David Alexander Reid

• 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 978-963-7031-04-5. p. 52–55. Full text in Research Archive
• 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. 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.

• Brown, Laurinda & Reid, David Alexander (2023). A Conversation about Differences. Constructivist Foundations. ISSN 1782-348X. 18(2), p. 277–279.
• 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

• 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. doi: 10.1007/s10763-023-10386-7. 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.

• 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 Twelfth Congress of the European Society for Research in Mathematics Education (CERME12). European Society for Research in Mathematics Education. ISSN 979-1-22-102537-8. p. 299–306.
• 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 978-84-1302-177-5. p. 267–274. Full text in Research Archive
• 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 978-84-1302-175-1. p. 211–212.
• 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 978-87-7507-525-6. p. 105–112. doi: 10.7146/aul.452. Full text in Research Archive
• 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. 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.

• 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.
• 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.
• 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.
• 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.
• 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.
• Barwell, Richard; Lunney Borden, Lisa; 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; Lunney Borden, Lisa & Barwell, Richard (Ed.), Researching Pedagogy and Practice with Canadian Mathematics Teachers. Information Age Publishing. ISSN 978-1-64802-137-4. 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.

• 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 (2020). Observing the Observers: Reflections on Our Research. In Reid, David Alexander; Suurtamm, Christine; Savard, Annie; Simmt, Elaine; Manuel, Dominic; Lunney Borden, Lisa & Barwell, Richard (Ed.), Researching Pedagogy and Practice with Canadian Mathematics Teachers. Information Age Publishing. ISSN 978-1-64802-137-4. p. 231–239. 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; Lunney Borden, Lisa & Barwell, Richard (Ed.), Researching Pedagogy and Practice with Canadian Mathematics Teachers. Information Age Publishing. ISSN 978-1-64802-137-4. p. 157–186. 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; Lunney Borden, Lisa & Barwell, Richard (Ed.), Researching Pedagogy and Practice with Canadian Mathematics Teachers. Information Age Publishing. ISSN 978-1-64802-137-4. p. 1–21. 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
• 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. 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.

• Hanna, Gila; Reid, David Alexander & de Villiers, Michael (2019). Proof Technology: Implications for Teaching, Proof Technology in Mathematics Research and Teaching. Springer. ISSN 978-3-030-28482-4. doi: 10.1007/978-3-030-28483-1_1.
• 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 978-3-030-15635-0. p. 3–31. doi: 10.1007/978-3-030-15636-7_1.
• 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.
• Ahmadpour Mobarakeh, Fatemeh; 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.
• 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.
• Reid, David Alexander (2019). Tensions in describing group problematizing. Constructivist Foundations. ISSN 1782-348X. 15(1), p. 63–65.
• 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.

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• Reid, David Alexander; Suurtamm, Christine; Savard, Annie; Simmt, Elaine; Manuel, Dominic & Lunney Borden, Lisa [Show all 7 contributors for this article] (2020). Researching Pedagogy and Practice with Canadian Mathematics Teachers. Information Age Publishing. ISBN 978-1-64802-137-4. 245 p. 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.

• 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. 40(2020). 60 p.
• Hanna, Gila; Reid, David Alexander & de Villiers, Michael (2019). Proof Technology in Mathematics Research and Teaching. Springer. ISBN 978-3-030-28482-4. 14(1). 379 p.

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• Reid, David Alexander & Carlsen, Martin (2023). An ALTA for Grade 5 Equation Solving .
• Reid, David Alexander (2023). Editorial. For the Learning of Mathematics. ISSN 0228-0671. 43(2), p. 24–24.
• Reid, David Alexander (2021). Mathematical Reasoning, Proof and Argumentation: an attempt at conceptual clarification .
• Reid, David Alexander; Bikner-Ahsbahs, Angelika; Janßen, Thomas & Vallejo-Vargas, Estela (2021). FORMS OF EPISTEMIC FEEDBACK . 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). Editorial. For the Learning of Mathematics. ISSN 0228-0671. 40(3), p. 2–2.
• Reid, David Alexander (2020). Preface. In Reid, David Alexander; Suurtamm, Christine; Savard, Annie; Simmt, Elaine; Manuel, Dominic; Lunney Borden, Lisa & Barwell, Richard (Ed.), Researching Pedagogy and Practice with Canadian Mathematics Teachers. Information Age Publishing. ISSN 978-1-64802-137-4. p. ix–xi. 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; Jones, Keith & Even, Ruhama (2019). INTERNATIONAL PERSPECTIVES ON PROOF AND PROVING.
• 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 978-3-030-15635-0. p. 393–405. doi: 10.1007/978-3-030-15636-7_19.
• 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. .
• Papadaki, Chrissa; Reid, David Alexander & Knipping, Christine (2019). Abduction in argumentation: Two representations that reveal its different functions. .

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