John David Monaghan

• Afram, Obed Opoku; Hadjerrouit, Said & Monaghan, John David (2026). Analysing group interaction sequences in technology-mediated mathematical modelling activities. Mathematics Education Research Journal. ISSN 1033-2170. doi: 10.1007/s13394-026-00568-1. Full text in Research Archive Show summary

  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.

• Afram, Obed Opoku; Hadjerrouit, Said & Monaghan, John David (2026). Students’ proclivity in using particular digital tools in mathematical modelling activities: an activity and affordance theoretical perspective. International Journal of Mathematical Education in Science and Technology. ISSN 0020-739X. p. 1–32. doi: https:/www.tandfonline.com/doi/full/10.1080/0020739X.2025.2598244. Full text in Research Archive Show summary

  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.

• Breive, Svanhild; Goos, Merrilyn & Monaghan, John David (2022). Interpreting a kindergarten episode through three perspectives on agency. For the Learning of Mathematics. ISSN 0228-0671. 42(1), p. 25–30. Full text in Research Archive Show summary

  This paper takes a ‘networking of theories’ approach to understand the complexity of the phenomenon of agency. We examine an episode, where a kindergarten teacher and nine children work on an addition problem, from three different perspectives: Valsiner’s zone theory; Radford’s theory of objectification; and Pickering’s dance of agency. Our networking of these approaches offers a way of thinking about agency as ‘forces’ that emerge through activity and operate on human actions. We end the paper by indicating that ethics, as a human relation, may be a catalyst for bringing out the potential that lies in the other agentic forces.

• Viirman, Olov Lui; Vivier, Laurent & Monaghan, John David (2022). The Limit Notion at Three Educational Levels in Three Countries. International Journal of Research in Undergraduate Mathematics Education. ISSN 2198-9745. 8, p. 222–244. doi: 10.1007/s40753-022-00181-0. Full text in Research Archive Show summary

  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 diferences 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.

• Bingolbali, Erhan; Demir, Gokhan & Monaghan, John David (2020). Knowledge of Sets: a Didactic Phenomenon. International Journal of Science and Mathematics Education. ISSN 1571-0068. doi: 10.1007/s10763-020-10106-5. Full text in Research Archive
• Rensaa, Ragnhild Johanne; Hogstad, Ninni Marie & Monaghan, John David (2020). Perspectives and reflections on teaching linear algebra. Teaching Mathematics and its Applications. ISSN 0268-3679. 39(4), p. 296–309. doi: 10.1093/teamat/hraa002. Full text in Research Archive Show summary

  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.

• Rensaa, Ragnhild Johanne; Hogstad, Ninni Marie & Monaghan, John David (2019). Themes within lecturers' views on the teaching of linear algebra. International Journal of Mathematical Education in Science and Technology. ISSN 0020-739X. 52(1), p. 107–123. doi: 10.1080/0020739X.2019.1668976. Full text in Research Archive Show summary

  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.

• Drijvers, Paul; Gitirana, Veronica; Monaghan, John David; Okumus, Samet; Besnier, Sylvaine & Pfeiffer, Cerenus [Show all 34 contributors for this article] (2019). Transitions towards digital resources: change, invariance, and orchestration. In Trouche, Luc; Gueudet, Ghislaine & Pepin, Birgit (Ed.), The 'Resource' Approach to Mathematics Education. Springer. ISSN 9783030203924. doi: 10.1007/978-3-030-20393-1_12. Full text in Research Archive
• Kidron, Ivy; Bosch, Marianna; Monaghan, John David & Palmer, Hanna (2018). Theoretical perspectives and approaches in mathematics education research. In Dreyfus, Tommy; Artigue, Michèle; Potari, Despina; Prediger, Susanne & Ruthven, Kenneth (Ed.), Developing Research in Mathematics Education: Twenty Years of Communication, Cooperation and Collaboration in Europe (European Research in Mathematics Education). Routledge. ISSN 9781138080294. p. 254–268. doi: 10.4324/9781315113562-19. Full text in Research Archive
• Fredriksen, Helge; Hadjerrouit, Said; Monaghan, John David & Rensaa, Ragnhild Johanne (2017). Exploring Tensions in a Mathematical Course for Engineers utilizing a Flipped Classroom Approach. In Dooley, Thérèse & Gueudet, Ghislaine (Ed.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME 10). European Society for Research in Mathematics Education. ISSN 9781873769737. p. 2057–2064. Full text in Research Archive Show summary

  Flipped Classroom approaches to teaching are becoming increasingly popular in higher education, but there is a lack of empirical research. We present here a study performed during an engineering course for 20 students at a Norwegian university, on student appropriation towards Flipped Classroom through interviews, questionnaire, video/quiz usage statistics and classroom filming. We approach this research through an activity theoretical framework, focusing on tensions experienced as the students try to tackle the demand of video preparation and active learning in class. In line with much of the recent research on the topic, we find that most students seem to appreciate more collaboration with peers and teacher. However, there is also evidence that the new form of teaching creates various tensions; a minor part of the cohort demonstrates conflicting beliefs about mathematics learning, resisting the active learning part of Flipped Classroom.

• Clay, Simon; Fotou, Nikolaos & Monaghan, John David (2017). The Use of Software in Academic Stream High School Mathematics Teaching. The International Journal for Technology in Mathematics Education. ISSN 1744-2710. 24(1), p. 37–45. Full text in Research Archive
• Aydin, Hatice & Monaghan, John David (2017). Encouraging students’ problem posing through importing visual images into mathematical software. Teaching Mathematics and its Applications. ISSN 0268-3679. doi: 10.1093/teamat/hrx005. Full text in Research Archive
• Monaghan, John David (2016). Developments Relevant to the Use of Tools in Mathematics, Tools and Mathematics: Instruments for Learning. Springer. ISSN 9783319023960. p. 163–180. doi: 10.1007/978-3-319-02396-0_7. Full text in Research Archive
• Monaghan, John David (2016). Games: Artefacts in gameplay, Tools and Mathematics: Instruments for Learning. Springer. ISSN 9783319023960. p. 417–431. doi: 10.1007/978-3-319-02396-0_18. Full text in Research Archive
• Monaghan, John David; Trouche, Luc; Borwein, Jonathan M & Noss, Richard (2016). Discussion of issues in chapters in Part II, Tools and Mathematics: Instruments for Learning. Springer. ISSN 9783319023960. p. 257–264. doi: 10.1007/978-3-319-02396-0_11. Full text in Research Archive
• Trouche, Luc; Borwein, Jonathan M & Monaghan, John David (2016). Discussion of issues in chapters in Part I, Tools and Mathematics: Instruments for Learning. Springer. ISSN 9783319023960. p. 139–160. Full text in Research Archive
• Monaghan, John David (2016). Tools, human development and mathematics, Tools and Mathematics: Instruments for Learning. Springer. ISSN 9783319023960. p. 91–115. doi: 10.1007/978-3-319-02396-0_4. Full text in Research Archive
• Monaghan, John David (2016). Activity theoretic approaches, Tools and Mathematics: Instruments for Learning. Springer. ISSN 9783319023960. p. 197–218. doi: 10.1007/978-3-319-02396-0_9. Full text in Research Archive
• Monaghan, John David (2016). Doing mathematics with tools: one task, four tools, Tools and Mathematics: Instruments for Learning. Springer. ISSN 9783319023960. p. 13–22. doi: 10.1007/978-3-319-02396-0_2. Full text in Research Archive
• Monaghan, John David (2016). Constructionism, Tools and Mathematics: Instruments for Learning. Springer. ISSN 9783319023960. p. 181–196. Full text in Research Archive
• Monaghan, John David (2016). The calculator debate, Tools and Mathematics: Instruments for Learning. Springer. ISSN 9783319023960. p. 305–331. doi: 10.1007/978-3-319-02396-0_13. Full text in Research Archive
• Monaghan, John David (2016). Tools and mathematics in real world, Tools and Mathematics: Instruments for Learning. Springer. ISSN 9783319023960. p. 333–356. doi: 10.1007/978-3-319-02396-0_14. Full text in Research Archive
• Monaghan, John David & Trouche, Luc (2016). Mathematics teachers and digital tools, Tools and Mathematics: Instruments for Learning. Springer. ISSN 9783319023960. p. 357–384. doi: 10.1007/978-3-319-02396-0_15. Full text in Research Archive
• Monaghan, John David (2016). Tasks and digital tools, Tools and Mathematics: Instruments for Learning. Springer. ISSN 9783319023960. p. 391–415. doi: 10.1007/978-3-319-02396-0_17. Full text in Research Archive
• Kortenkamp, Ulrich; Monaghan, John David & Trouche, Luc (2016). Jonathan M Borwein (1951–2016): exploring, experiencing and experimenting in mathematics – an inspiring journey in mathematics. Educational Studies in Mathematics. ISSN 0013-1954. p. 131–136. doi: 10.1007/s10649-016-9729-0. Full text in Research Archive
• Carlsen, Martin; Erfjord, Ingvald; Hundeland, Per Sigurd & Monaghan, John David (2016). Kindergarten teachers’ orchestration of mathematical activities afforded by technology: agency and mediation. Educational Studies in Mathematics. ISSN 0013-1954. 93(1), p. 1–17. doi: 10.1007/s10649-016-9692-9. Full text in Research Archive
• Avraamidou, Antri; Monaghan, John David & Walker, Alisha (2015). Mathematics and Non-School Gameplay. In Lowrie, Tom & Jorgensen, Robyn (Ed.), Digital Games and Mathematics Learning Potential, Promises and Pitfalls. Springer. ISSN 9789401795173. p. 11–20. doi: 10.1007/978-94-017-9517-3_2. Full text in Research Archive
• Monaghan, John David (2015). Tool use in mathematics: A framework. In Krainer, Konrad & Vondrova, Nada (Ed.), Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education. European Society for Research in Mathematics Education. ISSN 9788072908448. p. 2681–2687. Full text in Research Archive

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• Bosch, Marianna; Chevallard, Yves; Garcia, Francisco Javier & Monaghan, John David (2019). Working with the Anthropological Theory of the Didactic in Mathematics Education. Routledge. ISBN 9780367187705. 240 p. Full text in Research Archive
• Monaghan, John David; Borwein, Jonathan M & Trouche, Luc (2016). Tools and Mathematics: Instruments for Learning. Springer. ISBN 9783319023960. 483 p. Full text in Research Archive

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• Monaghan, John David (2018). Artefacts in the real world and artefacts in mathematics education research. Full text in Research Archive
• Monaghan, John David & Trouche, Luc (2017). Using tools for doing mathematics vs. using tools for teaching mathematics, differences and similarities. Full text in Research Archive
• Monaghan, John David (2017). Tools, tasks and mathematics. Full text in Research Archive
• Monaghan, John David (2017). The influence of technology/tools in conceptualizing mathematics. Full text in Research Archive
• Monaghan, John David (2017). Digital tool use in 14-21 mathematics education: where we’ve come from and where we might be going. Full text in Research Archive
• Umameh, Michael & Monaghan, John David (2017). A classification of resources used by mathematics teachers in an English high school. Full text in Research Archive
• Monaghan, John David & Trouche, Luc (2016). Introduction to the book, Tools and Mathematics: Instruments for Learning. Springer. ISSN 9783319023960. p. 3–12. Full text in Research Archive
• Monaghan, John David (2016). Tool and mathematics — tools matter. Full text in Research Archive
• Monaghan, John David (2016). The practices of mathematics education doctoral students. Full text in Research Archive
• Bosch, Marianna; Chevallard, Yves; Kidron, Ivy; Monaghan, John David; Palmer, Hanna & Bingolbali, Erhan [Show all 7 contributors for this article] (2015). Introduction to the papers of TWG17: Theoretical perspectives and approaches in mathematics education research. In Krainer, Konrad & Vondrova, Nada (Ed.), Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education. European Society for Research in Mathematics Education. ISSN 9788072908448. p. 2595–2598. Full text in Research Archive
• Dreyfus, Tommy; Gonzalez-Martin, Alejandro S.; Monaghan, John David; Nardi, Elena & Thompson, Pat (2023). The learning and teaching of calculus across disciplines - proceedings of the second calculus conference. MatRIC. Full text in Research Archive
• Hillesund, Eivind Rudjord; Monaghan, John David & Hadjerrouit, Said (2020). The resource decisions and documents of undergraduate engineering students in mathematics courses. Universitetet i Agder. ISSN 9788284270104. Full text in Research Archive Show summary

  This thesis concerns a multiple case study, carried out at three Norwegian universities. The goal was to find similarities and differences between how engineering students from different university contexts used resources to learn mathematics, and how they made decisions regarding their use of resources. My project had an inductive focus, networking thematic analysis (Braun & Clarke, 2006) with the theoretical framework of the documentational approach to didactics (Gueudet & Trouche, 2009). After my analysis, I also compared my results and conclusions to those of authors who have conducted research projects with a similar focus (i.e. Anastasikis, 2018; Gueudet & Pepin, 2016; Kanwal, 2018; Pepin & Kock, 2019). I generally found that my results were consistent with their reflections, but I had also identified trends that went beyond the ideas within the field. Given the wide focus of the project, the result are numerous, and vary greatly in generality and theoretic value. There are two overarching results that I consider particularly significant to the field of research: I identify an overall structure to students’ decision regarding resources. Students almost exclusively consider resources that are emphasized within the course at hand; that they are familiar with from previous educational experiences or that they are familiar with from non-mathematical activities (for instance YouTube and Google). They primarily make their decisions based on what seems suitable for the task at hand, with preference as a secondary concern. Examinations have a significant impact on what they consider suitable. Their preference for resources are based on quality criteria such as simplicity and that they are able to use the resources efficiently. I introduce the notion of didactical resource purposes. Students use resources for the four purposes of introduction, practice, evaluation and explanation. That is, they use resources to learn the theory and foundations of a topic; to gain experience working mathematically within the confines of the topic; to evaluate their answers, their learning process or their understanding of the topic and to actively search for information when they realize that there is a fact that they do not recall or an aspect of the topic that they do not understand well enough to accomplish their goals.

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