liu.seSearch for publications in DiVA
Change search
Link to record
Permanent link

Direct link
BETA
Publications (10 of 69) Show all publications
Frejd, P. & Bergsten, C. (2018). Professional modellers’ conceptions of the notion of mathematical modelling: Ideas for education. ZDM - the International Journal on Mathematics Education, 50(1-2), 117-127
Open this publication in new window or tab >>Professional modellers’ conceptions of the notion of mathematical modelling: Ideas for education
2018 (English)In: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704, Vol. 50, no 1-2, p. 117-127Article in journal (Refereed) Published
Abstract [en]

The notion of mathematical modelling has multiple interpretations in research literature and has been included in curriculum documents in various ways. This study presents a thematic analysis of nine professional modellers’ conceptions of the notion of mathematical modelling, representing scholarly knowledge. The result is organised according to four main aspects of modelling, that is description, understanding, abstraction and negotiation, representing key features of mathematical models and how people are affected by, or engage in, modelling work. The paper concludes with a discussion of some potential benefits for mathematics education that might be drawn from the study from the perspective of the ‘gap’ between mathematical modelling in educational and non-educational contexts, in terms of curriculum design and teaching practice.

Place, publisher, year, edition, pages
Springer, 2018
Keywords
The notion of mathematical modelling; Professional modellers; Curriculum development
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-147734 (URN)10.1007/s11858-018-0928-2 (DOI)000430868400010 ()
Available from: 2018-05-08 Created: 2018-05-08 Last updated: 2018-06-03Bibliographically approved
Engelbrecht, J., Bergsten, C. & Kågesten, O. (2017). Conceptual and procedural approaches to mathematics in the engineering curriculum: Views of qualified engineers. European Journal of Engineering Education, 42(5), 570-586
Open this publication in new window or tab >>Conceptual and procedural approaches to mathematics in the engineering curriculum: Views of qualified engineers
2017 (English)In: European Journal of Engineering Education, ISSN 0304-3797, E-ISSN 1469-5898, Vol. 42, no 5, p. 570-586Article in journal (Refereed) Published
Abstract [en]

The research interest underpinning this paper concerns the type ofmathematical knowledge engineering students may acquire during theirspecialised education in terms of the conceptual and proceduraldimensions of doing and using mathematics. This study draws oninterviews with 25 qualified engineers from South Africa and Swedenregarding their views on the role of mathematics in engineeringeducation, with special focus on the conceptual and procedural aspectsof mathematical knowledge. A thematic analysis of the interview dataled to the identification of two main themes. According to theconceptual view a predominantly conceptual approach is needed andvalued more than procedural skills, while the balanced view emphasisesa balance of conceptual understanding and procedural fluency as wellas links between them. It is suggested that the mathematical educationof engineers would need to be more conceptually oriented to preparefor the demands at the workplace.

Place, publisher, year, edition, pages
Taylor & Francis, 2017
Keywords
Conceptual and procedural knowledge; undergraduate mathematics; engineering education; views of engineers
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-139232 (URN)10.1080/03043797.2017.1343278 (DOI)000416683300008 ()2-s2.0-85021268611 (Scopus ID)
Projects
Conceptual and procedural understanding in mathematics courses for engineering students
Funder
Swedish Research Council
Available from: 2017-07-06 Created: 2017-07-06 Last updated: 2018-03-08Bibliographically approved
Bergsten, C. (2017). Mathematisation as didactic principle seen through teachers' descriptions of mathematical modelling. Paper presented at CIEAEM69. Quaderni di Ricerca in Didattica" QRDM (Mathematics), 27(2), 229-233
Open this publication in new window or tab >>Mathematisation as didactic principle seen through teachers' descriptions of mathematical modelling
2017 (English)In: Quaderni di Ricerca in Didattica" QRDM (Mathematics), ISSN 1592-5137, E-ISSN 1592-4424, Vol. 27, no 2, p. 229-233Article in journal (Refereed) Published
Abstract [en]

Considering the ‘popularity’ of mathematical modelling as an arena for using mathematisation as didactic principle, teachers’ conceptions of mathematical modelling in relation to how they view their main task as mathematics teachers, as well what use the mathematics students learn at school might be, was investigated drawing on interview data. While the teachers generally separated ‘reality’ and ‘mathematics’, the potential diversity of mathematical descriptions and the problematic nature of any “translation” were generally not discussed. Overall goals of teaching mathematics such as understanding, interest and usefulness were emphasised rather than relating modelling to mathematisation as didactic principle.

Abstract [fr]

Compte tenu de la «popularité» que la modélisation mathématique a gagnée en tant que domaine d'utilisation de la mathématisation comme principe didactique, les conceptions des enseignants de la modélisation mathématique par rapport à la façon dont ils considèrent leur tâche principale en tant que professeurs de mathématiques, ainsi que ce que les étudiants en mathématiques apprennent à l'école pourrait être, a été étudié en tirant parti des données d'entrevue. Bien que les enseignants se séparent généralement de la «réalité» et des «mathématiques», la diversité potentielle des descriptions mathématiques et la nature problématique de toute «traduction» n'ont généralement pas été discutées. Les objectifs généraux d'enseignement des mathématiques tels que la compréhension, l'intérêt et l'utilité ont été soulignés plutôt que de rapprocher la modélisation de la mathématisation en tant que principe didactique.

Place, publisher, year, edition, pages
Palermo, Italy: Gruppo Ricerca Insegnamento delle Matematiche (G R I M), 2017
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-147835 (URN)
Conference
CIEAEM69
Available from: 2018-05-15 Created: 2018-05-15 Last updated: 2018-05-22Bibliographically approved
Jablonka, E., Ashjari, H. & Bergsten, C. (2017). "Much palaver about greater than zero and such stuff" – First year engineering students’ recognition of university mathematics. International Journal of Research in Undergraduate Mathematics Education, 3(1), 69-107
Open this publication in new window or tab >>"Much palaver about greater than zero and such stuff" – First year engineering students’ recognition of university mathematics
2017 (English)In: International Journal of Research in Undergraduate Mathematics Education, ISSN 2198-9753, Vol. 3, no 1, p. 69-107Article in journal (Refereed) Published
Abstract [en]

Research under the key word ‘secondary-tertiary transition problem’ in mathematics education points to a range of difficulties students face when passing from learning mathematics at school to attending undergraduate mathematics courses. One of these problems concerns the change in criteria for what counts as a legitimate mathematical activity. Based on this observation, the aim of this study is to investigate the extent to which students enrolled in undergraduate mathematics courses are aware of such changes in criteria and how their reflective recognition relates to their academic success. The main body of empirical data comprises interviews with 60 undergraduate students, who were enrolled in different engineering programmes at two Swedish universities and attended compulsory mathematics courses. These interview data are complemented by the grades achieved by these students on all mathematics courses during their first year of enrolment. A group of their lecturers were also interviewed. In order to explore what counts as a legitimate mathematical activity, participants were presented with excerpts from different mathematics textbooks and asked which of these they would describe as more or less mathematical and why. As theoretical resources we selectively employ notions by means of which Bernstein conceptualised pedagogic discourse, elements of Halliday and Hasan’s social semiotics, and Eco’s idea of the model reader. The investigation shows that students focus on a considerably wide range of aspects of mathematics texts by which they (mis)recognise the specificity of the discourse, and how this relates to their academic success. The study not only provides a differentiated picture of students’ reflective recognition of levels of rigour, abstraction and formalisation in mathematics, but also offers a methodological contribution.

Place, publisher, year, edition, pages
Springer London, 2017
Keywords
School-university transition, Undergraduate mathematics, Engineering students, Mathematical rigour, Bernstein, Recognition rule
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-130698 (URN)10.1007/s40753-016-0037-y (DOI)
Projects
The transition from school mathematics to university mathematics: an integrated study of a cultural gap
Funder
Swedish Research Council
Available from: 2016-08-20 Created: 2016-08-20 Last updated: 2017-05-04
Frejd, P. & Bergsten, C. (2016). Mathematical modelling as a professional task. Educational Studies in Mathematics, 91(1), 11-35
Open this publication in new window or tab >>Mathematical modelling as a professional task
2016 (English)In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 91, no 1, p. 11-35Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Springer, 2016
Keywords
Mathematical modelling, Workplace mathematics, Computer support, Didactic transposition
National Category
Other Mathematics Probability Theory and Statistics Didactics
Identifiers
urn:nbn:se:liu:diva-123280 (URN)10.1007/s10649-015-9654-7 (DOI)000365752900006 ()
Available from: 2015-12-09 Created: 2015-12-09 Last updated: 2017-12-01
Bergsten, C. (2015). Beyond the representation given: The parabola and historical metamorphoses of meanings. In: C. Bergsten & B. Sriraman (Ed.), Refractions of mathematics education: Festschrift for Eva Jablonka (pp. 15-48). Charlotte, NC: Information Age Publishing
Open this publication in new window or tab >>Beyond the representation given: The parabola and historical metamorphoses of meanings
2015 (English)In: Refractions of mathematics education: Festschrift for Eva Jablonka / [ed] C. Bergsten & B. Sriraman, Charlotte, NC: Information Age Publishing, 2015, p. 15-48Chapter in book (Other academic)
Place, publisher, year, edition, pages
Charlotte, NC: Information Age Publishing, 2015
Series
Cognition, equity, and society : international perspectives
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-117994 (URN)978-1-68123-029-0 (ISBN)978-1-68123-030-6 (ISBN)978-1-68123-031-3 (ISBN)
Available from: 2015-05-19 Created: 2015-05-19 Last updated: 2016-11-30
Bergsten, C., Engelbrecht, J. & Kågesten, O. (2015). Conceptual or procedural mathematics for engineering students – views of two qualified engineers from two countries. International journal of mathematical education in science and technology, 46(7), 979-990
Open this publication in new window or tab >>Conceptual or procedural mathematics for engineering students – views of two qualified engineers from two countries
2015 (English)In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 46, no 7, p. 979-990Article in journal (Refereed) Published
Abstract [en]

This study forms part of a collaboration project between universities in South Africa and Sweden in which we investigate whether the emphasis in undergraduate mathematics courses for engineering students would benefit from being more conceptually oriented than a traditional more procedurally oriented way of teaching. In this paper, we report in some detail from two interviews with professional engineers, selected to represent two different ‘poles’ of engineering work. The aim was to explore different kinds of arguments regarding the role of mathematics in engineering work, as well as some common across contexts. Both interviewees feel that conceptual mathematics is more important for engineering work, although the role of the procedural aspect was seen by one of the interviewees also to be important, but in a very intricate way.

Place, publisher, year, edition, pages
Taylor & Francis Group, 2015
Keywords
engineering mathematics, practising engineers, conceptual and procedural knowledge, interviews
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-121846 (URN)10.1080/0020739X.2015.1075615 (DOI)
Funder
Swedish Research Council
Available from: 2015-10-09 Created: 2015-10-09 Last updated: 2017-12-01
Jablonka, E. & Bergsten, C. (2015). Positioning of the teacher in the improvement of mathematics classroom practice. In: Swapna Mukhopadhyay, Brian Greer (Ed.), Proceedings of the Eighth International Mathematics Education and Society Conference: . Paper presented at The Eighth International Mathematics Education and Society Conference (MES8), Portland, Oregon, United States, 21- 26 June 2015 (pp. 644-656). Portland, OR, USA: Mathematics Education and Society, 3
Open this publication in new window or tab >>Positioning of the teacher in the improvement of mathematics classroom practice
2015 (English)In: Proceedings of the Eighth International Mathematics Education and Society Conference / [ed] Swapna Mukhopadhyay, Brian Greer, Portland, OR, USA: Mathematics Education and Society , 2015, Vol. 3, p. 644-656Conference paper, Published paper (Other academic)
Abstract [en]

This paper is a hybrid between a discussion essay and a theoretical paper. Our concern is the positioning of teachers in contexts where the reshaping of educational institutions along with the commercialisation and com-modification of research carried out at universities, increasingly interferes with the intellectual freedom of both teachers and researchers. Funding of research in these contexts privileges ‘findings’ with direct implications for developing teachers’ classroom work. We discuss examples drawn from a range of studies, including classroom observation, curriculum design, and professional development settings in terms of the subjectivities attributed to the unauthorised position in the relations established in these practices.

Place, publisher, year, edition, pages
Portland, OR, USA: Mathematics Education and Society, 2015
Series
Mathematics Education and Society, ISSN 2077-9933 ; 8
National Category
Educational Sciences Didactics
Identifiers
urn:nbn:se:liu:diva-121530 (URN)000380609200052 ()
Conference
The Eighth International Mathematics Education and Society Conference (MES8), Portland, Oregon, United States, 21- 26 June 2015
Available from: 2015-09-23 Created: 2015-09-23 Last updated: 2016-11-30Bibliographically approved
Bergsten, C. & Sriraman, B. (Eds.). (2015). Refractions of mathematics education: Festschrift for Eva Jablonka. Charlotte, NC: Information Age Publishing
Open this publication in new window or tab >>Refractions of mathematics education: Festschrift for Eva Jablonka
2015 (English)Collection (editor) (Other academic)
Abstract [en]

The diversity of research in mathematics education has been addressed as both, a problem and a strength. When manifested through adherence to different intellectual roots and theoretical orientations, diversions constitute ‘refractions’ of mathematics education. The collection and analysis of empirical data in a study are by necessity refracted through the specific analytical lens employed, as well as the aim of the study itself. Refractions can also refer to looking at old phenomena through new lenses.The chapters in this book are refracted through philosophical, political, mathematical and personal lenses by distinguished authors in the field, addressing issues about the elusive experience of doing mathematics, purification of texts, refractions, mathematics and ethnomathematics, political messages in textbook tasks, mathematics education policy debate, the political in mathematics education research, philosophy and mathematics, meanings and representations, identity of mathematical modeling, and dilemmas in the teaching of calculus.An ancient Sanskrit adage states that Knowledge is something that grows when shared, but shrinks when hoarded. Academics engaged in the generation of new Knowledge are blessed with both the time and the freedom to engage in pursuits that allow for intellectual pleasure. As a phenomenon of the Zeitgeist many have succumbed to the increased corporatization of academic work, engaging in activities for monetary and self advancement purposes. Are there any real intellectuals left in academia, a là Adorno, Bourdieu, Chomsky, Foucault, among others? This Festschrift is dedicated to academics that don't bother with self promotion or aggrandizement of themselves or their ideas in simplistic terms.

Place, publisher, year, edition, pages
Charlotte, NC: Information Age Publishing, 2015. p. 223
Series
Cognition, equity, and society : international perspectives
National Category
Educational Sciences Didactics
Identifiers
urn:nbn:se:liu:diva-117993 (URN)978-1-68123-029-0 (ISBN)978-1-68123-030-6 (ISBN)978-1-68123-031-3 (ISBN)
Available from: 2015-05-19 Created: 2015-05-19 Last updated: 2016-11-30Bibliographically approved
Bergsten, C. & Jablonka, E. (2015). The construction of the ‘transition problem’ by a group of mathematics lecturers. In: Konrad Krainer, Nad'a Vondrová (Ed.), Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education: . Paper presented at The Ninth Congress of the European Society for Research in Mathematics Education (CERME9) (pp. 2053-2059). Prague, Czech Republic: Charles University in Prague, Faculty of Education and ERME
Open this publication in new window or tab >>The construction of the ‘transition problem’ by a group of mathematics lecturers
2015 (English)In: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education / [ed] Konrad Krainer, Nad'a Vondrová, Prague, Czech Republic: Charles University in Prague, Faculty of Education and ERME , 2015, p. 2053-2059Conference paper, Published paper (Refereed)
Abstract [en]

This paper presents views of university staff about what has become called the ‘transition problem’ when students start studying mathematics at university. The data are from a focus group interview with eight experienced university lecturers at a Swedish university department that offers mathematics courses for engineering students. We use the portrayal of the problem in the literature as an axis for the discussion.

Place, publisher, year, edition, pages
Prague, Czech Republic: Charles University in Prague, Faculty of Education and ERME, 2015
Keywords
undergraduate mathematics, lecturers, transition problem, focus group
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-125355 (URN)97-880-7290-844-8 (ISBN)
Conference
The Ninth Congress of the European Society for Research in Mathematics Education (CERME9)
Funder
Swedish Research Council
Available from: 2016-02-20 Created: 2016-02-20 Last updated: 2016-11-30
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-3681-3535

Search in DiVA

Show all publications