbooks in upper secondary school
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.

National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-103031 (URN)
Available from: 2014-01-10 Created: 2014-01-10 Last updated: 2017-12-06Bibliographically approved
3. Teachers’ conceptions of mathematical modelling at Swedish Upper Secondary school
Open this publication in new window or tab >>Teachers’ conceptions of mathematical modelling at Swedish Upper Secondary school
2012 (English)In: Journal of Mathematical Modelling and Application, ISSN 2178-2423, E-ISSN 2178-2423, Vol. 1, no 5, 17-40 p.Article in journal (Refereed) Published
Abstract [en]

Researchers argue that teachers’ conceptions (beliefs) about mathematical modelling have an impact on the low integration of modelling activities into the mathematics classroom. This paper presents a case study of 18 teachers, investigating their conceptions about mathematical modelling and their experiences of working with modelling activities in Swedish upper secondary school. The results, based on an analysis with a grounded theory inspired coding strategy, indicate that the teachers’ conceptions of the notion mathematical modelling relates to designing a mathematical model based on a situation. It is also concluded that the teachers have minor experience of the notion of mathematical modelling in mathematics class, but in physics class modelling is used as a common activity. Overall the teachers in this study seem not to give priority to integrate mathematical modelling into their everyday mathematics teaching. One reason may be related to teachers’ conceptions about mathematics where more than every other teacher expressed that some of the modelling items discussed during the interviews were not considered to be mathematics.

Place, publisher, year, edition, pages
Blumenau: Universidade Regional de Blumenau, 2012
Keyword
mathematical modelling; teachers’ conceptions; upper secondary school
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-89496 (URN)
Available from: 2013-02-26 Created: 2013-02-26 Last updated: 2017-12-06
4. Modes of modelling assessment-a literature review
Open this publication in new window or tab >>Modes of modelling assessment-a literature review
2013 (English)In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 84, no 3, 413-438 p.Article in journal (Refereed) Published
Abstract [en]

This paper presents a critical review of literature investigating assessment of mathematical modelling. Written tests, projects, hands-on tests, portfolio and contests are modes of modelling assessment identified in this study. The written tests found in the reviewed papers draw on an atomistic view on modelling competencies, whereas projects are described to assess a more holistic modelling competence but obstacles regarding reliability of assessing projects are identified. The outcome of this investigation also indicates that the criteria used in frameworks or modes of assessment seldom are derived from a theoretical analysis, but more often based on ad hoc constructions, experience from assessment situations or empirical studies of students work. Finally, this study suggests that an elaborated view on the meaning of quality of mathematical models is needed in order to assess the quality of students work with mathematical models.

Place, publisher, year, edition, pages
Springer Verlag (Germany), 2013
Keyword
Mathematical modelling, Assessment, Literature review, Modelling competence
National Category
Medical and Health Sciences
Identifiers
urn:nbn:se:liu:diva-100474 (URN)10.1007/s10649-013-9491-5 (DOI)000325702900008 ()
Available from: 2013-11-08 Created: 2013-11-08 Last updated: 2017-12-06
5. The bottleneck problem in modelling revisited
Open this publication in new window or tab >>The bottleneck problem in modelling revisited
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper Sfard's theory of commognition is used to investigate how two students work collaboratively to develop mathematical models in a natural school setting. The students' communication is analysed from both an insider and an outsider perspective to recreate the construction of their developed models in terms of realization trees. The analysis shows how the students draw on different discourses and that the models evolved through activities of recognition and negotiation. In particular, the students formulated their mathematical models using already known mathematical models. However, these latter models were tacit models in that they were not explicitly mentioned or discussed during the developmental process. To facilitate students’ capability to productively engage in mathematical modelling, the result of this study points to the need renegotiate the learning-teaching agreement so that it incorporates activities offering the students opportunities to practice negotiation and recognition.

National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-103036 (URN)
Available from: 2014-01-10 Created: 2014-01-10 Last updated: 2014-06-23Bibliographically approved

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