John David Monaghan

• 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. 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.
• 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.

• 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 978-3-030-20392-4. doi: 10.1007/978-3-030-20393-1_12.
• 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.

• 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 978-1138080294. p. 254–268. doi: 10.4324/9781315113562-19.
• 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 978-1-873769-73-7. 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.

• 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.
• 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.
• Monaghan, John David & Trouche, Luc (2016). Mathematics teachers and digital tools, Tools and Mathematics: Instruments for Learning. Springer. ISSN 978-3-319-02396-0. p. 357–384. doi: 10.1007/978-3-319-02396-0_15.
• 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 978-3-319-02396-0. p. 257–264. doi: 10.1007/978-3-319-02396-0_11.
• 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 978-3-319-02396-0. p. 139–160.
• Monaghan, John David (2016). Games: Artefacts in gameplay, Tools and Mathematics: Instruments for Learning. Springer. ISSN 978-3-319-02396-0. p. 417–431. doi: 10.1007/978-3-319-02396-0_18.
• Monaghan, John David (2016). Tasks and digital tools, Tools and Mathematics: Instruments for Learning. Springer. ISSN 978-3-319-02396-0. p. 391–415. doi: 10.1007/978-3-319-02396-0_17.
• Monaghan, John David (2016). Tools and mathematics in real world, Tools and Mathematics: Instruments for Learning. Springer. ISSN 978-3-319-02396-0. p. 333–356. doi: 10.1007/978-3-319-02396-0_14.
• Monaghan, John David (2016). The calculator debate, Tools and Mathematics: Instruments for Learning. Springer. ISSN 978-3-319-02396-0. p. 305–331. doi: 10.1007/978-3-319-02396-0_13.
• Monaghan, John David (2016). Activity theoretic approaches, Tools and Mathematics: Instruments for Learning. Springer. ISSN 978-3-319-02396-0. p. 197–218. doi: 10.1007/978-3-319-02396-0_9.
• Monaghan, John David (2016). Constructionism, Tools and Mathematics: Instruments for Learning. Springer. ISSN 978-3-319-02396-0. p. 181–196.
• Monaghan, John David (2016). Developments Relevant to the Use of Tools in Mathematics, Tools and Mathematics: Instruments for Learning. Springer. ISSN 978-3-319-02396-0. p. 163–180. doi: 10.1007/978-3-319-02396-0_7.
• Monaghan, John David (2016). Tools, human development and mathematics, Tools and Mathematics: Instruments for Learning. Springer. ISSN 978-3-319-02396-0. p. 91–115. doi: 10.1007/978-3-319-02396-0_4.
• Monaghan, John David (2016). Doing mathematics with tools: one task, four tools, Tools and Mathematics: Instruments for Learning. Springer. ISSN 978-3-319-02396-0. p. 13–22. doi: 10.1007/978-3-319-02396-0_2.
• 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.
• 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
• 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 978-80-7290-844-8. p. 2681–2687.
• 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 978-94-017-9517-3. p. 11–20. doi: 10.1007/978-94-017-9517-3_2.

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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.
• Monaghan, John David; Borwein, Jonathan M & Trouche, Luc (2016). Tools and Mathematics: Instruments for Learning. Springer. ISBN 978-3-319-02396-0. 483 p.

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• Monaghan, John David (2018). Artefacts in the real world and artefacts in mathematics education research.
• Monaghan, John David (2017). Tools, tasks and mathematics.
• Monaghan, John David (2017). The influence of technology/tools in conceptualizing mathematics.
• Monaghan, John David (2017). Digital tool use in 14-21 mathematics education: where we’ve come from and where we might be going.
• Monaghan, John David & Trouche, Luc (2017). Using tools for doing mathematics vs. using tools for teaching mathematics, differences and similarities.
• Umameh, Michael & Monaghan, John David (2017). A classification of resources used by mathematics teachers in an English high school.
• Monaghan, John David; Trouche, Luc & Borwein, Jonathan M (2016). Interlude, Tools and Mathematics: Instruments for Learning. Springer. ISSN 978-3-319-02396-0. p. 385–388.
• Monaghan, John David & Trouche, Luc (2016). Introduction to the book, Tools and Mathematics: Instruments for Learning. Springer. ISSN 978-3-319-02396-0. p. 3–12.
• Monaghan, John David (2016). Tool and mathematics — tools matter.
• Monaghan, John David (2016). The practices of mathematics education doctoral students.
• 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 978-80-7290-844-8. p. 2595–2598.
• 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.
• 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 978-82-8427-010-4. Full text in Research Archive

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