David Alexander Reid

• Reid, David Alexander (2025). Proof-related competences in Nordic mathematics curricula: a cross-cultural comparison | NOMAD Nordic Studies in Mathematics Education. NOMAD – Nordisk matematikkdidaktikk. ISSN 1104-2176. 30(3), p. 101–122. doi: 10.7146/nomad.v30i3.151471. Full text in Research Archive Show summary

  This article examines the presentation and progression of proof-related competencies in the national curricula of Denmark, Finland, Norway, and Sweden. Building on Hemmi, Lepik, and Viholainen’s (2013) work, this study provides an updated analysis of curricular expectations regarding proof and proving across Nordic countries, refining the framework used in prior research. Findings indicate that Denmark and Finland emphasise proof-related competencies more consistently across school levels than Norway and Sweden, with “proof” explicitly referenced in upper grades. This study highlights differences in curricular emphasis and suggests that future applications of the analytic framework might include textbook analysis to further illuminate proof competency development.

• Reid, David Alexander & Carlsen, Martin (2025). Designing learning activities to promote algebraic thinking: Equation solving in Grade 5. In Skott, Charlotte Krog; Blomhøj, Morten; Eckert, Andreas; Elicer, Raimundo; Herheim, Rune; Kristinsdóttir, Bjarnheiður; Larsen, Dorte Moeskær; Nortvedt, Guri A.; Nyström, Peter; Sigurjónsson, Jóhann Örn & Tamborg, Andreas Lindenskov (Ed.), Interplay between research and teaching practice in mathematics education : Proceedings of NORMA24, The tenth Nordic Conference on Mathematics Education, Copenhagen, 2024. Svensk förening för MatematikDidaktisk Forskning - SMDF. ISSN 9789198402483. p. 104–111. Full text in Research Archive Show summary

  The aim of this study is to give insights into the design, implementation, and re-design of a teachinglearning activity on algebra at fifth grade. The mathematical topic was linear equations. Drawing on algebraic thinking as a theoretical construct, two progressions are analyzed, from arithmetic equations to algebraic equations and from actions on concrete objects to symbolic manipulations. The study reports design principles developed from a pilot study and theory, and the design-based research process in which an algebra learning-teaching activity (ALTA) was co-designed by mathematics teachers and researchers, through which the design principles were revised. The revised design principles are reported.

• Torkildsen, Hermund André; Forbregd, Tore Alexander; Reid, David Alexander & Kanwal, Shaista (2025). Norwegian Mathematics Teacher Educators’ and Research Mathematicians’ Views on Different Aspects of Mathematical Definitions: a Comparative Judgement Study. International Journal of Science and Mathematics Education. ISSN 1571-0068. 23, p. 2157–2180. doi: 10.1007/s10763-024-10534-7. Full text in Research Archive Show summary

  In this article we investigate the extent to which characteristics used to describe mathematical definitions in mathematics education research literature reflect what is important to research mathematicians and mathematics teacher educators. We report results from a comparative judgement survey of 57 research mathematicians and 62 mathematics teacher educators. Our results indicate that the two groups are mostly in agreement about the rankings, however, there are some differences. Research mathematicians rank most highly characteristics related to non-ambiguity and non-contradiction, while mathematics teacher educators rank characteristics related to comprehension and referential clarity as highly as characteristics related to non-ambiguity and non-contradiction. Neither group ranked minimality highly, even though this is the characteristic most often listed in the mathematics education research literature. Our study contributes towards a more consistent characterization of mathematical definitions in mathematics education research.

• Shinno, Yusuke; Bredow, Fiene; Knipping, Christine Dorothea; Hakamata, Ryoto; Miyakawa, Takeshi & Otani, Hiroki [Show all 7 contributors for this article] (2024). A preliminary analysis of two proof lessons from an international comparative perspective: A case study on German and Japanese grade 8 classrooms. Proceedings of the International Groups for the Psychology of Mathematics Education. ISSN 0771-100X. Full text in Research Archive
• Moutsios-Rentzos, Andreas; Buchbinder, Orly; Azrou, Nadia; Bredow, Fiene; Deslis, Dimitrios & Durand-Guerrier, Viviane [Show all 8 contributors for this article] (2023). An introduction to TWG1: Argumentation and proof. In Drijvers, Paul; Csapodi, Csaba; Palmer, Hanna; Gosztonyi, Katalin & Kónya, Eszter (Ed.), Proceedings of the thirteenth Congress of the European Society for Research in Mathematics Education (CERME13). European Society for Research in Mathematics Education. ISSN 9789637031045. p. 52–55. Full text in Research Archive Show summary

  Argumentation and proof is a research area that continues to attract the wide interest of the mathematics education research community, which was also evident in CERME13. CERME13 was the first in-person conference after a period of online meetings, which was reflected on the great interest of the participants who were actively engaged in practicing and promoting communication, cooperation, and collaboration. In Thematic Working Group 1 (TWG1; “Argumentation and proof”), 48 participants from 20 different countries discussed and reflected upon the 34 papers and 6 posters presented in TWG1. The papers of TWG1 were organized in four topics: a) Argumentation and proof in teacher training and education, b) Argumentation and proof in school and university mathematics, c) Theoretical and epistemological perspectives about argumentation and proof, and d) Argumentation and proof in mathematical activity, modelling, and problem solving. The work of TWG1 was organized in whole-group sessions and (parallel) split-group sessions to maximize active participation and to ensure the coherence and unity of the TWG1 spirit in the split-groups. The main points of interest of each split-group session were reported in a whole-group session, so that an overview of all TWG1 papers would be obtained. In this introductory chapter, drawing upon the discussions of our group, the TWG1 papers are organized in three themes: a) Theoretical and epistemological perspectives about argumentation and proof, b) Argumentation and proof in teacher education and training, and c) Argumentation and proof in school and university.

• Bikner-Ahsbahs, Angelika; Döring, Tania; Janßen, Thomas & Reid, David Alexander (2023). A Pragmatic Approach to Theorizing Interdisciplinary Design Research on Interactive Math Learning Systems: The Case of a Multimodal Algebra Learning System with Tangible User Interfaces. In Pepin, Birgit; Gueudet, Ghislaine & Choppin, Jeff (Ed.), Handbook of Digital Resources in Mathematics Education. Springer. ISSN 9783030950606. p. 1–33. doi: 10.1007/978-3-030-95060-6_3-1. Full text in Research Archive Show summary

  The design of digital curriculum resources for the teaching and learning of a mathematical concept often requires including knowledge from mathematics education early into the technological design process. In the MAL project, researchers from Human-Computer Interaction and Mathematics Education established an interdisciplinary approach to develop a Multimodal Algebra Learning system (MAL system) in order to integrate necessary knowledge from both disciplines from the beginning. This article presents three layers of theorizing necessary to guide the scientific research and development in such an interdisciplinary design approach. The first layer is about theorizing the notion of design. It informs theorizing on the second layer which ties the two disciplines together by a topic-specific design approach, where the MAL system serves as a boundary object whose development requires researchers to cross the boundary between the two disciplines. Within this approach, a third layer of theorizing focuses on the construction of a pragmatic theory frame for our user-centered design of the MAL system. The pragmatic theory frame is set up, philosophically grounded in pragmatism and further developed over the course of the design research leading to design guidelines. We elaborate this frame, illustrate how we applied it in the design research, and improve it by formative evaluation studies. The resulting design research path enriches and tunes design choices. With the help of the Toulmin scheme, we illustrate our local pragmatic theory that describes and predicts under which conditions the final design guidelines for the MAL system would foster teaching/learning algebra conceptually. Tying the parts together, we extract a theoretical template for the transfer.

• Vallejo-Vargas, Estela A & Reid, David Alexander (2023). Influences of a Virtual Manipulatives Context on Argumentation About Integers. International Journal of Science and Mathematics Education. ISSN 1571-0068. 22, p. 585–608. doi: 10.1007/s10763-023-10386-7. Full text in Research Archive Show summary

  This article presents a case study of two Grade 5 boys’ argumentation concerning addition and subtraction of negative numbers while using an interactive tablet-based application simulating positive and negative tiles. We examine the properties of integers they conjectured, and the kinds of evidence and arguments they used to support their conjectures. The proof-based teaching theory used to develop the tasks, and the features of the virtual manipulative environment, are described. The results show that the tasks, in combination with the virtual manipulative environment, allowed the boys to perform calculations that they had not been able to perform previously, that in one instance one boy used a deductive argument to explain a conjecture they had made, and that a known weakness of the counterbalance model of integers that was used was not a problem in this case.

• Brown, Laurinda & Reid, David Alexander (2023). A Conversation about Differences. Constructivist Foundations. 18(2), p. 277–279. Full text in Research Archive
• Bikner-Ahsbahs, Angelika; Vallejo-Vargas, Estela; Rohde, Steffen; Janßen, Thomas; Reid, David Alexander & Alexandrovsky, D. [Show all 9 contributors for this article] (2023). The Role of Feedback When Learning with a Digital Artifact: A Theory Networking Case on Multimodal Algebra Learning. Hiroshima Journal of Mathematics Education (HJME). ISSN 0919-1720. 16, p. 95–116. doi: 10.24529/hjme.1607. Full text in Research Archive Show summary

  How digital feedback supports teaching/learning with a digital tool is not yet well understood. In a networking of theories approach, Activity Theory and the Instrumental Approach are combined to investigate the role of digital feedback for the teaching/learning of integers with the MAL-system, a multimodal algebra learning system. The MAL-system is designed as a multitouch tangible user interface with feedback functions allowing students to mathematically operate with (negative) numbers represented as virtual tiles. We explore the role of digital feedback by a multi-case study at the grade five level, in which we conducted experimental task-based interviews of four student pairs, each supported by a tutor. Findings show that (digital) feedback mediates the teaching/learning activity in a supportive way. Reflection on the way the two theories are combined reveals that they can be regarded as locally integrated into a layered model e

• Reid, David Alexander (2022). 'Reasoning' in national curricula and standards. In Hodgen, Jeremy; Geraniou, Eirini; Bolondi, Giorgio; Feretti, Federica & Ferretti, Federica (Ed.), Proceedings of the 12th Congress of the European Society for Research in Mathematics Education (CERME12). European Society for Research in Mathematics Education. ISSN 9791221025378. p. 299–306. Full text in Research Archive Show summary

  The differing meanings and usages of terms related to argumentation and proof have been discussed in the literature and related to differences in language (e.g., Sekiguchi & Miyazaki, 2000), professional context (e.g., Godino & Recio, 1997), and epistemological perspectives (e.g., Balacheff, 2008). Here I will contribute to this literature by examining the use of the word ‘reasoning’ in the 2020 Norwegian national mathematics curriculum, in the 2000 National Council of Teachers of Mathematics (NCTM) Standards and in the 2003 Education Standards of the German Kultusminister Konferenz (KMK). I will identify differences in usage, make connections to related terms such as ‘argumentation’ and ‘proof’, and suggest a ramework for further discussion of these differences.

• Reid, David Alexander; Shinno, Yusuke & Fujita, Taro (2022). International perspectives on proof and proving: recent results and future directions. In Fernández, Ceneida; Llinares, Salvador; Gutiérrez, Ángel & Planas, Nuria (Ed.), Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education. Universidad de Alicante. ISSN 9788413021751. p. 211–212. Full text in Research Archive
• Otani, Hiroki; Reid, David Alexander & Shinno, Yusuke (2022). How are proof and proving conceptualized in mathematics curriculum documents in the USA and Japan? In Fernandez, C.; Llinares, S.; Gutierrez, A & Planas, N (Ed.), Proceedings of the 45 th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3). Universidad de Alicante. ISSN 9788413021775. p. 267–274. Full text in Research Archive Show summary

  Only a few international comparative studies have reported on proof and proving in curriculum documents. This report proposes a method of comparing the meaning of proof-related words in two specific countries’ curriculum documents (the USA and Japan) through quantitative and interpretative analyses. Using a text mining approach to explore text data, we found that the co-occurrence network of the words “proof” and “prove” in curriculum documents from the two countries is quite different. In the USA, the word “proof” is concerned with justification and “prove” is used as a general process, while in Japan “proof” is more related to discovery and “prove” is more associated with specific theorems

• Reid, David Alexander; Bikner-Ahsbahs, Angelika; Janßen, Thomas & Vallejo-Vargas, Estela (2022). FORMS OF EPISTEMIC FEEDBACK. In Jankvist, Uffe Thomas; Elicer, Raimundo; Clark-Wilson, Alison; Weigand, Hans-Georg & Thomsen, Marianne (Ed.), Proceedings of the 15th International Conference on Technology in Mathematics Teaching(ICTMT 15). Aarhus Universitetsforlag. ISSN 9788775075256. p. 105–112. doi: 10.7146/aul.452. Full text in Research Archive Show summary

  Feedback in a digital learning system has two functions, a pragmatic and an epistemic one. In previous papers, we were concerned with the pragmatic function, showing how digital feedback initiates acting with the system in groups of students. This paper addresses the epistemic function of this feedback by describing how feedback supports understanding algebraic principles. We report on an investigation of learning algebraic rules conducted with a virtual manipulative learning system, distinguishing, identifying and describing different forms of epistemic feedback, that is, how feedback provided by the learning system fosters disclosing and using algebraic principles.

• Reid, David Alexander; Shinno, Yosuke; Komatsu, Kotaro & Tsujiyama, Yosuke (2021). TOULMIN ANALYSIS OF META-MATHEMATICAL ARGUMENTATION IN A JAPANESE GRADE 8 CLASSROOM. In Maitree, Inprasitha; Changsri, Narumon & Boonsena, Nisakorn (Ed.), Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education. Thailand Society of Mathematics Education. ISSN 9786169383000. p. 324–341. Full text in Research Archive Show summary

  In this research report we aim to analyse argumentation at two levels, using the so-called Toulmin model. We examine the structure of the mathematical argumentation, as well as the nature of the meta-mathematical argumentation justifying the validity of some proofs and the rejection of others in a Japanese grade 8 classroom. The results show that the analysis of a meta-mathematical argument allows us to gain a deeper insight into the proving process, although the role of the statements is more difficult to determine.

• Cramer, Jenny; Knipping, Christine; Reid, David Alexander & Specht, Birte (2021). Documenting and developing the current German lexicon. In Mesiti, Carmel; Artigue, Michèle; Hollingsworth, Hilary; Cao, Yiming & Clarke, David (Ed.), Teachers Talking about their Classrooms Learning from the Professional Lexicons of Mathematics Teachers around the World. Routledge. ISSN 9780367376932. Full text in Research Archive
• Cramer, Jenny; Knipping, Christine; Reid, David Alexander & Specht, Birte (2021). German lexicon. In Mesiti, Carmel; Artigue, Michèle; Hollingsworth, Hilary; Cao, Yiming & Clarke, David (Ed.), Teachers Talking about their Classrooms Learning from the Professional Lexicons of Mathematics Teachers around the World. Routledge. ISSN 9780367376932. Full text in Research Archive
• Cramer, Jenny Christine; Knipping, Christine Dorothea; Reid, David Alexander & Specht, Birte (2021). Documenting and developing the German lexicon. In Mesiti, Carmel; Artigue, Michèle; Hollingsworth, Hilary; Cao, Yiming & Clarke, David (Ed.), Teachers Talking about their Classrooms Learning from the Professional Lexicons of Mathematics Teachers around the World. Routledge. ISSN 9780367376932. Full text in Research Archive
• Reid, David Alexander; Cramer, Jenny; Knipping, Christine & Specht, Birte (2021). German Lexicon. In Mesiti, Carmel; Artigue, Michèle; Hollingsworth, Hilary; Cao, Yiming & Clarke, David (Ed.), Teachers Talking about their Classrooms Learning from the Professional Lexicons of Mathematics Teachers around the World. Routledge. ISSN 9780367376932. Full text in Research Archive
• Janßen, Thomas; Vallejo-Vargas, Estela; Bikner-Ahsbahs, Angelika & Reid, David Alexander (2020). Design and Investigation of a Touch Gesture for Dividing in a Virtual Manipulative Model for Equation-solving. Digital Experiences in Mathematics Education. ISSN 2199-3246. 6(2), p. 166–190. doi: 10.1007/s40751-020-00070-8. Full text in Research Archive
• Barwell, Richard; Borden, Lisa Lunney; Manuel, Dominic; Reid, David Alexander; Savard, Annie & Simmt, Elaine [Show all 7 contributors for this article] (2020). Researching Mathematics Pedagogy. In Reid, David Alexander; Suurtamm, Christine; Savard, Annie; Simmt, Elaine; Manuel, Dominic; Borden, Lisa Lunney & Barwell, Richard (Ed.), Researching Pedagogy and Practice with Canadian Mathematics Teachers. Information Age Publishing. ISSN 9781648021374. p. 213–230. Full text in Research Archive Show summary

  This book reports results from a research program that sought to develop and employ research methods to compare teachers’ practices and beliefs across Canada. It provides insight into the challenge of such research, and describes teachers’ contexts, beliefs and practices, and how they differ, in four regions and across two languages. Using a multivocal ethnography approach (Tobin, 1999) teachers were involved in the preparation and discussion of videos of their own teaching and that of others. This approach resulted in not only insights into the teachers’ pedagogies and practices, but also opportunities for the teachers to reflect on their own teaching in new ways, and for researchers to reflect on research practices and orientations. The work is innovative in several ways. In a field crowded with research on teachers’ practices, beliefs and knowledge this research helps to unearth the implicit values that underlie the way teachers see teaching itself. Through the process of observation of each other’s practice, the teachers became aware of their own pedagogies, giving them new insights into their values and practices. Researchers also engaged in a parallel process of reflection on their own practices as observers of teachers, with similar insights into the values guiding their work.

• Reid, David Alexander (2020). Observing Teachers: Comparing Middle School Teachers’ Pedagogies in Four Regions of Canada. In Reid, David Alexander; Suurtamm, Christine; Savard, Annie; Simmt, Elaine; Manuel, Dominic; Borden, Lisa Lunney & Barwell, Richard (Ed.), Researching Pedagogy and Practice with Canadian Mathematics Teachers. Information Age Publishing. ISSN 9781648021374. p. 1–21. Full text in Research Archive Show summary

  The Observing Teachers research program was a collaborative research project that examined middle school mathematics pedagogy in four regions of Canada. This introduction sets out some of the background context and shared research foci and methods that defined the research program at the outset. The research grew and evolved as it progressed, and the chapters of this book provide insights into that evolution.

• Reid, David Alexander (2020). Observing the Observers: Reflections on Our Research. In Reid, David Alexander; Suurtamm, Christine; Savard, Annie; Simmt, Elaine; Manuel, Dominic; Borden, Lisa Lunney & Barwell, Richard (Ed.), Researching Pedagogy and Practice with Canadian Mathematics Teachers. Information Age Publishing. ISSN 9781648021374. p. 231–239. Full text in Research Archive Show summary

  This book reports results from a research program that sought to develop and employ research methods to compare teachers’ practices and beliefs across Canada. It provides insight into the challenge of such research, and describes teachers’ contexts, beliefs and practices, and how they differ, in four regions and across two languages. Using a multivocal ethnography approach (Tobin, 1999) teachers were involved in the preparation and discussion of videos of their own teaching and that of others. This approach resulted in not only insights into the teachers’ pedagogies and practices, but also opportunities for the teachers to reflect on their own teaching in new ways, and for researchers to reflect on research practices and orientations. The work is innovative in several ways. In a field crowded with research on teachers’ practices, beliefs and knowledge this research helps to unearth the implicit values that underlie the way teachers see teaching itself. Through the process of observation of each other’s practice, the teachers became aware of their own pedagogies, giving them new insights into their values and practices. Researchers also engaged in a parallel process of reflection on their own practices as observers of teachers, with similar insights into the values guiding their work.

• Reid, David Alexander (2020). Seeking Patterns in Pedagogy: A Topical Analysis. In Reid, David Alexander; Suurtamm, Christine; Savard, Annie; Simmt, Elaine; Manuel, Dominic; Borden, Lisa Lunney & Barwell, Richard (Ed.), Researching Pedagogy and Practice with Canadian Mathematics Teachers. Information Age Publishing. ISSN 9781648021374. p. 157–186. Full text in Research Archive Show summary

  This book reports results from a research program that sought to develop and employ research methods to compare teachers’ practices and beliefs across Canada. It provides insight into the challenge of such research, and describes teachers’ contexts, beliefs and practices, and how they differ, in four regions and across two languages. Using a multivocal ethnography approach (Tobin, 1999) teachers were involved in the preparation and discussion of videos of their own teaching and that of others. This approach resulted in not only insights into the teachers’ pedagogies and practices, but also opportunities for the teachers to reflect on their own teaching in new ways, and for researchers to reflect on research practices and orientations. The work is innovative in several ways. In a field crowded with research on teachers’ practices, beliefs and knowledge this research helps to unearth the implicit values that underlie the way teachers see teaching itself. Through the process of observation of each other’s practice, the teachers became aware of their own pedagogies, giving them new insights into their values and practices. Researchers also engaged in a parallel process of reflection on their own practices as observers of teachers, with similar insights into the values guiding their work.

• Reid, David Alexander (2020). Learning to teach a mathematical emotional orientation, FLM Monograph 1: Proceedings of a Symposium on Learning in Honour of Laurinda Brown. FLM Publishing Association. ISSN 9781777046705. p. 44–48. Full text in Research Archive
• Janßen, Thomas; Vallejo-Vargas, Estela; Bikner-Ahsbahs, Angelika & Reid, David Alexander (2020). Design and Investigation of a Touch Gesture for Dividing in a Virtual Manipulative Model for Equation-solving. Digital Experiences in Mathematics Education. ISSN 2199-3246. 6, p. 166–190. doi: 10.1007/s40751-020-00070-8. Full text in Research Archive
• Reid, David Alexander (2019). Tensions in describing group problematizing. Constructivist Foundations. 15(1), p. 63–65. Full text in Research Archive
• Reid, David Alexander & Vallejo-Vargas, Estela (2019). Evidence and argument in a proof based teaching theory. ZDM: Mathematics Education. ISSN 1863-9690. 51, p. 807–823. doi: 10.1007/s11858-019-01027-x. Full text in Research Archive
• Knipping, Christine & Reid, David Alexander (2019). Argumentation Analysis for Early Career Researchers. In Kaiser, Gabriele (Eds.), Compendium for Early Career Researchers in Mathematics Education. Springer. ISSN 9783030156350. p. 3–31. doi: 10.1007/978-3-030-15636-7_1. Full text in Research Archive
• Hanna, Gila; Reid, David Alexander & Villiers, Michael de (2019). Proof Technology: Implications for Teaching, Proof Technology in Mathematics Research and Teaching. Springer. ISSN 9783030284824. doi: 10.1007/978-3-030-28483-1_1. Full text in Research Archive
• Cervantes-Barraza, Jonathan; Cabañas-Sánchez, Guadalupe & Reid, David Alexander (2019). Complex Argumentation in Elementary School. PNA: Revista de investigación en Didáctica de la Matemática. ISSN 1886-1350. Full text in Research Archive
• Mobarakeh, Fatemeh Ahmadpour; Reid, David Alexander & Mohammad, Reza Fadaee (2019). Students’ ways of understanding a proof. Mathematical Thinking and Learning. ISSN 1098-6065. 21(2), p. 85–104. doi: 10.1080/10986065.2019.1570833. Full text in Research Archive
• Cervantes-Barraza, Jonathan; Cabañas-Sánchez, Guadalupe & Reid, David Alexander (2019). Complex Argumentation in Elementary School. PNA: Revista de investigación en Didáctica de la Matemática. ISSN 1886-1350. 13(4), p. 221–246. doi: 10.30827/pna.v13i4.8279. Full text in Research Archive Show summary

  This paper describes a study of mathematical argumentation in primary school. The principal aim is to explore the nature of complex argumentation at a structural level. The context of the study was a teaching experiment involving nine tasks that promoted argumentation among fifth graders. We use the framework and method of reconstructing complex argumentation in the classroom proposed by Knipping (2008). The findings show that complex argumentation at a structural level in the context of refuting conclusions is characterized by a source-like structure with the addition of a new refutation argument element.

• Janßen, Thomas; Reid, David Alexander; Vallejo-Vargas, Estela; Bikner-Ahsbahs, Angelika & Malaka, Rainer (2018). Multimodal Algebra Learning: From Math Manipulatives to Tangible User Interfaces. i-com Zeitschrift für interaktive und kooperative Medien. ISSN 1618-162X. doi: 10.1515/icom-2018-0027. Full text in Research Archive

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• Coles, Alf & Reid, David Alexander (2020). FLM Monograph 1: Proceedings of a Symposium on Learning in Honour of Laurinda Brown. FLM Publishing Association. ISBN 9781777046705. 60 p. Full text in Research Archive
• Reid, David Alexander; Suurtamm, Christine; Savard, Annie; Simmt, Elaine; Manuel, Dominic & Borden, Lisa Lunney [Show all 7 contributors for this article] (2020). Researching Pedagogy and Practice with Canadian Mathematics Teachers. Information Age Publishing. ISBN 9781648021374. 245 p. Full text in Research Archive Show summary

  This book reports results from a research program that sought to develop and employ research methods to compare teachers’ practices and beliefs across Canada. It provides insight into the challenge of such research, and describes teachers’ contexts, beliefs and practices, and how they differ, in four regions and across two languages. Using a multivocal ethnography approach (Tobin, 1999) teachers were involved in the preparation and discussion of videos of their own teaching and that of others. This approach resulted in not only insights into the teachers’ pedagogies and practices, but also opportunities for the teachers to reflect on their own teaching in new ways, and for researchers to reflect on research practices and orientations. The work is innovative in several ways. In a field crowded with research on teachers’ practices, beliefs and knowledge this research helps to unearth the implicit values that underlie the way teachers see teaching itself. Through the process of observation of each other’s practice, the teachers became aware of their own pedagogies, giving them new insights into their values and practices. Researchers also engaged in a parallel process of reflection on their own practices as observers of teachers, with similar insights into the values guiding their work.

• Hanna, Gila; Reid, David Alexander & Villiers, Michael de (2019). Proof Technology in Mathematics Research and Teaching. Springer. ISBN 9783030284824. 379 p. Full text in Research Archive

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• Reid, David Alexander (2026). A pathway between representations. Mathematics Teaching. ISSN 0025-5785. 301, p. 12–17. doi: https:/atm.org.uk/write/MediaUploads/Journals/MT301/04.pdf. Full text in Research Archive
• Jåtun, Ole Nikolai & Reid, David Alexander (2025). MATHEMATICAL PROOFS IN JAPANESE AND NORWEGIAN GRADE 5–9 TEXTBOOKS. Full text in Research Archive Show summary

  This study compares the presentation of proofs in Norwegian and Japanese Grade 5– 9 mathematics textbooks, focusing on logical, mathematical, and didactical structures. Proof and proving have distinct roles in the curricula of these two countries, with Norway recently emphasizing reasoning and argumentation, while Japan has long incorporated proof into mathematics education. The research focuses on specific theorems such as the sum of interior angles in a triangle, and the Pythagorean theorem. The results reveal differences in how proofs are introduced, structured, and integrated into the learning process across these educational systems.

• Nilsen, Karoline Kongshavn & Reid, David Alexander (2025). Bevis på barnetrinnet. Tangenten - Tidsskrift for matematikkundervisning. ISSN 0802-8192. 36(1), p. 6–10. Full text in Research Archive
• Reid, David Alexander (2024). Editorial. For the Learning of Mathematics. ISSN 0228-0671. 44(1), p. 2–2. Full text in Research Archive
• Reid, David Alexander & Carlsen, Martin (2023). An ALTA for Grade 5 Equation Solving. Full text in Research Archive
• Reid, David Alexander (2023). Editorial. For the Learning of Mathematics. ISSN 0228-0671. 43(2), p. 24–24. Full text in Research Archive
• Reid, David Alexander (2021). Mathematical Reasoning, Proof and Argumentation: an attempt at conceptual clarification. Full text in Research Archive
• Reid, David Alexander; Bikner-Ahsbahs, Angelika; Janßen, Thomas & Vallejo-Vargas, Estela (2021). FORMS OF EPISTEMIC FEEDBACK. Full text in Research Archive Show summary

  Feedback in a digital learning system has two functions, a pragmatic and an epistemic one. In previous papers, we were concerned with the pragmatic function, showing how digital feedback initiates acting with the system in groups of students. This paper addresses the epistemic function of this feedback by describing how feedback supports understanding algebraic principles. We report on an investigation of learning algebraic rules conducted with a virtual manipulative learning system, distinguishing, identifying and describing different forms of epistemic feedback, that is, how feedback provided by the learning system fosters disclosing and using algebraic principles.

• Reid, David Alexander (2020). Preface. In Reid, David Alexander; Suurtamm, Christine; Savard, Annie; Simmt, Elaine; Manuel, Dominic; Borden, Lisa Lunney & Barwell, Richard (Ed.), Researching Pedagogy and Practice with Canadian Mathematics Teachers. Information Age Publishing. ISSN 9781648021374. p. ix–xi. Full text in Research Archive Show summary

  This book reports results from a research program that sought to develop and employ research methods to compare teachers’ practices and beliefs across Canada. It provides insight into the challenge of such research, and describes teachers’ contexts, beliefs and practices, and how they differ, in four regions and across two languages. Using a multivocal ethnography approach (Tobin, 1999) teachers were involved in the preparation and discussion of videos of their own teaching and that of others. This approach resulted in not only insights into the teachers’ pedagogies and practices, but also opportunities for the teachers to reflect on their own teaching in new ways, and for researchers to reflect on research practices and orientations. The work is innovative in several ways. In a field crowded with research on teachers’ practices, beliefs and knowledge this research helps to unearth the implicit values that underlie the way teachers see teaching itself. Through the process of observation of each other’s practice, the teachers became aware of their own pedagogies, giving them new insights into their values and practices. Researchers also engaged in a parallel process of reflection on their own practices as observers of teachers, with similar insights into the values guiding their work.

• Reid, David Alexander (2020). Editorial. For the Learning of Mathematics. ISSN 0228-0671. 40(3), p. 2–2. Full text in Research Archive
• Barwell, Richard & Reid, David Alexander (2019). For the Learning of Mathematics: An Introduction to the Journal and the Writing Within It. In Kaiser, Gabriele (Eds.), Compendium for Early Career Researchers in Mathematics Education. Springer. ISSN 9783030156350. p. 393–405. doi: 10.1007/978-3-030-15636-7_19. Full text in Research Archive
• Reid, David Alexander; Jones, Keith & Even, Ruhama (2019). INTERNATIONAL PERSPECTIVES ON PROOF AND PROVING. Full text in Research Archive
• Papadaki, Chrissa; Reid, David Alexander & Knipping, Christine (2019). Abduction in argumentation: Two representations that reveal its different functions. Full text in Research Archive
• Janßen, Thomas; Reid, David Alexander & Bikner-Ahsbahs, Angelika (2019). Issues in modelling subtraction terms in a manipulative environment for linear equations—and a possible solution. Full text in Research Archive

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