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Mathematical modelling in upper secondary school in Sweden: An exploratory investigation
Linköpings universitet, Matematiska institutionen, Tillämpad matematik. Linköpings universitet, Tekniska högskolan.
2011 (Engelska)Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Linköping: Linköping University Electronic Press , 2011. , 72 s.
Serie
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1471Studies in Science and Technology Education, ISSN 1652-5051 ; 37
Nationell ämneskategori
Matematik
Identifikatorer
URN: urn:nbn:se:liu:diva-66304ISBN: 978-91-7393-223-3 (tryckt)OAI: oai:DiVA.org:liu-66304DiVA: diva2:403178
Presentation
2011-03-22, 10:15 (Svenska)
Handledare
Tillgänglig från: 2011-03-11 Skapad: 2011-03-11 Senast uppdaterad: 2016-11-30Bibliografiskt granskad
Delarbeten
1. Revisiting Perspectives on Mathematical Models and Modelling
Öppna denna publikation i ny flik eller fönster >>Revisiting Perspectives on Mathematical Models and Modelling
2010 (Engelska)Ingår i: Mathematics andmathematics education: Cultural and social dimensions: Proceedings ofMadif 7, / [ed] C. Bergsten, E. Jablonka, & T. Wedege, Svensk förening för matematikdidaktisk forskning , 2010, 80-90 s.Konferensbidrag (Övrigt vetenskapligt)
Abstract [en]

This paper presents a literature review of the notions of mathematical models and modelling from three different theoretical perspectives in order to analyse students’ descriptions in a future empirical study. Similarities and differences between the perspectives are discussed and suggestions regarding how to use the different perspectives and examples of possible research questions are given.

Ort, förlag, år, upplaga, sidor
Svensk förening för matematikdidaktisk forskning, 2010
Serie
Skrifter från Svensk förening för matematikdidaktisk forskning, ISSN 1651-3274 ; 7
Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:liu:diva-66300 (URN)91-973934-6-0 (ISBN)
Konferens
Te Seventh Mathematics Education Research Seminar, Stockholm, January 26-27
Tillgänglig från: 2011-03-11 Skapad: 2011-03-11 Senast uppdaterad: 2011-03-11Bibliografiskt granskad
2. First results from a study investigating Swedish upper secondary students’ mathematical modelling competencies
Öppna denna publikation i ny flik eller fönster >>First results from a study investigating Swedish upper secondary students’ mathematical modelling competencies
2009 (Engelska)Konferensbidrag (Övrigt vetenskapligt)
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.

Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:liu:diva-54317 (URN)
Konferens
14th International Conference on the Teaching of Mathematical Modelling and Applications (ICTMA 14), University of Hamburg, 27th to 31st July, Germany
Tillgänglig från: 2010-03-09 Skapad: 2010-03-09 Senast uppdaterad: 2014-06-23Bibliografiskt granskad
3. On Swedish Upper Secondary Students’ Descriptions of the Notions of Mathematical Models and Modelling
Öppna denna publikation i ny flik eller fönster >>On Swedish Upper Secondary Students’ Descriptions of the Notions of Mathematical Models and Modelling
2010 (Engelska)Ingår i: Mathematics andmathematics education: Cultural and social dimensions: Proceedings ofMadif 7, / [ed] C. Bergsten, E. Jablonka, & T. Wedege, Svensk förening för matematikdidaktisk forskning , 2010, 80-90 s.Konferensbidrag (Övrigt vetenskapligt)
Abstract [en]

This paper analyses 263 Swedish upper secondary students’ descriptions of the notions of mathematical models and modelling using a coding scheme inspired by grounded theory, resulting in 34 coding categories. These are reduced and brought together in seven broader categories capturing different dimensions of the students’ expressed views of mathematical models and modelling. It is found that the students prominently connect mathematical models and modelling with aspects of problem solving and with applying mathematics in extra-mathematical situations. Mathematical models are also equated with mathematical formulae and modelling is considered to be a constructive and creative activity.

Ort, förlag, år, upplaga, sidor
Svensk förening för matematikdidaktisk forskning, 2010
Serie
Skrifter från Svensk förening för matematikdidaktisk forskning, ISSN 1651-3274 ; 7
Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:liu:diva-66301 (URN)
Konferens
Te Seventh Mathematics Education Research Seminar, Stockholm, January 26-27
Tillgänglig från: 2011-03-11 Skapad: 2011-03-11 Senast uppdaterad: 2011-03-11Bibliografiskt granskad
4. An investigation of mathematical modelling in the Swedish national course tests in mathematics
Öppna denna publikation i ny flik eller fönster >>An investigation of mathematical modelling in the Swedish national course tests in mathematics
2011 (Engelska)Ingår i: Proceedings of CERME 7, The Seventh Congress of the European Society for Research in Mathematics Education, 2011Konferensbidrag (Övrigt vetenskapligt)
Abstract [en]

Mathematical modelling is one competence assessed in the Swedish national course tests in mathematics (NCT) in upper secondary school. This paper presents, with empirical data from the NCT, a content analysis about what aspects of mathematical modelling are assessed and how it is assessed. The main conclusion is that only fragments (intra-mathematical aspects) of the modelling process are being assessed.

Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:liu:diva-66302 (URN)
Konferens
The Seventh Congress of the European Society for Research in Mathematics Education, 9-13 February, Rzeszów, Poland
Tillgänglig från: 2011-03-11 Skapad: 2011-03-11 Senast uppdaterad: 2011-03-11Bibliografiskt granskad
5. Teachers’ conceptions of mathematical modelling at Swedish Upper Secondary school
Öppna denna publikation i ny flik eller fönster >>Teachers’ conceptions of mathematical modelling at Swedish Upper Secondary school
2011 (Engelska)Rapport (Övrigt vetenskapligt)
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 only minor experience of the notion of mathematical modelling in the mathematics class, but in physics class modelling is used as a common activity.

Förlag
34 s.
Serie
LiTH-MAT-R, ISSN 0348-2960 ; 2011:4
Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:liu:diva-66303 (URN)
Tillgänglig från: 2011-03-11 Skapad: 2011-03-11 Senast uppdaterad: 2011-03-11Bibliografiskt granskad

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