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Bergsten, C. (2018). Mathematical approaches (2ed.). In: Steve Lerman (complete book) and Eva Jablonka (section editor) (Ed.), Encyclopedia of Mathematics Education: (pp. 1-8). Cham: Springer
Öppna denna publikation i ny flik eller fönster >>Mathematical approaches
2018 (Engelska)Ingår i: Encyclopedia of Mathematics Education / [ed] Steve Lerman (complete book) and Eva Jablonka (section editor), Cham: Springer, 2018, 2, s. 1-8Kapitel i bok, del av antologi (Refereegranskat)
Abstract [en]

Research in mathematics education is interdisciplinary. According to Higginson (1980), mathematics, philosophy, psychology, and sociology are contributing disciplines to mathematics education (similar to what Michael Otte called Bezugsdisziplinen; Otte et al. 1974, p. 20). Linguistics and semiotics could be added. Framing of research, by means of theories or methods from these, amounts to different approaches, mathematics itself being one obvious choice. According to one view, mathematics education as a research field belongs to mathematics: at the second International Congress on Mathematical Education (ICME) in Exeter, Zofia Krygowska suggested that mathematics education should be classified as “a part of mathematics with a status similar to that of analysis or topology” (Howson 1973, p. 48). Another view sees mathematics education as an autonomous science (didactics of mathematicsas Hans Georg Steiner in 1968 called the new discipline he wanted to establish; see...

Ort, förlag, år, upplaga, sidor
Cham: Springer, 2018 Upplaga: 2
Nyckelord
Contributing discipline, Didactical analysis, Didactic transposition, Mathematical analysis. Mathematical approach, Mathematics education community, Mathematical structure
Nationell ämneskategori
Didaktik
Identifikatorer
urn:nbn:se:liu:diva-151062 (URN)10.1007/978-3-319-77487-9_95-7 (DOI)978-3-319-77487-9 (ISBN)
Tillgänglig från: 2018-09-12 Skapad: 2018-09-12 Senast uppdaterad: 2018-09-12Bibliografiskt granskad
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
Öppna denna publikation i ny flik eller fönster >>Professional modellers’ conceptions of the notion of mathematical modelling: Ideas for education
2018 (Engelska)Ingår i: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704, Vol. 50, nr 1-2, s. 117-127Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
Springer, 2018
Nyckelord
The notion of mathematical modelling; Professional modellers; Curriculum development
Nationell ämneskategori
Didaktik
Identifikatorer
urn:nbn:se:liu:diva-147734 (URN)10.1007/s11858-018-0928-2 (DOI)000430868400010 ()
Tillgänglig från: 2018-05-08 Skapad: 2018-05-08 Senast uppdaterad: 2018-06-03Bibliografiskt granskad
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
Öppna denna publikation i ny flik eller fönster >>Conceptual and procedural approaches to mathematics in the engineering curriculum: Views of qualified engineers
2017 (Engelska)Ingår i: European Journal of Engineering Education, ISSN 0304-3797, E-ISSN 1469-5898, Vol. 42, nr 5, s. 570-586Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
Taylor & Francis, 2017
Nyckelord
Conceptual and procedural knowledge; undergraduate mathematics; engineering education; views of engineers
Nationell ämneskategori
Didaktik
Identifikatorer
urn:nbn:se:liu:diva-139232 (URN)10.1080/03043797.2017.1343278 (DOI)2-s2.0-85021268611 (Scopus ID)
Projekt
Conceptual and procedural understanding in mathematics courses for engineering students
Forskningsfinansiär
Vetenskapsrådet
Tillgänglig från: 2017-07-06 Skapad: 2017-07-06 Senast uppdaterad: 2019-01-09Bibliografiskt granskad
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
Öppna denna publikation i ny flik eller fönster >>Mathematisation as didactic principle seen through teachers' descriptions of mathematical modelling
2017 (Engelska)Ingår i: Quaderni di Ricerca in Didattica" QRDM (Mathematics), ISSN 1592-5137, E-ISSN 1592-4424, Vol. 27, nr 2, s. 229-233Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
Palermo, Italy: Gruppo Ricerca Insegnamento delle Matematiche (G R I M), 2017
Nationell ämneskategori
Didaktik
Identifikatorer
urn:nbn:se:liu:diva-147835 (URN)
Konferens
CIEAEM69
Tillgänglig från: 2018-05-15 Skapad: 2018-05-15 Senast uppdaterad: 2018-05-22Bibliografiskt granskad
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
Öppna denna publikation i ny flik eller fönster >>"Much palaver about greater than zero and such stuff" – First year engineering students’ recognition of university mathematics
2017 (Engelska)Ingår i: International Journal of Research in Undergraduate Mathematics Education, ISSN 2198-9753, Vol. 3, nr 1, s. 69-107Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
Springer London, 2017
Nyckelord
School-university transition, Undergraduate mathematics, Engineering students, Mathematical rigour, Bernstein, Recognition rule
Nationell ämneskategori
Didaktik
Identifikatorer
urn:nbn:se:liu:diva-130698 (URN)10.1007/s40753-016-0037-y (DOI)
Projekt
The transition from school mathematics to university mathematics: an integrated study of a cultural gap
Forskningsfinansiär
Vetenskapsrådet
Tillgänglig från: 2016-08-20 Skapad: 2016-08-20 Senast uppdaterad: 2017-05-04
Frejd, P. & Bergsten, C. (2016). Mathematical modelling as a professional task. Educational Studies in Mathematics, 91(1), 11-35
Öppna denna publikation i ny flik eller fönster >>Mathematical modelling as a professional task
2016 (Engelska)Ingår i: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 91, nr 1, s. 11-35Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
Springer, 2016
Nyckelord
Mathematical modelling, Workplace mathematics, Computer support, Didactic transposition
Nationell ämneskategori
Annan matematik Sannolikhetsteori och statistik Didaktik
Identifikatorer
urn:nbn:se:liu:diva-123280 (URN)10.1007/s10649-015-9654-7 (DOI)000365752900006 ()
Tillgänglig från: 2015-12-09 Skapad: 2015-12-09 Senast uppdaterad: 2017-12-01
Bergsten, C. (2016). Studying mathematics at university: Views of first year engineering students. In: R. Göller, R. Biehler, R. Hochmuth, H-G. Rück (Ed.), Didactics of mathematics in higher education as a scientific discipline: Conference Proceedings. Paper presented at Didactics of mathematics in higher education as a scientific discipline, Kassel, Germany, 2017 (pp. 458-465). Kassel
Öppna denna publikation i ny flik eller fönster >>Studying mathematics at university: Views of first year engineering students
2016 (Engelska)Ingår i: Didactics of mathematics in higher education as a scientific discipline: Conference Proceedings / [ed] R. Göller, R. Biehler, R. Hochmuth, H-G. Rück, Kassel, 2016, s. 458-465Konferensbidrag, Publicerat paper (Refereegranskat)
Abstract [en]

As part of a larger project investigating the transition from secondary to tertiary mathematics educa-tion in Sweden, interviews with 60 engineering students at the end of their first year of study sug-gest that shifts during the transition from individualised to collective study approaches and from de-pendent to apprenticed student positions, as well as student life, contribute to students’ views on university studies as a generally highly valuable experience.

Ort, förlag, år, upplaga, sidor
Kassel: , 2016
Serie
khdm-Report ; 17-05
Nationell ämneskategori
Didaktik
Identifikatorer
urn:nbn:se:liu:diva-148885 (URN)
Konferens
Didactics of mathematics in higher education as a scientific discipline, Kassel, Germany, 2017
Tillgänglig från: 2018-06-21 Skapad: 2018-06-21 Senast uppdaterad: 2018-08-09
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
Öppna denna publikation i ny flik eller fönster >>Beyond the representation given: The parabola and historical metamorphoses of meanings
2015 (Engelska)Ingår i: Refractions of mathematics education: Festschrift for Eva Jablonka / [ed] C. Bergsten & B. Sriraman, Charlotte, NC: Information Age Publishing, 2015, s. 15-48Kapitel i bok, del av antologi (Övrigt vetenskapligt)
Ort, förlag, år, upplaga, sidor
Charlotte, NC: Information Age Publishing, 2015
Serie
Cognition, equity, and society : international perspectives
Nationell ämneskategori
Didaktik
Identifikatorer
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)
Tillgänglig från: 2015-05-19 Skapad: 2015-05-19 Senast uppdaterad: 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
Öppna denna publikation i ny flik eller fönster >>Conceptual or procedural mathematics for engineering students – views of two qualified engineers from two countries
2015 (Engelska)Ingår i: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 46, nr 7, s. 979-990Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
Taylor & Francis Group, 2015
Nyckelord
engineering mathematics, practising engineers, conceptual and procedural knowledge, interviews
Nationell ämneskategori
Didaktik
Identifikatorer
urn:nbn:se:liu:diva-121846 (URN)10.1080/0020739X.2015.1075615 (DOI)
Forskningsfinansiär
Vetenskapsrådet
Tillgänglig från: 2015-10-09 Skapad: 2015-10-09 Senast uppdaterad: 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
Öppna denna publikation i ny flik eller fönster >>Positioning of the teacher in the improvement of mathematics classroom practice
2015 (Engelska)Ingår i: 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, s. 644-656Konferensbidrag, Publicerat paper (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Portland, OR, USA: Mathematics Education and Society, 2015
Serie
Mathematics Education and Society, ISSN 2077-9933 ; 8
Nationell ämneskategori
Utbildningsvetenskap Didaktik
Identifikatorer
urn:nbn:se:liu:diva-121530 (URN)000380609200052 ()
Konferens
The Eighth International Mathematics Education and Society Conference (MES8), Portland, Oregon, United States, 21- 26 June 2015
Tillgänglig från: 2015-09-23 Skapad: 2015-09-23 Senast uppdaterad: 2016-11-30Bibliografiskt granskad
Organisationer
Identifikatorer
ORCID-id: ORCID iD iconorcid.org/0000-0002-3681-3535

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