This qualitative case study investigates the interaction sequences that emerge among secondary school students engaged in mathematical modelling tasks using digital technologies. The study focuses on four groups of 14–17-year-old students in southern Norway, varying in achievement levels, as they worked on two distinct mathematical modelling tasks. Task 1 involved numerical manipulation and function development based on given data, while Task 2 required qualitative decision-making without explicit numerical constraints. Recorded interactions, comprising video and screen-capture data, were analysed using thematic analysis, focusing on pseudo, asymmetrical, reactive and mutual interaction sequences. The findings indicate that Task 1 predominantly elicited asymmetrical interaction sequences, with high-performing students taking the lead in proposing solutions, reflecting limited exchange patterns. In contrast, Task 2 fostered more reactive and mutual interaction sequences, supporting balanced and equitable exchanges within groups. Additionally, group composition shaped interaction patterns: same-achievement, high-performing upper secondary groups and mixed-achievement lower secondary groups demonstrated more mutual and reactive interaction sequences across tasks, while mixed-achievement upper secondary groups exhibited more varied patterns. The study highlights how task design, group composition and digital technology use interact to influence collaborative learning dynamics in mathematical modelling.

This paper reports on a qualitative study of three Norwegian lower secondary school students (grade 9) collaboratively solving a mathematical modelling task using digital tools. Drawing on Activity and Affordance Theory as a theoretical framework, the study investigates how affordances and constraints influence students' proclivity to use particular digital tools in mathematical modelling activities. Data were collected through video, audio and screen-capture software recordings. Thematic analysis was applied to identify technological and mathematical affordances and constraints that influence students' proclivity to select or switch between digital tools in a mathematical modelling activity. The findings provide insight into the rationale behind students' proclivity to select or switch between digital tools, showing how they navigate digital environments in real-time. The contribution of this paper lies at both theoretical and empirical levels. Theoretically, it advances research by combining Activity and Affordance Theory to offer a more comprehensive framework for analysing tool use in mathematical modelling. Empirically, it provides evidence of how students adapt their strategies in response to perceived affordances and constraints. Together, these contributions enhance current understanding of digital tool use in mathematical modelling by highlighting not only which tools students choose, but also why and how those choices emerge in practice.

Calculus plays an important role in economics, especially within economic theory. However, the way economists use calculus differs from how mathematicians understand and teach calculus. In this paper, we first present examples from micro- and macroeconomics illustrating the kind of calculus used in economics concretely. We then provide an overview on features of calculus in economics which we draw from the examples. Finally, we point out challenges for economics students relating the mathematical content in the examples presented and the features identified, and discuss several consequences for teaching calculus to economics students. The paper advances knowledge in as much as the specificities of calculus for economics students have received scant attention in mathematics education research, despite the high relevance of economics for modern society and the large number of students enrolled in economics study programs.

This book is for people who teach calculus – and especially for people who teach student teachers, who will in turn teach calculus. The calculus considered is elementary calculus of a single variable. The book interweaves ideas for teaching with calculus content and provides a reader-friendly overview of research on learning and teaching calculus along with questions on educational and mathematical discussion topics. Written by a group of international authors with extensive experience in teaching and research on learning/teaching calculus both at the school and university levels, the book offers a variety of approaches to the teaching of calculus so that you can decide the approach for you. Topics covered include A history of calculus and how calculus differs over countries today Making sense of limits and continuity, differentiation, integration and the fundamental theorem of calculus (chapters on these areas form the bulk of the book) The ordering of calculus concepts (should limits come first?) Applications of calculus (including differential equations) The final chapter looks beyond elementary calculus. Recurring themes across chapters include whether to take a limit or a differential/infinitesimal approach to calculus and the use of digital technology in the learning and teaching of calculus. This book is essential reading for mathematics teacher trainers everywhere.

This paper documents how the limit concept is treated in high school, at a university and in teacher education in England, France and Sweden. To this end we make use of vignettes, data-grounded accounts of the situation at the three levels in the three countries. These are analysed using the Anthropological Theory of the Didactic (ATD). While university praxeologies are relatively similar across the three countries, greater differences manifest themselves in high school and teacher education. For instance, at the high school level, in France a local praxeology on the limits of sequences is taught, which is not the case in England or Sweden. Results from the analysis of limits are extrapolated to comment on implications for the teaching of calculus, and for teacher education, in the three countries. The paper also raises methodological issues in our approach.

This paper presents ‘expert opinions’ on what should be taught in a first-year linear algebra course at university; the aim is to gain a generic picture and general guiding principles for such a course. Drawing on a Delphi method, 14 university professors—called ‘experts’ in this study—addressed the following questions: What should be on a first-year linear algebra undergraduate course for engineering and/or mathematics students? How could such courses be taught? What tools (if any) are essential to these two groups of students? The results of the investigation, these experts’ opinions, mainly concern what should be in a linear algebra course (e.g. problem-solving and applications) and what students should be able to do. The experts also emphasized that certain theoretical aspects (e.g. proofs, abstract structures, definitions and relationships) were more important to mathematics students. There was no real consensus among the experts on teaching methods or the use of digital tools, but this lack of consensus is interesting in itself. The results are discussed in relation to extant research.

This paper looks at the practices (or praxeologies) of mathematics education doctoral students and their supervisors from the perspectives of activity theory and the anthropological theory of the didactic. The paper examines three ways to view mathematics education research before discussing : research methods and methodologies ; the debate on qualitative and quantitative research ; and implications for the supervision of doctoral students.

This paper reports on themes that arose in an investigation of university lecturers’ views on the teaching of linear algebra. This focus on themes was the initial part of a study concentrating on four areas: What is important to teach in a first course in linear algebra? Are there teaching methods which are particularly suited for such a course? Are there tools that should/should not be used; and do the answers to these questions vary according to the degree (Engineering or Mathematics) the students follow? Questionnaire data was coded using thematic analysis which generated 11 themes related to the four questions above. The Results section presents the themes. The Discussion section considers the themes as a whole; splits – dualities – in teaching linear algebra; students’ challenges with abstraction; aspects of doing mathematics; and pedagogical issues.

This chapter reports on the work of Working Group 4 and focuses on the integration of digital resources into mathematics teaching and learning practices. There are five central sections, focusing on, instrumental genesis, instrumental orchestration, the documentational approach to didactics, digital resources and teacher education, and the design of learning environments with the use of digital resources. A range of constructs and theoretical approaches are covered in these five sections, and the opening section comments on construct validity and issues in "networking" theoretical frameworks. The chapter can be viewed as a literature review which surveys past and present (at the time of writing) scholarship with an eye to possible future research. The chapter is extensive in several dimensions: a large range of digital resources and applications are considered; the subjects using digital resources are not just teachers but also students, student teachers and student teacher educators. Issues raised in the sections include individual and collective use of resources, the adaptation of these resources for specific learning goals and to prepare (pre- and in-service) teachers for the use of digital resources.

This article addresses university students' problem posing with a particular focus on importing photographs (of nature and of human constructions) into mathematical software to pose problems about mathematical properties of the object in the photograph. Student work is presented which leads to a discussion on the potential of the mathematical software GeoGebra to aid student mathematicizing and problem posing from visual images.

Drawing from the experience of writing a book with a research mathematician (*), the lecture will highlight the variability of tool use for achieving a mathematical task, depending on the user and on the finality of the activity encompassing this task. This reflection will lead to evidence some conditions for a fruitful use of tools in the context of doing/learning/teaching mathematics. (*) Monaghan, J., Trouche, L., & Borwein, J. (2016). Tools and mathematics, instruments for learning. Springer

This paper reports on classroom observations of senior high school mathematics lessons with a focus on the use of digital technology. The observations were of teachers enrolled in an in-service course Teaching Advanced Mathematics. The paper reports selected results and comments on: software that was observed to have been used; the use (or not) of software for specific topics; who used the software and for what purpose; and implications for teacher development programmes.