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  • 1.
    Bergman Ärlebäck, Jonas
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Frejd, Peter
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    First results from a study investigating Swedish upper secondary students' mathematical modelling competencies2010In: EIMI 2010 Conference: Educational interfaces between mathematics and industry : proceedings / [ed] Araújo, Adérito; Fernandes, António; Azevedo, Assis; Rodrigues, José Francisco, Lissabon: Centro Internacional de Matemática , 2010, p. 63-74Conference paper (Refereed)
  • 2.
    Bergman Ärlebäck, Jonas
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology. Linköping University, Faculty of Educational Sciences.
    Frejd, Peter
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Modelling from the Perspective of Commognition – An emerging framework2013In: Teaching mathematical modelling: Connecting to research and Practice / [ed] Gloria Ann Stillman, Gabriele Kaiser, Werner Blum, Jill P. Brown, Springer Netherlands, 2013, p. 47-56Chapter in book (Refereed)
    Abstract [en]

    This bookprovides readers with an overview of recent international research and developments in the teaching and learning of modelling and applications from a variety of theoretical and practical perspectives. There is a strong focus on pedagogical issues for teaching and learning of modelling as well as research into teaching and practice. The teaching of applications of mathematics and mathematical modelling from the early years through primary and secondary school and at tertiary level is rising in prominence in many parts of the world commensurate with an ever-increasing usage of mathematics in business, the environment, industry and everyday life. The authors are all members of the International Community of Teachers of Mathematical Modelling and Applications and important researchers in mathematics education and mathematics. The book will be of interest to teachers, practitioners and researchers in universities, polytechnics, teacher education, curriculum and policy.

  • 3.
    Bergman Ärlebäck, Jonas
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Frejd, Peter
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    The bottleneck problem in modelling revisitedManuscript (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.

  • 4.
    Bergsten, Christer
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Frejd, Peter
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    Preparing pre-service mathematics teachers for STEM education: an analysis of lesson proposals2019In: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704, Vol. 51, no 6, p. 941-953Article in journal (Refereed)
    Abstract [en]

    Based on an investigation of research literature on the role of mathematics within the context of STEM education and twenty-first century skills, this explorative study presents and analyses 19 pre-service teachers’ lesson proposals for innovative STEM activities in secondary mathematics classrooms. Drawing on a categorisation of twenty-first century skills and key concepts from Realistic Mathematics Education and Basil Bernstein’s writings, the analysis indicated a use of detailed instructions regarding what students should do but unspecified criteria for their expected knowledge productions. Rather than serving as a digital tool for problem solving, programming was used for the purpose of generalising students’ conceptual knowledge in mathematics. At the same time a focus on modelling and applications in the STEM activities tended to weaken the disciplinary character of mathematics. The learning of various twenty-first century skills was promoted to different extents. The study raises a discussion of affordances and constraints regarding students’ access to mathematical knowledge through different modes of integration of mathematics and other STEM subjects aiming to support the development of twenty-first century skills.

  • 5.
    Frejd, Peter
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    An analysis of mathematical modelling in Swedish textbooks in upper secondary school2013In: Nordisk matematikkdidaktikk, ISSN 1104-2176, Vol. 18, no 3, p. 59-95Article in journal (Refereed)
    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.

  • 6.
    Frejd, Peter
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    An investigation of mathematical modelling in the Swedish national course tests in mathematics2011In: Proceedings of CERME 7, The Seventh Congress of the European Society for Research in Mathematics Education, 2011Conference paper (Other academic)
    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.

  • 7.
    Frejd, Peter
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    Mathematical Modelling as a Professional Activity – Lessons for the Classroom2017In: Mathematical Modelling and Applications: Crossing and Researching Boundaries in Mathematics Education / [ed] Gloria Ann StillmanWerner BlumGabriele Kaiser, Cham: Springer, 2017, p. 371-388Chapter in book (Refereed)
    Abstract [en]

    This chapter presents a discussion about similarities and differences between working with mathematical modelling in ‘school’ and mathematical modelling as a ‘professional task’ in the workplace based on empirical and theoretical research studies. Issues discussed concern goals; technology; division of labour, communication and collaboration; model construction, including the application and adaption of pre-defined models; projects; and risks involved in using the models. Based on this discussion and examples from innovative teaching practices, approaches to simulate modelling as a ‘professional activity’ in educational settings are explored and exemplified with a role play activity.

  • 8.
    Frejd, Peter
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Mathematical modelling in upper secondary school in Sweden: An exploratory investigation2011Licentiate 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.

    List of papers
    1. Revisiting Perspectives on Mathematical Models and Modelling
    Open this publication in new window or tab >>Revisiting Perspectives on Mathematical Models and Modelling
    2010 (English)In: Mathematics andmathematics education: Cultural and social dimensions: Proceedings ofMadif 7, / [ed] C. Bergsten, E. Jablonka, & T. Wedege, Svensk förening för matematikdidaktisk forskning , 2010, p. 80-90Conference paper, Published paper (Other academic)
    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.

    Place, publisher, year, edition, pages
    Svensk förening för matematikdidaktisk forskning, 2010
    Series
    Skrifter från Svensk förening för matematikdidaktisk forskning, ISSN 1651-3274 ; 7
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-66300 (URN)91-973934-6-0 (ISBN)
    Conference
    Te Seventh Mathematics Education Research Seminar, Stockholm, January 26-27
    Available from: 2011-03-11 Created: 2011-03-11 Last updated: 2011-03-11Bibliographically approved
    2. 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, 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.

    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
    3. On Swedish Upper Secondary Students’ Descriptions of the Notions of Mathematical Models and Modelling
    Open this publication in new window or tab >>On Swedish Upper Secondary Students’ Descriptions of the Notions of Mathematical Models and Modelling
    2010 (English)In: Mathematics andmathematics education: Cultural and social dimensions: Proceedings ofMadif 7, / [ed] C. Bergsten, E. Jablonka, & T. Wedege, Svensk förening för matematikdidaktisk forskning , 2010, p. 80-90Conference paper, Published paper (Other academic)
    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.

    Place, publisher, year, edition, pages
    Svensk förening för matematikdidaktisk forskning, 2010
    Series
    Skrifter från Svensk förening för matematikdidaktisk forskning, ISSN 1651-3274 ; 7
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-66301 (URN)
    Conference
    Te Seventh Mathematics Education Research Seminar, Stockholm, January 26-27
    Available from: 2011-03-11 Created: 2011-03-11 Last updated: 2011-03-11Bibliographically approved
    4. An investigation of mathematical modelling in the Swedish national course tests in mathematics
    Open this publication in new window or tab >>An investigation of mathematical modelling in the Swedish national course tests in mathematics
    2011 (English)In: Proceedings of CERME 7, The Seventh Congress of the European Society for Research in Mathematics Education, 2011Conference paper, Published paper (Other academic)
    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.

    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-66302 (URN)
    Conference
    The Seventh Congress of the European Society for Research in Mathematics Education, 9-13 February, Rzeszów, Poland
    Available from: 2011-03-11 Created: 2011-03-11 Last updated: 2017-09-18Bibliographically approved
    5. 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
    2011 (English)Report (Other academic)
    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.

    Publisher
    p. 34
    Series
    LiTH-MAT-R, ISSN 0348-2960 ; 2011:4
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-66303 (URN)
    Available from: 2011-03-11 Created: 2011-03-11 Last updated: 2011-03-11Bibliographically approved
  • 9.
    Frejd, Peter
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Modelling Assessment of Mathematical Modelling – a Literature Review2012In: Modelling Assessment of Mathematical Modelling – a Literature Review / [ed] C. Bergsten, E Jablonka, & M. Raman, Linköping: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2012, p. 81-90Conference paper (Other academic)
    Abstract [en]

    This paper presents a critical review of literature investigating assessment of mathematical modelling. Written tests as described in the reviewed papers draw on an atomistic view on modelling competencies while studies adopting more holistic approaches are rare. To assess the quality of students' work with mathematical models, an elaborated view on the meaning of quality of mathematical models seems to be needed.

  • 10.
    Frejd, Peter
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Modes of Mathematical Modelling: An analysis of how modelling is used and interpreted in and out of school settings2014Doctoral 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.

    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: 2018-09-01Bibliographically 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, p. 59-95Article 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)000343409200057 ()
    Available from: 2014-01-10 Created: 2014-01-10 Last updated: 2018-03-09Bibliographically 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, p. 17-40Article 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
    Keywords
    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, p. 413-438Article 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
    Keywords
    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
  • 11.
    Frejd, Peter
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Modes of modelling assessment-a literature review2013In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 84, no 3, p. 413-438Article in journal (Refereed)
    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.

  • 12.
    Frejd, Peter
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Old algebra textbooks: a resource for modern teaching2013In: BSHM Bulletin, ISSN 1749-8430, E-ISSN 1749-8341, Vol. 28, no 1, p. 25-36Article in journal (Refereed)
    Abstract [en]

    This paper is the result of a comparative literature study aimed at identifying relevant historical mathematical contexts that may be applicable to present day mathematics education. Five Swedish textbooks in algebra from the period around the year 1800 are scrutinized. A content analysis and a comparison between seven categories shows that there exist several historical features that may be used in teaching. These have the potential to serve both teachers and learners of mathematics.

  • 13.
    Frejd, Peter
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    On Swedish Upper Secondary Students’ Descriptions of the Notions of Mathematical Models and Modelling2010In: Mathematics andmathematics education: Cultural and social dimensions: Proceedings ofMadif 7, / [ed] C. Bergsten, E. Jablonka, & T. Wedege, Svensk förening för matematikdidaktisk forskning , 2010, p. 80-90Conference paper (Other academic)
    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.

  • 14.
    Frejd, Peter
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Revisiting Perspectives on Mathematical Models and Modelling2010In: Mathematics andmathematics education: Cultural and social dimensions: Proceedings ofMadif 7, / [ed] C. Bergsten, E. Jablonka, & T. Wedege, Svensk förening för matematikdidaktisk forskning , 2010, p. 80-90Conference paper (Other academic)
    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.

  • 15.
    Frejd, Peter
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Teachers’ conceptions of mathematical modelling at Swedish Upper Secondary school2011Report (Other academic)
    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.

  • 16.
    Frejd, Peter
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Teachers’ conceptions of mathematical modelling at Swedish Upper Secondary school2012In: Journal of Mathematical Modelling and Application, ISSN 2178-2423, E-ISSN 2178-2423, Vol. 1, no 5, p. 17-40Article in journal (Refereed)
    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.

  • 17.
    Frejd, Peter
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    What is the role and place of mathematics education in (Swedish) vocational education?2018In: International journal for research in mathematics education, Vol. 8, no 2, p. 16-29Article in journal (Refereed)
    Abstract [en]

    This paper presents a discussion of some characteristic features about the role and place of mathematics education in vocational education. Based on examples from the Swedish vocational educational system, research studies and curricula, it is concluded that central roles of vocational mathematics education include the connection of informal and formal mathematics as well as facilitation of the use of technology such as artefacts, ICT, and pen and paper. To smoothen the transition from school to workplace the place of vocational mathematics education relates to different learning environments and activities that connect the classroom and workplaces. For creating a starting point for discussions about how vocational mathematics education might be organized analogies are used. They act as tools to visualize and pin point characteristic features that make impact on teaching to prepare individuals for future work and life.

  • 18.
    Frejd, Peter
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    First results from a study investigating Swedish upper secondary students’ mathematical modelling competencies2009Conference 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.

  • 19.
    Frejd, Peter
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    Bergman Ärlebäck, Jonas
    Initial results from an intervention: affordances and constraints of using a mobile game app.2017In: Mathematical Modelling and Applications: Crossing and Researching Boundaries in Mathematics Education / [ed] Gloria Ann StillmanWerner BlumGabriele Kaiser, Cham: Springer , 2017, p. 517-527Chapter in book (Refereed)
    Abstract [en]

    This chapter presents the design and results from the first iteration of a classroom activity using the context and simulation provided by a commercial game app for smartphones and tablets. The aim was to study students’ experiences of an intervention entailing the game app in order to inform a more mature design with the long-term goal of being able to develop principles to design and implement modelling activities using game apps. An analysis focusing on the interplay between the designed intervention environment and students’ work from two upper secondary classes resulted in information in terms of affordances to inform the redesign. In addition, students experienced the activity as interesting and engaging, but with significant gender differences. The results inform a discussion of the role of new technology and simulation within classroom teaching and learning of mathematical modelling.

  • 20.
    Frejd, Peter
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Initial Results of an Intervention Using a Mobile Game App to Simulate a Pandemic Outbreak2017In: Mathematical modelling and applications: Crossing and researching boundaries in mathematics education / [ed] Gloria Stillman, Werner Blum, Werner and Gabriele Kaiser, Cham: Springer, 2017, p. 517-527Chapter in book (Refereed)
    Abstract [en]

    This chapter presents the design and results from the first iteration of a classroom activity using the context and simulation provided by a commercial game app for smartphones and tablets. The aim was to study students’ experiences of an intervention entailing the game app in order to inform a more mature design with the long-term goal of being able to develop principles to design and implement modelling activities using game apps. An analysis focusing on the interplay between the designed intervention environment and students’ work from two upper secondary classes resulted in information in terms of affordances to inform the redesign. In addition, students experienced the activity as interesting and engaging, but with significant gender differences. The results inform a discussion of the role of new technology and simulation within classroom teaching and learning of mathematical modelling.

  • 21.
    Frejd, Peter
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    Mathematical modelling as a professional task2016In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 91, no 1, p. 11-35Article in journal (Refereed)
    Abstract [en]

    Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model constructors. The research question was: How can mathematical modelling by professional mathematical model constructors be characterised? The analysis of our interview data inspired by the coding procedure of grounded theory led us to the description of three main types of modelling activities as a characterisation of mathematical modelling as a professional task. In data-generated modelling the models are developed principally from quantitative data drawing on no or only some assumed knowledge of the system being modelled, while in theory-generated modelling the models are developed based on established theory. In the third activity, model-generated modelling, the development of new models is based on already established models. For all types, the use of computer support and communication between clients, constructors and other experts are central aspects. Finally, the three types of modelling activities are related to existing theoretical descriptions of mathematical modelling and the relevance of the study for mathematical modelling in education is discussed.

  • 22.
    Frejd, Peter
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Bergsten, Christer
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Mathematical modelling as a professional task: Implications for educationManuscript (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.

  • 23.
    Frejd, Peter
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    Geiger, Vincent
    Learning Sciences Institute Australia, Australian Catholic University, Brisbane CBD, Australia.
    Exploring the notion of mathematical literacy in school curriculum documents2017In: Mathematical Modelling and Applications: Crossing and Researching Boundaries in Mathematics Education / [ed] Gloria Ann StillmanWerner BlumGabriele Kaiser, Springer, 2017, p. 255-263Chapter in book (Refereed)
    Abstract [en]

    The notion of mathematical literacy has gained momentum internationally during recent time through the influence of the Programme of International Student Assessment and national concerns about the ability of citizens to use mathematics effectively in   in person, civic and work life. Accordingly, it is to be expected that these concerns should be reflected in relevant curriculum documents. This chapter presents a content analysis of a sample of 12 national curricula documents in relation to mathematical literacy. The analysis shows that there does not appear to be general agreement about the definition and of mathematical literacy within the analysed documents. We conclude the chapter by considering the implications for practice of the identified variations in understandings of mathematical literacy internationally.

  • 24.
    Frejd, Peter
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    Lundberg, Anna L. V.
    Linköping University, Department of Mathematics. Linköping University, Faculty of Science & Engineering.
    Begreppen modellering och problemlösning i skolan och i yrkeslivet2015Other (Other academic)
  • 25.
    Geiger, Vincent
    et al.
    Learning Sciences Institute Australia, Faculty of Education and Arts, Australia.
    Bergman Ärlebäck, Jonas
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Frejd, Peter
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Interpreting curricula to find opportunities for modeling: case studies from Australia and Sweden2016In: Annual Perspectives in Mathematics Education (APME) 2016: Mathematical modeling and modeling mathematics / [ed] Christian R. Hirsch, Amy Roth McDuffie, Reston, VA: National Council of Teachers of Mathematics , 2016, p. 207-215Chapter in book (Refereed)
  • 26.
    Muhrman, Karolina
    et al.
    Linköping University, Department of Behavioural Sciences and Learning, Education and Adult Learning. Linköping University, Faculty of Educational Sciences.
    Frejd, Peter
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    Elevers erfarenheter kring ett projekt om matematik med yrkesinriktning.2018In: Perspectives on professional development of  mathematics teachers: Proceedings of Madif 11 / [ed] Häggström, Y. Liljekvist, J. Bergman Ärlebäck, M. Fahlgren, & O. Olande, Linköping: SMDF , 2018, p. 161-170Conference paper (Refereed)
    Abstract [sv]

    Forskning visar att elever har svårigheter att rekontextualisera sina matematikkun- skaper från skolkontexten till yrkeslivskontexten om matematikundervisningen saknar koppling till yrkeslivet. I artikeln analyseras, utifrån Bernsteins teorier, intervjuer med elever på tre yrkesprogram som deltagit i en interventionsstudie med målet att knyta matematiken närmare elevernas yrkesinriktning. Resultaten tyder på matema- tikämnet har en stark klassifikation och inramning som är svår att förändra, men om klassifikation och inramning förändras mot ett mer ämnesintegrerat arbetssätt verkar elevernas förmåga att rekontextualisera sina matematikkunskaper förbättras. Undervisningsmiljö och användandet av autentiska problem diskuteras som centrala faktorer för att detta ska ske.

1 - 26 of 26
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