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Revisiting Theories That Frame Research on Teaching Mathematics with Digital Technology

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The Mathematics Teacher in the Digital Era

Part of the book series: Mathematics Education in the Digital Era ((MEDE,volume 16))

Abstract

In this chapter, we offer an overview of some of the major trends in theory development and use in relation to teaching mathematics with digital technology. We showcase some of the developments that have occurred since the first edition of this book (2014). We also provide a deep review of the multiple ways in which the instrumental approach has evolved over time, as a way to exemplify how theory development responds to new questions and new theoretical insights. Throughout the chapter, we make explicit the philosophical assumptions on which these theories depend—particularly the binaries they reify—and use these to open up consideration of different assumptions and how they might matter to our field of research.

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Notes

  1. 1.

    Although the component ideas were drawn from different sources in the general literature on teaching, as Ruthven (2014) writes: “The Structuring Features of Classroom Practice framework (Ruthven 2009) was devised by bringing a range of concepts from earlier studies of classroom organisation and interaction and of teacher craft knowledge and thinking to bear on this specific issue of technology integration” (p. 386).

  2. 2.

    For each journal, we searched for articles that had the word “teacher”, “teaching” or words related to teachers’ classroom practices (e.g., questioning, assessment, etc.) and words related to technology (e.g., ICT, software, DGE, etc.). We also read the abstract and research questions to determine whether the article related to aspects of teaching mathematics with technology. This produced a final sample of 67 articles. We thank Canan Gunes for her help with this research.

  3. 3.

    This has been a long-standing binary that has served to distinguish those who can think from whose who cannot (animals, plants, stones, etc.). In mathematics, this binary has been at stake in discussions of computer-based proofs—can machines think and know and learn, and therefore produce acceptable proofs, or must this be done by humans in order to be valid? A whole part of the research activity in computer science, via the field of semantics, is occupied with precisely this question and the search for rigorous justifications in computer science.

  4. 4.

    Social constructivism recognises the importance of social interactions in the classroom in the processes of teaching and learning, but this does not change its epistemological commitment to knowledge arising from the individual.

  5. 5.

    As a counterpoint though, two leading scholars of this socio-political turn have studied the role of interactive whiteboards, arguing that this technology exacerbates existing inequities—see Zevenbergen and Lerman (2008).

References

  • Abdu, R., Schwarz, B., & Mavrikis, M. (2015). Whole-class scaffolding for learning to solve mathematics problems together in a computer – Supported environment. ZDM Mathematics Education, 47(7), 1163–1178.

    Article  Google Scholar 

  • Akkerman, S., & Bakker, A. (2011). Boundary crossing and boundary objects. Review of Educational Research, 81(2), 132–169.

    Article  Google Scholar 

  • Aldon, G., & Panero, M. (2020). Can digital technology change the way mathematics skills are assessed? ZDM Mathematics Education, 52(7), 1333–1348.

    Article  Google Scholar 

  • Artigue, M. (1996). Using computer algebraic systems to teach mathematics: A didactic perspective. In E. Barbin & A. Douady (Eds.), Teaching mathematics: The relationship between knowledge, curriculum and practice (pp. 223–239). TOPIQUES éditions.

    Google Scholar 

  • Artigue, M. (1997). Le logiciel DERIVE comme révélateur de phénomènes didactiques liés à l’utilisation d’environnements informatiques pour l’apprentissage. Educational Studies in Mathematics, 33, 133–169.

    Article  Google Scholar 

  • Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. The International Journal of Computers for Mathematics Learning, 7(3), 245–274. (hal-02367871).

    Article  Google Scholar 

  • Artigue, M. (2020). ICMI AMOR MOOC: Michèle Artigue Unit. https://www.mathunion.org/icmi/awards/amor/michele-artigue-unit. Accessed 6 Oct 2021.

  • Artigue, M., Cazes, C., Haspekian, M., Khanfour, R., & Lagrange, JB. (2013). Gestes, cognition incarnée et artefacts : une analyse bibliographique pour une nouvelle dimension dans les travaux didactiques au LDAR. Cahiers du laboratoire de didactique André Revuz, n°8, IREM Paris 7. ISSN 2105–5203. http://docs.irem.univ-paris-diderot.fr/up/publications/IPS13006.pdf

  • Arzarello, F. (2006). Semiosis as a multimodal process. Revista Latinoamericana de Investigación en Matemática Educativa RELIME, 9(Extraordinario 1), 267–299.

    Google Scholar 

  • Arzarello, F., & Robutti, O. (2004). Approaching functions through motion experiments. Educational Studies in Mathematics, 57(3), 305–308.

    Google Scholar 

  • Arzarello, F., & Robutti, O. (2008). Framing the embodied mind approach within a multimodal paradigm. In L. English (Ed.), Handbook of International Research In Mathematics Education (pp. 720–749).

    Google Scholar 

  • Arzarello, F., Olivero, F., Paola, D., & Robutti, O. (2002). A cognitive analysis of dragging practises in Cabri environments. ZDM: Zentralblatt für Ditaktik derMathematik, 34(3), 6–72.

    Google Scholar 

  • Arzarello, F., Paola, D., Robutti, O., & Sabena, C. (2009). Gestures as semiotic resources in the mathematics classroom. Educational Studies in Mathematics, 70(2), 97–109.

    Article  Google Scholar 

  • Arzarello, F., Robutti, O., Sabena, C., Cusi, A., Garuti, R., Malara, N. A., & Martignone, F. (2014). Meta-didactical transposition: A theoretical model for teacher education programs. In A. Clark-Wilson et al. (Eds.), The mathematics teacher in the digital era, mathematics education in the digital era 2 (pp. 347–372). Springer.

    Chapter  Google Scholar 

  • Arzarello, F., Robutti, O., & Thomas, M. (2015). Growth point and gestures: Looking inside mathematical meanings. Educational Studies in Mathematics, 90(1), 19–37.

    Article  Google Scholar 

  • Bairral, M., & Arzarello, F. (2015). The use of hands and manipulation touchscreen in high school geometry classes. In CERME 9-Ninth Congress of the European Society for Research in Mathematics Education (pp. 2460–2466).

    Google Scholar 

  • Bakker, A., Kent, P., Hoyles, C., & Noss, R. (2011). Designing for communication at work: A case of technology-enhanced boundary objects. International Journal of Educational Research, 50(1), 26–32.

    Article  Google Scholar 

  • Balacheff, N. (1994). Didactique et intelligence artificielle. Recherches en Didactique des Mathématiques, 14(1–2), 9–42.

    Google Scholar 

  • Ball, D. L., & Bass, H. (2003). Toward a practice-based theory of mathematical knowledge for teaching. In B. Davis & E. Simmt (Eds.), Proceedings of the 2002 annual meeting of the Canadian Mathematics Education Study Group Edmonton (pp. 3–14). CMESG/GDEDM.

    Google Scholar 

  • Barquero, B., Bosch, M., & Gascón, J. (2013). The ecological dimension in the teaching of mathematical modelling at university. Recherches en didactique des mathématiques, 33(3), 307–338.

    Google Scholar 

  • Bartolini Bussi, M. G., & Baccaglini-Frank, A. (2015). Geometry in early years: Sowing seeds for a mathematical definition of squares and rectangles. ZDM, 47(3), 391–405.

    Article  Google Scholar 

  • Bartolini Bussi, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: Artifacts and signs after a Vygotskian perspective. In L. English et al. (Eds.), Handbook of international research in mathematics education (2nd ed., pp. 746–783). Routledge.

    Google Scholar 

  • Besnier, S., & Gueudet, G. (2016). Usages de ressources numériques pour l’enseignement des mathématiques en maternelle: orchestrations et documents. Perspectivas da Educação Matemática, 9(21), 28 dez. 2016.

    Google Scholar 

  • Bosch, M., & Gascon, J. (2006). Twenty-five years of the didactic transposition. ICMI Bulletin, 58, 51–65.

    Google Scholar 

  • Bozkurt, G., & Ruthven, K. (2017). Classroom-based professional expertise: A mathematics teacher’s practice with technology. Educational Studies in Mathematics, 94(3), 309–328. https://doi.org/10.1007/s10649-016-9732-5

    Article  Google Scholar 

  • Brousseau, G. (2002). Les doubles jeux de l’enseignement des mathématiques. Questions éducatives, l’école et ses marges: Didactique des mathématiques, Revue du Centre de Recherches en Education de l’Université Saint Etienne (22–23), pp. 83–155. hal-00516813.

    Google Scholar 

  • Butler, S. (1872). Erewhon. Trübner & C.

    Google Scholar 

  • Caniglia, B. J., & Meadows, M. (2018). Pre-service mathematics teachers’ use of web resources. International Journal for Technology in Mathematics Education, 25(3), 17–34.

    Google Scholar 

  • Carlsen, M., Erfjord, I., Hundeland, P. S., & Monaghan, J. (2016). Kindergarten teachers’ orchestration of mathematical activities afforded by technology: Agency and mediation. Educational Studies in Mathematics, 93(1).

    Google Scholar 

  • Chevallard, Y. (1985). La transposition didactique – du savoir savant au savoir enseigné. La Pensée Sauvage.

    Google Scholar 

  • Chevallard, Y. (1989). Le passage de l’arithmétique à l’algèbre dans l’enseignement des mathématiques au collège. Deuxième partie. Perspectives curriculaires : la notion de modélisation. Petit x, 19, 43–72.

    Google Scholar 

  • Chevallard, Y. (1992). Concepts fondamentaux de la didactique: perspectives apportées par une approche anthropologique. Recherches en Didactique des Mathématiques, 12(1), 73–112.

    Google Scholar 

  • Chevallard, Y. (1999). L’analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherche en Didactique des Mathématiques, 19(2), 221–266.

    Google Scholar 

  • Chevallard, Y. (2002). Organiser l’étude: 3. Ecologie & régulation. XIe école d’été de didactique des mathématiques (Corps, 2130 de agosto de 2001) (4156). Grenoble: La Pensée Sauvage.

    Google Scholar 

  • Chevallard, Y., & Bosch, M. (2020). Didactic transposition in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education. Springer.

    Google Scholar 

  • Chevallard, Y., & Sensevy, G. (2020). Anthropological approaches in mathematics education, French perspectives. In S. Lerman (Ed.), Encyclopedia of mathematics education. Springer.

    Google Scholar 

  • Chorney, S. (2017). Circles, materiality and movement. For the Learning of Mathematics, 37(3), 45–49.

    Google Scholar 

  • Clark-Wilson, A. (2014). A methodological approach to researching the development of teachers’ knowledge in a multi-representational technological setting. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics teacher in the digital age (pp. 276–295). Springer.

    Google Scholar 

  • Cobb, P. (1988). The tension between theories of learning and instruction in mathematics education. Educational Psychologist, 23(2), 87–103.

    Article  Google Scholar 

  • Defouad, B. (2000). Etude de genèses instrumentales liées à l’utilisation d’une calculatrice symbolique en classe de première S (p. 7). Thèse de doctorat. Université Paris.

    Google Scholar 

  • Donald, M. (1991). Origins of the modern mind: Three stages in the evolution of culture and cognition. Harvard University Press.

    Google Scholar 

  • Drijvers, P. (2004). Learning algebra in a computer algebra environment. International Journal for Technology in Mathematics Education, 11(3), 77–90.

    Google Scholar 

  • Drijvers, P. (2012). Teachers transforming resources into orchestration. In G. Gueudet, B. Pepin, & L. Trouche (Eds.), From text to ‘lived resources’: Curriculum material and mathematics teacher development (pp. 265–281). Springer.

    Google Scholar 

  • Drijvers, P. (2019). Embodied instrumentation: Combining different views on using digital technology in mathematics education. In Eleventh Congress of the European Society for Research in Mathematics Education. Utrecht University.

    Google Scholar 

  • Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool: Instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2), 213–234.

    Article  Google Scholar 

  • Drijvers, P., Tacoma, S., Besamusca, A., Doorman, M., & Boon, P. (2013). Digital resources inviting changes in mid-adopting teachers’ practices and orchestrations. ZDM Mathematics Education, 45(7), 987–1001.

    Article  Google Scholar 

  • Drijvers, P., Gitirana, V., Monaghan, J., Okumus, S., Besnier, S., Pfeiffer, C., … Rodrigues, A. (2019). Transitions toward digital resources: Change, invariance, and orchestration. In L. Trouche et al. (Eds.), The ‘Resource’ approach to mathematics education (pp. 389–444). Springer Nature Switzerland AG.

    Chapter  Google Scholar 

  • Edwards, L. D. (2009). Gestures and conceptual integration in mathematical talk. Educational Studies in Mathematics, 70(2), 127–141.

    Article  Google Scholar 

  • Glanfield, F., Thom, J. S., & Ghostkeeper, E. (2020). Living landscapes, Archi-text-ures, and land-guaging Algo-rhythms. Canadian Journal of Science, Mathematics, and Technology Education, 20, 246–263.

    Article  Google Scholar 

  • Goldin-Meadow, S. (2005). Hearing gesture: How our hands help us think. Harvard University Press.

    Book  Google Scholar 

  • Grosz, E. (2012). The nature of sexual difference: Irigaray and Darwin. Angelaki, 17(2), 69–93.

    Article  Google Scholar 

  • Gueudet, G., & Trouche, L. (2009). Towards new documentation systems for mathematics teachers. Educational Studies in Mathematics, 71, 199–218.

    Article  Google Scholar 

  • Guin, D., & Trouche, L. (1998). The complex process of converting tools into mathematical instruments: The case of calculators. International Journal of Computers for Mathematical Learning, 3(3), 195–227.

    Article  Google Scholar 

  • Guin, K., Ruthven, R., & Trouche, L. (Eds.). (2005). The didactical challenge of symbolic calculators: Turning a computational device into a mathematical instrument. Springer.

    Google Scholar 

  • Gutiérrez, R. (2013). The sociopolitical turn in mathematics education. Journal for Research in Mathematics Education, 44(1), 37–68.

    Article  Google Scholar 

  • Haspekian, M. (2005). An “instrumental approach” to study the integration of a computer tool into mathematics teaching: The case of spreadsheets. The International Journal of Computers for Mathematics Learning, 10(2), 109–141.

    Article  Google Scholar 

  • Haspekian, M. (2011). The co-construction of a mathematical and a didactical instrument. In M. Pytak, E. Swoboda, & T. Rowland (Eds.), Proceedings of CERME 7 (pp. 2298–2307).

    Google Scholar 

  • Haspekian, M. (2017). Computer science in mathematics new curricula at primary school: New tools, new teaching practices? In G. A. & J. Trgalova (Eds.), Proceedings of ICTMT 13 (pp. 23–31).

    Google Scholar 

  • Healy, L., & Kynigos, C. (2010). Charting the microworld territory over time: Design and construction in mathematics education. ZDM Mathematics Education, 42, 63–76.

    Article  Google Scholar 

  • Hegedus, S. J., & Moreno-Armella, L. (2009). Intersecting representation and communication infrastructures. ZDM, 41(4), 399–412.

    Article  Google Scholar 

  • Højsted, I. H. (2020). Teachers reporting on dynamic geometry utilization related to reasoning competency in Danish lower secondary school. Digital Experiences in Mathematics Education, 6(1), 91–105.

    Article  Google Scholar 

  • Hoyles, C. (1992). Illuminations and reflections: Teachers, methodologies and mathematics. In W. Geelin & K. Graham (Eds.), Proceedings of the 16th Conference of the Internal Group for the Psychology of Mathematics Education (Vol. 3, pp. 263–286). University of New Hampshire.

    Google Scholar 

  • Jackiw, N. (2013). Touch and multitouch in dynamic geometry: Sketchpad explorer and ‘digital’ mathematics. In E. Faggiano & A. Montone (Eds.), Proceedings of the 11th International Conference on Technology in Mathematics Teaching (pp. 149–155). Università degli Studi di Bari Aldo Moro.

    Google Scholar 

  • Kaput, J. (1989). Linking representations in the symbol systems of Algebra. In S. Wagner & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (pp. 167–194). NCTM.

    Google Scholar 

  • Keeling, K. (2019). Queer Times, Black Futures. New York University Press.

    Google Scholar 

  • Kynigos, C. (2007). Half-based Logo microworlds as boundary objects in integrated design. Informatics in Education, 6(2), 335–358.

    Article  Google Scholar 

  • Lagrange, J. B. (1999). Techniques and concepts in pre-calculus using CAS: A two year classroom experiment with the TI92. The International Journal for Computer Algebra in Mathematics Education, 6(2), 143–165.

    Google Scholar 

  • Lagrange, J.-B., Artigue, M., Laborde, C., & Trouche, L. (2003). Technology and mathematics educaiton: A multidimensional study of the evolution of research and innovation. In A. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. Leung (Eds.), Second international handbook of mathematics education (pp. 237–269). Springer.

    Chapter  Google Scholar 

  • Lakoff, G., & Núñez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. Basic Books.

    Google Scholar 

  • Latour, B. (1987). Science in action. Harvard University Press.

    Google Scholar 

  • Lemke, J. (2000). Across the scales of time: Artifacts, activities, and meanings in ecosocial systems. Mind, Culture, and Activity, 7(4), 273–290.

    Article  Google Scholar 

  • Lerman, S. (1996). Intersubjectivity in mathematics learning: A challenge to the radical constructivist paradigm? Journal for Research in Mathematics Education, 27(2), 133–150.

    Article  Google Scholar 

  • Mariotti, M. A. (2002). The influence of technological advances on students’ mathematics learning (pp. 695–723). Handbook of International Research in Mathematics Education.

    Google Scholar 

  • Mariotti, M. A. (2009). Artifacts and signs after a Vygotskian perspective: The role of the teacher. ZDM, 41(4), 427–440.

    Article  Google Scholar 

  • Maschietto, M., & Soury-Lavergne, S. (2013). Designing a duo of material and digital artifacts: The pascaline and Cabri Elem e-books in primary school mathematics. ZDM, 45(7), 959–971.

    Article  Google Scholar 

  • Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for integrating technology in teacher knowledge. Teachers College Record, 108(6), 1017–1054.

    Article  Google Scholar 

  • Moschkovich, J. (2002). A situated and sociocultural perspective on bilingual mathematics learners. Mathematical Thinking and Learning, 4(2–3), 189–212.

    Article  Google Scholar 

  • Nemirovsky, R., & Ferrara, F. (2008). Mathematical imagination and embodied cognition. Educational Studies of Mathematics, 70(2), 159–174.

    Article  Google Scholar 

  • Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings: Learning cultures and computers. Kluwer.

    Book  Google Scholar 

  • Panero, M., & Aldon, G. (2016). How teachers evolve their formative assessment practices when digital tools are involved in the classroom. Digital Experiences in Mathematics Education, 2(1), 70–86.

    Article  Google Scholar 

  • Papert, S. (1980). Mindstorms: Children, computers and powerful ideas. Harvester Press.

    Google Scholar 

  • Pickering, A. (1995). The mangle of practice: Time, agency and science. University of Chicago Press.

    Book  Google Scholar 

  • Prediger, S., Bikner-Ahsbahs, A., & Arzarello, F. (2008). Networking strategies and methods for connecting theoretical approaches: First steps towards a conceptual framework. ZDM – The International Journal on Mathematics Education, 40(2), 165–178.

    Article  Google Scholar 

  • Rabardel, P. (1995). Les hommes et les outils contemporains. Armand Colin. English version accessible at https://halshs.archives-ouvertes.fr/file/index/docid/1020705/filename/people_and_technology.pdf

    Google Scholar 

  • Rabardel, P. (2002). People and technology – A cognitive appraoch to contemporary instruments. https://hal.archivesouvertes.fr/file/index/docid/1020705/filename/people_and_technology.pdf. Accessed 17 July 2022.

  • Radford, L. (2008). Theories in mathematics education: A brief inquiry into their conceptual differences. In Working paper. Prepared for the ICMI survey team 7. The notion and role of theory in mathematics education research. Available: http://www.luisradford.ca/pub/31_radfordicmist7_EN.pdf

    Google Scholar 

  • Robert, A., & Rogalski, J. (2002). Le système complexe et coherent des pratiques des enseignants de mathématiques: une double approche. Revue Canadienne de l’enseignement des sciences, des mathématiques et des technologies, 2(4), 505–528.

    Google Scholar 

  • Robutti, O. (2020). Meta-didactical transposition. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 611–619). Springer.

    Chapter  Google Scholar 

  • Robutti, O., Aldon, G, Cusi, A., Olsher, S., Panero, M., Cooper, J., Carante, P. & Prodromou, T. (2019). Boundary objects in mathematics education and their role across communities of teachers and researchers in interaction. In G. M. Lloyd (Ed.). Participants in mathematics teacher education (Vol. 3, International Handbook of Mathematics Teacher Education). Sense Publishers.

    Google Scholar 

  • Ruthven, K. (2009). Towards a naturalistic conceptualisation of technology integration in classroom practice: The example of school mathematics. Education and Didactique, 3(1), 131–152.

    Article  Google Scholar 

  • Ruthven, K. (2014). Frameworks for analysing the expertise that underpins successful integration of digital technologies into everyday teaching practice. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics teacher in the digital era: An international perspective on technology focused professional development (pp. 373–393). Springer.

    Chapter  Google Scholar 

  • Schwarz, B. B., De-Groot, R., Mavrikis, M., & Dragon, T. (2015). Learning to learn together with CSCL tools. International Journal of Computer-Supported Collaborative Learning, 10(3).

    Google Scholar 

  • Shaffer, D. W., & Kaput, J. (1999). Mathematics and virtual culture: A cognitive evolutionary perspective on technology and mathematics education. Educational Studies in Mathematics, 37(2), 97–119.

    Article  Google Scholar 

  • Shulman, L. (1986). Those who understand: Knowledge and growth in teaching. Educational Researcher, 15(2), 4–14.

    Article  Google Scholar 

  • Siemens, G. (2005). Connectivism: A learning theory for the digital age. International Journal of Instructional Technology and Distance Learning, 2(1), 3–10.

    Google Scholar 

  • Simonsen, L. M., & Dick, T. P. (1997). Teachers’ perceptions of the impact of graphing calculators in the mathematics classroom. Journal of Computers in Mathematics and Science Teaching, 16(2), 239–368.

    Google Scholar 

  • Sinclair, N. (2001). The aesthetic is relevant. For the Learning of Mathematics, 21(1), 25–33.

    Google Scholar 

  • Sinclair, N. (2013). Touch counts: An embodied, digital approach to learning number. In E. Faggiano & A. Montone (Eds.), Proceedings of ICTMT12 (pp. 262–267). University of Bari.

    Google Scholar 

  • Sinclair, N., & de Freitas, E. (2014). The haptic nature of gesture: Rethinking gesture with new multitouch digital technologies. Gesture, 14(3), 351–374.

    Article  Google Scholar 

  • Sinclair, N., & Heyd-Metzuyanim, E. (2014). Learning number with Touch Counts: The role of emotions and the body in mathematical communication. Technology, Knowledge and Learning, 19(1–2), 81–99.

    Article  Google Scholar 

  • Sinclair, N., & Jackiw, N. (2005). Understanding and projecting ICT trends. In S. Johnston-Wilder & D. Pimm (Eds.), Teaching secondary mathematics effectively with technology (pp. 235–252). Open University Press.

    Google Scholar 

  • Sinclair, N., de Freitas, E., & Ferrara, F. (2013). Virtual encounters: The murky and furtive world of mathematical inventiveness. ZDM – The International Journal on Mathematics Education, 45(2), 239–252.

    Google Scholar 

  • Sinclair, N., Chorney, S., Gunes, C., & Bakos, S. (2020). Disruptions in meanings: Teachers’ experiences of multiplication in Touch Times. ZDM: Mathematics Education. [On-line first].

    Google Scholar 

  • Smit, J., Van Eerde, H. A. A., & Bakker, A. (2013). A conceptualization of whole-class scaffolding. British Educational Research Journal, 39(5), 817–834.

    Article  Google Scholar 

  • Smythe, S., Hill, C., MacDonald, M., Dagenais, D., Sinclair, N., & Toohey, K. (2017). Disrupting boundaries in education and research. Cambridge University Press.

    Book  Google Scholar 

  • Snaza, N., Applebaum, P., Bayne, S., Carlson, D., Morris, M., Rotas, N., Standlin, J., Wallin, J., & Weaver, J. (2014). Toward a posthuman education. Journal of Curriculum Theorizing, 30, 39–55.

    Google Scholar 

  • Star, S., & Griesemer, J. (1989). Institutional ecology, translations’ and boundary objects: Amateurs and professionals in Berkeley’s Museum of Vertebrate Zoology, 1907–39. Social Studies of Science, 19(3), 387–420.

    Article  Google Scholar 

  • Steinbring, H., Bartolini Bussi, M. G., & Sierpinska, A. (1998). Language and communication in the mathematics classroom. National Council of Teachers of Mathematics.

    Google Scholar 

  • Stinson, D., & Walshaw, M. (2017). Exploring different theoretical frontiers for different (and uncertain) possibilities in mathematics education research. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 128–155). National Council of Teachers of Mathematics.

    Google Scholar 

  • Tahta, D. (1981). Some thoughts arising from the new Nicolet films. Mathematics Teaching, 94, 25–29.

    Google Scholar 

  • Taranto, E., Robutti, O., & Arzarello, F. (2020). Learning within MOOCs for mathematics teacher education. ZDM – The International Journal on Mathematics Education. https://doi.org/10.1007/s11858-020-01178-2

  • Tharp, M. L., Fitzsimmons, J. A., & Ayers, R. L. (1997). Negotiating a technological shift: Teacher perception of the implementation of graphing calculators. Journal of Computers in Mathematics and Science Teaching, 16(4), 551–575.

    Google Scholar 

  • Thomas, M. O. J., & Palmer, J. M. (2014). Teaching with digital technology: Obstacles and opportunities. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics teacher in the digital era: An international perspective on technology focused professional development (pp. 71–89). Springer.

    Chapter  Google Scholar 

  • Tragalová, J., & Tabach, M. (2018). In search for standards: Teaching mathematics in technological environments. In L. Ball, P. Drijvers, S. Ladel, H.-S. Siller, M. Tabach, & C. Vale (Eds.), Uses of technology in primary and secondary mathematics education: Tools, topics and trends (pp. 387–397). Springer.

    Chapter  Google Scholar 

  • Trouche, L. (1997). A propos de l’apprentissage de fonctions dans un environnement de calculatrices, étude des rapports entre processus de conceptualisation et processus d’instrumentation. Thèse de doctorat. Université de Montpellier.

    Google Scholar 

  • Trouche, L. (2000). La parabole du gaucher et de la casserole à bec verseur: Étude des rocessus d’apprentissage dans un environment de calculatrices symboliques. Education Studies in Mathematics, 41, 239–264.

    Google Scholar 

  • Trouche, L. (2004). Managing complexity of human/machine interactions in computerized learning environments. International Journal of Computers for Mathematics Learning, 9(3), 281–307.

    Article  Google Scholar 

  • Trouche, L. (2005). Instrumental genesis, individual and social aspects. In D. Guin, K. Ruthven, & L. Trouche (Eds.), The didactical challenge of symbolic calculators: Turning a computational device into a mathematical instrument (pp. 197–230). Springer.

    Chapter  Google Scholar 

  • Trouche, L. (2019). Evidencing missing resources of the documentational approach to didactics. Toward ten programs of research/development for enriching this approach. In L. Trouche, G. Gueudet, & B. Pepin (Eds.), The ‘resource’ approach to mathematics education (pp. 447–489). Springer.

    Chapter  Google Scholar 

  • Trouche, L. (2020). Instrumentation in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 404–412). Springer.

    Chapter  Google Scholar 

  • Trouche, L., & Drijvers, P. (2010). Handled technology: Flashback into the future. ZDM. The International Journal on Mathematics Education, 42(7), 667–681.

    Google Scholar 

  • Trouche, L., Gueudet, G., & Pepin, B. (2019). The “resource” approach in mathematics education. Springer.

    Book  Google Scholar 

  • Vergnaud, G. (1990). La théorie des champs conceptuels. Recherches en Didactique des Mathématiques, 10(2,3), 133–170.

    Google Scholar 

  • Vergnaud, G. (2009). The theory of conceptual fields. Human Development, 52, 83–94.

    Article  Google Scholar 

  • Vérillon, P., & Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology of Education, 10(1), 77–101.

    Article  Google Scholar 

  • Whitacre, I., Hensberry, K., Schellinger, J., & Findley, K. (2019). Variations on play with interactive computer simulations: Balancing competing priorities. International Journal of Mathematical Education in Science and Technology, 50(5), 665–681.

    Article  Google Scholar 

  • Wiseman, D., Lunney Borden, L., Beatty, R., et al. (2020). Whole-some artifacts: (STEM) teaching and learning emerging from and contributing to community. Canadian Journal of Science, Mathematics, and Technology Education, 20, 264–280.

    Article  Google Scholar 

  • Zevenbergen, R., & Lerman, S. (2008). Learning environments using interactive whiteboards: New learning spaces or reproduction of old technologies? Mathematics Education Research Journal, 20(1), 108–126.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Education, Simon Fraser University, Burnaby, BC, Canada

    Nathalie Sinclair

  2. Université Paris Cité, EDA, F-75006, Paris, France

    Mariam Haspekian

  3. Dipartimento di Matematica, Università di Torino, Torino, Italy

    Ornella Robutti

  4. UCL Institute of Education, University College London, London, UK

    Alison Clark-Wilson

Authors
  1. Nathalie Sinclair
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  2. Mariam Haspekian
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  3. Ornella Robutti
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  4. Alison Clark-Wilson
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Corresponding author

Correspondence to Nathalie Sinclair .

Editor information

Editors and Affiliations

  1. UCL Institute of Education, University College London, London, UK

    Alison Clark-Wilson

  2. Dipartimento di Matematica, Università di Torino, Torino, Italy

    Ornella Robutti

  3. Faculty of Education, Simon Fraser University, Burnaby, BC, Canada

    Nathalie Sinclair

Appendix: List of the Journals Reviewed

Appendix: List of the Journals Reviewed

  1. 1.

    International Journal of Science, Mathematics & Technology Learning (From Volume 21 Issue 2 to Volume 27 Issue 1)

  2. 2.

    International Journal of Mathematical Education in Science and Technology (From Volume 46 Issue 1 to Volume 51 Issue 8)

  3. 3.

    Educational Studies in Mathematics (From Volume 88 Issue 1 to Volume 105 Issue 2)

  4. 4.

    Digital Experiences in Mathematics Education (From Volume 1 Issue 1 to Volume 6 Issue 3)

  5. 5.

    International Journal for Technology in Mathematics Education (From Volume 22 Issue 1 to Volume 27 Issue 3)

  6. 6.

    International Journal of Science and Mathematics Education (From Volume 13 Issue 1 to Volume 18 Issue 8)

  7. 7.

    ZDM Mathematics Education (From Volume 47 Issue 1 to Volume 52 Issue 7)

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Sinclair, N., Haspekian, M., Robutti, O., Clark-Wilson, A. (2022). Revisiting Theories That Frame Research on Teaching Mathematics with Digital Technology. In: Clark-Wilson, A., Robutti, O., Sinclair, N. (eds) The Mathematics Teacher in the Digital Era. Mathematics Education in the Digital Era, vol 16. Springer, Cham. https://doi.org/10.1007/978-3-031-05254-5_15

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