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Bergsten, C. & Frejd, P. (2019). Preparing pre-service mathematics teachers for STEM education: an analysis of lesson proposals. ZDM - the International Journal on Mathematics Education, 51(6), 941-953
Open this publication in new window or tab >>Preparing pre-service mathematics teachers for STEM education: an analysis of lesson proposals
2019 (English)In: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704, Vol. 51, no 6, p. 941-953Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Springer, 2019
Keywords
STEM education, Twenty-first century skills, Pre-service teachers, Mathematical modelling, Horizontal and vertical mathematisation, Classification and framing
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-161672 (URN)10.1007/s11858-019-01071-7 (DOI)000501020200006 ()2-s2.0-85068998045 (Scopus ID)
Note

Funding agencies:  Linkoping University

Available from: 2019-11-05 Created: 2019-11-05 Last updated: 2020-01-09Bibliographically approved
Bergsten, C. & Jablonka, E. (2019). Understanding the secondary-tertiary transition in mathematics education: Contribution of theories to interpreting empirical data. In: Jankvist, U. T., Van den Heuvel-Panhuizen, M., & Veldhuis, M. (Ed.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education: CERME11, February 6 – 10, 2019. Paper presented at Eleventh Congress of the European Society for Research in Mathematics Education, Utrecht, the Netherlands, February 6 – 10, 2019. Utrecht, Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME
Open this publication in new window or tab >>Understanding the secondary-tertiary transition in mathematics education: Contribution of theories to interpreting empirical data
2019 (English)In: Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education: CERME11, February 6 – 10, 2019 / [ed] Jankvist, U. T., Van den Heuvel-Panhuizen, M., & Veldhuis, M., Utrecht, Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME , 2019Conference paper, Published paper (Refereed)
Abstract [en]

The paper reports a review of studies on the secondary-tertiary transition in mathematics. With an interest in the contribution of theories, it intends to explore what insights empirical studies using new theoretical lenses have added. While there is a move towards socio-cultural theorizing, some dimensions pertaining to issues of social (re)production still appear under-researched.

Place, publisher, year, edition, pages
Utrecht, Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME, 2019
Keywords
university mathematics, sector transition, theories, socio-cultural studies
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-163275 (URN)
Conference
Eleventh Congress of the European Society for Research in Mathematics Education, Utrecht, the Netherlands, February 6 – 10, 2019
Projects
The transition from school mathematics to university mathematics: an integrated study of a cultural gap
Funder
Swedish Research Council, 2009-7799-71108-23
Available from: 2020-01-23 Created: 2020-01-23 Last updated: 2020-02-06Bibliographically approved
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
Open this publication in new window or tab >>Mathematical approaches
2018 (English)In: Encyclopedia of Mathematics Education / [ed] Steve Lerman (complete book) and Eva Jablonka (section editor), Cham: Springer, 2018, 2, p. 1-8Chapter in book (Refereed)
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...

Place, publisher, year, edition, pages
Cham: Springer, 2018 Edition: 2
Keywords
Contributing discipline, Didactical analysis, Didactic transposition, Mathematical analysis. Mathematical approach, Mathematics education community, Mathematical structure
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-151062 (URN)10.1007/978-3-319-77487-9_95-7 (DOI)978-3-319-77487-9 (ISBN)
Available from: 2018-09-12 Created: 2018-09-12 Last updated: 2018-09-12Bibliographically approved
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)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: 2019-01-09Bibliographically 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. (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
Open this publication in new window or tab >>Studying mathematics at university: Views of first year engineering students
2016 (English)In: Didactics of mathematics in higher education as a scientific discipline: Conference Proceedings / [ed] R. Göller, R. Biehler, R. Hochmuth, H-G. Rück, Kassel, 2016, p. 458-465Conference paper, Published paper (Refereed)
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.

Place, publisher, year, edition, pages
Kassel: , 2016
Series
khdm-Report ; 17-05
National Category
Didactics
Identifiers
urn:nbn:se:liu:diva-148885 (URN)
Conference
Didactics of mathematics in higher education as a scientific discipline, Kassel, Germany, 2017
Available from: 2018-06-21 Created: 2018-06-21 Last updated: 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
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
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-3681-3535

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