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.

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.

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.

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.

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.

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.

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.

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.

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.

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.