The 'Resource' Approach to Mathematics Education pp 389-444 | Cite as
Transitions Toward Digital Resources: Change, Invariance, and Orchestration
Abstract
This chapter reports on the work of Working Group 4 and focuses on the integration of digital resources into mathematics teaching and learning practices. There are five central sections, focusing on, instrumental genesis, instrumental orchestration, the documentational approach to didactics, digital resources and teacher education, and the design of learning environments with the use of digital resources. A range of constructs and theoretical approaches are covered in these five sections, and the opening section comments on construct validity and issues in “networking” theoretical frameworks. The chapter can be viewed as a literature review which surveys past and present (at the time of writing) scholarship with an eye to possible future research. The chapter is extensive in several dimensions: a large range of digital resources and applications are considered; the subjects using digital resources are not just teachers but also students, student teachers and student teacher educators. Issues raised in the sections include individual and collective use of resources, the adaptation of these resources for specific learning goals and to prepare (pre- and in-service) teachers for the use of digital resources.
Keywords
Digital resources instrumental genesis instrumental orchestration documentational approach to didactics teacher education design of learning environmentsReferences
- Adler, J. (2000). Conceptualising resources as a theme for teacher education. Journal of Mathematics Teacher Education, 3(3), 205–224.CrossRefGoogle Scholar
- Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52(3), 215–241.CrossRefGoogle Scholar
- Artigue, M. (1990). Ingénierie didactique. Recherches en didactique des mathématiques, 9(3), 281–307.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. International Journal of Computers for Mathematical Learning, 7, 245–274.CrossRefGoogle Scholar
- Artzt, A. F., Armour-Thomas, E., Curcio, C., & Gurl, T. J. (2015). Becoming a reflective mathematics teacher: A guide for observations and self-assessment (3rd ed.). New York: Routledge.CrossRefGoogle Scholar
- Assis, C., Gitirana, V., & Trouche, L. (2018). The metamorphosis of resource systems of prospective teacher: From studying to teaching. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)sources 2018 international conference (pp. 39–42). Lyon: ENS de Lyon, Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563
- Assude, T. (2007). Teacher’s practices and degree of ICT integration. In D. Pitta-Pantazi, & G. Philippou (Eds.), Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (pp. 1339–1348). Larnaca: University of Cyprus and ERME.Google Scholar
- Assude, T., Buteau, C., & Forgasz, H. (2010). Factors influencing implementation of technology-rich mathematics curriculum and practices. In C. Hoyles & J.-B. Lagrange (Eds.), Mathematics education and technology – Rethinking the terrain. The 17th ICMI study (pp. 405–419). New York: Springer.Google Scholar
- Atkinson, B. (2012). Rethinking reflection: Teachers’ critiques. The Teacher Educator, 47, 175–194.CrossRefGoogle Scholar
- Bailleul, M., & Thémines, J. F. (2013). L’ingénierie de formation : formalisation d’expériences en formation d’enseignants. In A. Vergnioux (Ed.),. Traité d’ingénierie de la formation L’Harmattan (pp. 85–112). Paris.Google Scholar
- Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools. Utrecht: CD Beta Press.Google Scholar
- Balacheff, N. (1994). La transposition informatique. Note sur un nouveau problème pour la didactique. In M. Artigue, R. Gras, C. Laborde, & P. Tavignot (Eds.), Vingt ans de Didactique des Mathématiques en France (pp. 364–370). Grenoble: La Pensée Sauvage.Google Scholar
- Barbosa, A., & Vale, I. (2018). Math trails: A resource for teaching and learning. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)sources 2018 international conference (pp. 183–186). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Barth-Cohen, L. A., Little, A. J., & Abrahamson, D. (2018). Building reflective practices in a pre-service math and science teacher education course that focuses on qualitative video analysis. Journal of Science Teacher Education, 29(2), 83–101.CrossRefGoogle Scholar
- Bellemain, F., Tiburcio, R., Silva, C., & Gitirana, V. (2016). Function Studium software. Recife-PE: LEMATEC Research Group.Google Scholar
- Bellemain, F., Rodrigues, A., & Rodrigues, A. D. (2018). LEMATEC Studium: A support resource for teaching mathematics. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)sources 2018 international conference (pp. 255–258). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Ben-Zvi, D. (2006). Scaffolding students’ informal inference and argumentation. In A. Rossman & B. Chance (Eds.), Proceedings of the Seventh International Conference on Teaching Statistics (CD-ROM). Voorburg: International Statistical Institute.Google Scholar
- Besnier, S. (2016). Le travail documentaire des professeurs à l’épreuve des ressources technologiques : Le cas de l’enseignement du nombre à l’école maternelle. PhD. Brest: Université de Bretagne Occidentale, https://tel.archives-ouvertes.fr/tel-01397586/document
- Besnier, S. (2018). Orchestrations at kindergarten: Articulation between manipulatives and digital resources. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)sources 2018 international conference (pp. 259–262). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Besnier, S., & Gueudet, G. (2016). Usages de ressources numériques pour l’enseignement des mathématiques en maternelle : orchestrations et documents. Perspectivas em Educação Matemática, 9(21), 978–1003.Google Scholar
- Billington, M. (2009). Establishing didactical praxeologies: teachers using digital tools in upper secondary mathematics classrooms. In V. Durand-Guerrier, S. Soury-Lavergne & F. Arzarello (Eds.), Proceedings of the Sixth Congress of European Research in Mathematics Education (pp. 1330–1339). Lyon, France: ENS de Lyon.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.CrossRefGoogle Scholar
- Brousseau, G. (1997). Theory of didactical situations in mathematics. Didactique des mathématiques, 1970–1990 (edited and translated by N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield). Dordrecht, NL. Kluwer Academic Publishers.Google Scholar
- Brown, M. W. (2009). The teacher-tool relationship: Theorizing the design and use of curriculum materials. In J. T. Remillard, B. A. Herbel-Eisenmann, & G. M. Lloyd (Eds.), Mathematics teachers at work: Connecting curriculum materials and classroom instruction (pp. 17–36). New York: Routledge.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), 1–17.CrossRefGoogle Scholar
- Carton, T. (2018a). From digital “bricolage” to the start of collective work – What influences do secondary teachers non-formal digital practices have on their documentation work? In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)sources 2018 international conference (pp. 263–266). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Carton, T. (2018b). Case study: How teachers’ everyday creativity can be associated with an edtech player’s strategies. Présenté au XXIe Congrès de la SFSIC – Création, créativité et médiations, Saint-Denis, 13-15 juin 2018.Google Scholar
- Cayton, C., Hollebrands, K., Okumuş, S., & Boehm, E. (2017). Pivotal teaching moments in technology-intensive secondary geometry classrooms. Journal of Mathematics Teacher Education, 20(1), 75–100.CrossRefGoogle Scholar
- Chevallard, Y. (2002). Organiser l’étude. 1. Structures & fonctions. Actes de la XIe école d’été de didactique des mathématiques (pp. 3–32). La Pensée Sauvage : Grenoble. http://yves.chevallard.free.fr/spip/spip/IMG/pdf/Organiser_l_etude_1.pdf
- Choppin, J. (2018). Exploring teachers’ design processes with different curriculum programs. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceeedings of the re(s)sources 2018 international conference (pp. 267–270). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Cuevas, C. A., Villamizar, F. Y., & Martínez, A. (2017). Aplicaciones de la tecnología digital para activiDADes didácticas que promuevan una mejor comprensión del tono como cualiDAD del sonido para cursos tradicionales de física en el nivel básico. Enseñanza de las Ciencias, 35(3), 129–150.Google Scholar
- Cunha, E. (2018). Digital resources: Origami folding instructions as lever to mobilize geometric concepts to solve problems. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Ed.), Proceeedings of the Re(s)sources 2018 International Conference (pp. 271–274). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563
- Deblois, L. (2012). De l’ancien élève à l’enseignant. Quel parecours. In J. Proulx, C. Corriveau, & H. Squalli (Eds.), Formation mathématique pour l’enseignement des mathématiques (pp. 313–320). Québec: Presses de l’Université du Québec.Google Scholar
- Dick, T., & Burrill, G. (2016). Design and implementation principles for dynamic interactive mathematics technologies. In M. Niess, S. Driskell, & K. Hollebrands (Eds.), Handbook of research on transforming mathematics teacher education in the digital age (pp. 23–52). Hershey: IGI Global Publishers.CrossRefGoogle Scholar
- Drijvers, P., & Trouche, L. (2008). From artifacts to instruments: A theoretical framework behind the orchestra metaphor. In G. W. Blume & M. K. Heid (Eds.), Research on technology and the teaching and learning of mathematics. Cases and perspectives (Vol. 2, pp. 363–392). Charlotte: Information Age.Google Scholar
- Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. P. (2010). The teacher and the tool: Instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2), 213–234.CrossRefGoogle Scholar
- Drijvers, P., Godino, J. D., Font, V., & Trouche, L. (2013a). One episode, two lenses. Educational Studies in Mathematics, 82(1), 23–49.CrossRefGoogle Scholar
- Drijvers, P., Tacoma, S., Besamusca, A., Doorman, M., & Boon, P. (2013b). Digital resources inviting changes in mid-adopting teachers’ practices and orchestrations. ZDM – Mathematics Education, 45(7), 987–1001.CrossRefGoogle Scholar
- Duval, R. (1993). Registres de représentation sémiotique et fonctionnement cognitif de la pensée. Annales de didactique et de sciences cognitives, 5(1), 37–65.Google Scholar
- Engeström, Y. (1987). Learning by expanding: An activity-theoretical approach to developmental research. Helsinki: Orienta-Konsultit.Google Scholar
- Erfjord, I. (2011). Teachers’ initial orchestration of students’ dynamic geometry software use: Consequences for students’ opportunities to learn mathematics. Technology, Knowledge and Learning, 16(1), 35–54.Google Scholar
- Essonnier, N. K. (2018). Étude de la conception collaborative de ressources numériques mathématiques au sein d’une communauté d’intérêt. PhD. Lyon: Université de Lyon, https://tel.archives-ouvertes.fr/tel-01868226/document
- Essonnier, N., & Trgalová, J. (2018). Collaborative design of digital resources: Role of designers’ resource systems and professional knowledge. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceeedings of the re(s)sources 2018 international conference (pp. 61–64). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Essonnier, N., Kynigos, C., Trgalová, J., & Daskolia, M. (2018). Role of context in social creativity for the design of digital resources. In L. Fan, L. Trouche, S. Rezat, C. Qi, & J. Visnovska (Eds.), Research on mathematics textbooks and Teachers’ resources: Advances and issues (pp. 215–233). Cham: Springer.CrossRefGoogle Scholar
- Faggiano, E., Montone, A., & Mariotti, M. A. (2016). Creating a synergy between manipulatives and virtual artefacts to conceptualize axial symmetry at Primary School. In C. Csíkos, A. Rausch, & J. Szitányi (Eds.), Proceedigns of the 40th conference of the international group for the Psychology of Mathematics Education: PME 40 (Vol. 2, pp. 235–242). Szeged: International Group for the Psychology of Mathematics Education.Google Scholar
- Farrell, A. (1996). Roles and behaviors in technology-integrated precalculus classrooms. Journal of Mathematical Behavior, 15(1), 35–53.CrossRefGoogle Scholar
- Ferrara, F., & Sinclair, N. (2016). An early algebra approach to pattern generalisation: Actualising the virtual through words, gestures and toilet paper. Educational Studies in Mathematics, 92(1), 1–19.CrossRefGoogle Scholar
- Fidje, A. S. (2018). Orchestrating the use of student-produced videos in mathematics teaching. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)sources 2018 international conference (pp. 275–278). Lyon: ENS de Lyon. In Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.
- Fischer, G. (2001). Communities of interest: Learning through the interaction of multiple knowledge systems. In S. Bjørnestad, R. Moe, A. Mørch, & A. Opdahl (Eds.), Proceedings of the 24th Information Systems Research Seminar in Scandinavia (pp. 1–14). Bergen: The University of BergenGoogle Scholar
- Gibson, J. J. (1977). The ecological approach to visual perception. Boston: Houghton Mifflin.Google Scholar
- Gueudet, G., & Trouche, L. (2008). Du travail documentaire des enseignants?: Genèses, collectifs, communautés. Le cas des mathématiques. Education & Didactique, 2(3), 7–33.CrossRefGoogle Scholar
- Gueudet, G., & Trouche, L. (2009a). Towards new documentational systems for mathematics teachers? Educational Studies in Mathematics, 71(3), 199–218.CrossRefGoogle Scholar
- Gueudet, G., & Trouche, L. (2009b). Vers de nouveaux systèmes documentaires des professeurs de mathématiques?). In I. Bloch & F. Conne (Eds.), Nouvelles perspectives en didactique des mathématiques. Cours de la XIVe école d’été de didactique des mathématiques (pp. 109–133). Paris: La Pensée Sauvage.Google Scholar
- Gueudet, G., & Trouche, L. (2010). Des ressources aux documents, travail du professeur et genèses documentaires. In G. Gueudet & L. Trouche (Eds). Ressources vives: le travail documentaire des professeurs en mathématiques (pp. 57–74). Paideia, Rennes: Presses Universitaires de Rennes & INRP.Google Scholar
- Gueudet, G., & Trouche, L. (2011). Mathematics teacher education advanced methods: An example in dynamic geometry. ZDM – Mathematics Education, 43(3), 399–411.CrossRefGoogle Scholar
- Gueudet, G., Sacristan, A., Soury-Lavergne, S., & Trouche, L. (2012). Online paths in mathematics teacher training: New resources and new skills for teacher educators. ZDM – Mathematics Education, 44(6), 717–731.CrossRefGoogle Scholar
- Gueudet, G., Pepin, B., & Trouche, L. (2013). Collective work with resources: An essential dimension for teacher documentation. ZDM – Mathematics Education, 45(7), 1003–1016.CrossRefGoogle Scholar
- Gueudet, G., Pepin, B., Sabra, H., & Trouche, L. (2016). Collective design of an e-textbook: Teachers’ collective documentation. Journal of Mathematics Teacher Education, 19(2), 187–203.CrossRefGoogle Scholar
- Guin, D., & Trouche, L. (1999). The complex process of converting tools into mathematical instruments: The case of calculators. International Journal of Computers for Mathematical Learning, 3(3), 195–227.CrossRefGoogle Scholar
- Hadjerrouit, S. (2017). Assessing the affordances of SimReal+ and their applicability to support the learning of mathematics in teacher education. Issues in Informing Science and Information Technology Education, 14, 121–138.CrossRefGoogle Scholar
- Heid, M., K. (2008). Calculator and computer technology in the K-12 curriculum some observations from a US perspective. In Z. Ususkin, & E. Willmore (Eds.), Mathematics curriculum in Pacific rim countries-China, Japan, Korea, and Singapore: Proceedings of a conference (pp. 293–304). Charlotte, Information Age Publishing.Google Scholar
- Herbst, P., Chazan, D., Chen, C., Chieu, V. M., & Weiss, M. (2011). Using comics-based representations of teaching, and technology, to bring practice to teacher education courses. ZDM – Mathematics Education, 43(1), 91–103.CrossRefGoogle Scholar
- Hollebrands, K., & Okumus, S. (2018). Secondary mathematics teachers’ instrumental integration in technology-rich geometry classrooms. Journal of Mathematical Behavior, 49(1), 82–94.CrossRefGoogle Scholar
- Hollebrands, K., & Zbiek, R. (2004). Teaching mathematics with technology: An evidence-based road map for the Journey. In R. Rubenstein & G. Bright (Eds.), Perspectives on the teaching of mathematics: Sixty-sixth yearbook (pp. 259–270). Reston: National Council of Teachers of Mathematics.Google Scholar
- Hollebrands, K., McCulloch, A. W., & Lee, H. S. (2016). Prospective teachers; incorporation of technology in mathematics lesson plans. In M. Niess, S. Driskell, & K. Hollebrands (Eds.), Handbook of research on transforming mathematics teacher education in the digital age (pp. 272–292). Hershey: IGI Global.CrossRefGoogle Scholar
- Hoyles, C., & Noss, R. (1992). A pedagogy for mathematical microworlds. Educational Studies in Mathematics, 23(1), 31–57.CrossRefGoogle Scholar
- Igliori, S. B. C., & Almeida, M. V. (2018). Un support numérique pour le travail de documentation des enseignants de mathématiques de l’EFII (Collège, en France). In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceeedings of the re(s)sources 2018 international conference (pp. 288–291). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Ignácio, R., Lima, R., & Gitirana, V. (2018). The birth of the documentary system of mathematics pre-service teachers in a supervised internship with the creation of a digital textbook chapter. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceeedings of the re(s)sources 2018 international conference (pp. 292–295). Lyon: ENS de Lyon. retrieved on November 8th 2018 at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Jameau, A., & Le Hénaff, C. (2018). Resources for science teaching in a foreign language. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceeedings of the re(s)sources 2018 international conference (pp. 79–82). Lyon: ENS de Lyon. retrieved on November 8th 2018 at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Jaworski, B. (2014). Reflective practicioner in mathematics education. In S. Lerman (Ed.), Encyclopedia in mathematics education (pp. 529–532). Dordrecht: Springer.CrossRefGoogle Scholar
- Jones, W. (2007). Personal information management. Annual Review of Information Science and Technology, 41(1), 453–504.CrossRefGoogle Scholar
- Kaput, J. J. (1995). Overcoming physicality and the eternal present: Cybernetic manipulatives. In R. Sutherland & J. Mason (Eds.), Exploiting mental imagery with computers in mathematics education (pp. 161–177). Berlin: Springer.CrossRefGoogle Scholar
- Kennewell, S. (2001). Using affordances and constraints to evaluate the use of information and communications technology in teaching and learning. Journal of Information Technology for Teacher Education, 10(1–2), 101–116.CrossRefGoogle Scholar
- Kidron, I., Bosch, M., Monaghan, J., & Palmér, H. (2018). Theoretical perspectives and approaches in mathematics education research. In T. Dreyfus, M. Artigue, D. Potari, S. Prediger, & K. Ruthven, (Eds.), Developing Research in Mathematics Education: Twenty years of communication, cooperation and collaboration in Europe. London: Routledge.Google Scholar
- Kieran, C., Boileau, A., Tanguay, D., & Drijvers, P. (2013). Design researchers’ documentational genesis in a study on equivalence of algebraic expressions. ZDM – Mathematics Education, 45(7), 1045–1056.CrossRefGoogle Scholar
- Kirchner, P., Strijbos, J.-W., Kreijns, K., & Beers, B. J. (2004). Designing electronic collaborative learning environments. Educational Technology Research and Development, 52(3), 47–66.CrossRefGoogle Scholar
- Koehler, M. J., & Mishra, P. (2009). What is technological pedagogical content knowledge? Contemporary Issues in Technology and Teacher education, 9(1), 60–70.Google Scholar
- Konold, C., & Miller, C. D. (2005). TinkerPlots: Dynamic data exploration (computer software, Version 1.0). Emeryville: Key Curriculum Press.Google Scholar
- Kozaklı Ülger, T., & Tapan Broutin, M. S. (2018). Transition from a paper-pencil to a technology enriched environment: A teacher’s use of technology and resource selection. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)sources 2018 international conference (pp. 344–347). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Lagrange, J. B., & Monaghan, J. (2009). On the adoption of a model to interpret teachers’ use of technology in mathematics lessons. In V. Durand-Guerrier, S. Soury-Lavergne & F. Arzarello (Eds.). Proceedings of the Sixth Congress of European Research in Mathematics Education (pp. 1605–1614). Lyon: ENS de Lyon.Google Scholar
- Lakoff, G., & Núñez, R. E. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.Google Scholar
- Lealdino Filho, P., & Mercat, C. (2018). Teaching computational thinking in classroom environments: A case for unplugged scenario. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)sources 2018 international conference (pp. 296–299). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Leroyer, L. (2018). The capacity to think of transmission of knowledge from learning supports: A proposition of a conceptual model. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceeedings of the re(s)sources 2018 international conference (pp. 203–206). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Lester, F. K. (2005). On the theoretical, conceptual, and philosophical foundations for research in mathematics education. ZDM – Mathematics Education, 37(6), 457–467.CrossRefGoogle Scholar
- Leung, A., & Bolite-Frant, J. (2015). Designing mathematics tasks: The role of tools. In A. Watson & M. Ohtani (Eds.), Task design in mathematics education:. The 22nd ICMI study (pp. 191–225). Cham: Springer.CrossRefGoogle Scholar
- Lucena, R. (2018). Metaorquestração Instrumental: um modelo para repensar a formação teórico-prática de professores de matemática. Doctoral thesis. Mathematics and Technological Education Pos-graduation Program. Recife-Brazil: UFPE.Google Scholar
- Lucena, R., Gitirana, V., & Trouche, L. (2018). Instrumental meta-orchestration for teacher education. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)sources 2018 international conference (pp. 300–303). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Males, L., Setniker, A., & Dietiker, L. (2018). What do teachers attend to in curriculum materials? In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)sources 2018 international conference (pp. 207–210). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Martinez, M., Cruz, R., & Soberanes, A. (2018). The mathematical teacher: A case study of instrumental genesis in the UAEM. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)sources 2018 international conference (pp. 211–214). Lyon: ENS de Lyon. retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.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 – Mathematics Education, 45(7), 959–971.CrossRefGoogle Scholar
- Mercat, C., Lealdino Filho, P., & El-Demerdash, M. (2017). Creativity and technology in mathematics : From story telling to algorithmic with Op’Art. Acta Didactica Napocensia, 10(1), 63–70.CrossRefGoogle Scholar
- Messaoui, A. (2018). The complex process of classifying resources, an essential component of documentation expertise. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the res(s)ource 2018 international conference (pp. 83–87). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017–1054.CrossRefGoogle Scholar
- Monaghan, J. (2016). Developments relevant to the use of tools in mathematics. In J. Monaghan, L. Trouche, & J. M. Borwein (Eds.), Tools and mathematics: Instruments for learning (pp. 163–180). New York: Springer.CrossRefGoogle Scholar
- Naftaliev, E. (2018). Prospective teachers’ interactions with interactive diagrams: Semiotic tools, challenges and new paths. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the res(s)ource 2018 international conference (pp. 304–307). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Naftaliev, E., & Yerushalmy, M. (2017). Design digital tasks: Interactive diagrams as resource and constraint. In A. Leung & A. Baccaglini-Frank (Eds.), The role and potential of using digital technologies in designing mathematics education tasks (pp. 153–173). Cham: Springer.CrossRefGoogle Scholar
- Nascimento, J., Jr., Carvalho, E., & Farias, L. M. (2018). Creation of innovative teaching situation through instrumental genesis to maximize teaching specific content: Acid-base chemical balance. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the res(s)ource 2018 international conference (pp. 308–311). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Ndlovu, M., Wessels, D., & De Villiers, M. (2011). An instrumental approach to modelling the derivative in sketchpad. Pythagoras, 32(2), 1–15.CrossRefGoogle Scholar
- Nongni, G, & DeBlois, L. (2017). Planification de l’enseignement de l’écart-type en utilisant les ressources documentaires. In A. Adihou, J. Giroux, A. Savard, & K.M. Huy (Eds.). Données, variabilité et tendance vers le futur. Acte du Colloque du GDM (pp. 205–2012). Canada, Québec: Université McGill.Google Scholar
- Nongni, G., & DeBlois. (2018). Planning of the teaching of the standard deviation using digital documentary resources. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)sources 2018 international conference (pp. 312–315). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563
- Norman, D. A. (1988). The psychology of everyday things. New York: Basic Books.Google Scholar
- Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings: Learning cultures and computers. Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
- Okumus, S., & Ipek, A.S. (2018). Pre-service mathematics teachers’ investigation of the constraints of mathematical tools. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)source 2018 international conference (pp. 316–319). Lyon: ENS de Lyon, retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563
- Orozco, J., Cuevas, A., Madrid, H., & Trouche, L. (2018). A proposal of instrumental orchestration to introduce eigenvalues and eigenvectors in a first course of linear algebra for engineering students. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)sources 2018 international conference (pp. 320–323). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Papert, S., & Harel, I. (1991). Preface, situating constructionism. In I. Harel & S. Papert (Eds.), Constructionism, research reports and essays, 1985–1990 (p. 1). Norwood: Ablex.Google Scholar
- Pea, R. D. (1985). Beyond amplification: Using the computer to reorganize mental functioning. Educational Psychologist, 20(4), 167–182.CrossRefGoogle Scholar
- Pepin, B., Gueudet, G., & Trouche, L. (2013). Re-sourcing teachers’ work and interactions: A collective perspective on resources, their use and transformation. ZDM – Mathematics Education, 45(7), 929–943.CrossRefGoogle Scholar
- Pepin, B., Gueudet, G., & Trouche, L. (2017). Refining teacher design capacity: Mathematics teachers’ interactions with digital curriculum resources. ZDM – Mathematics Education, 49(5), 799–812.CrossRefGoogle Scholar
- Pfeiffer, C. R. (2017). A study of the development of mathematical knowledge in a GeoGebra-focused learning environment. Unpublished PhD dissertation. Stellenbosch: Stellenbosch University.Google Scholar
- Pfeiffer, C. R., & Ndlovu, M. (2018). Teaching and learning of function transformations in a GeoGebra-focused learning environment. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)sources 2018 international conference (pp. 324–327). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Piaget, J. (1955). The construction of reality in the child. London: Routledge & Kegan Paul Limited.Google Scholar
- Prieur, M. (2016). La conception codisciplinaire de métaressources comme appui à l’évolution des connaissances des professeurs de sciences. Les connaissances qui guident un travail de préparation pour engager les élèves dans l’élaboration d’hypothèses ou de conjectures. PhD. Lyon: Université de Lyon, https://hal.archives-ouvertes.fr/tel-01364778v2/document
- Psycharis, G., & Kalogeria, E. (2018). TPACK addressed by trainee teacher educators’ documentation work. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)source 2018 international conference (pp. 328–331). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Rabardel, P. (1995). Les hommes et les technologies: Approche cognitive des instruments contemporains. Paris: Armand Colin.Google Scholar
- Ratnayake, I., & Thomas, M. (2018). Documentational genesis during teacher collaborative development of tasks incorporating digital technology. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)source 2018 international conference (pp. 219–222). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Remillard, J. (2010). Modes d’engagement : comprendre les transactions des professeurs avec les ressources curriculaires en mathématiques. In G. Gueudet, & L. Trouche (Eds.), Ressources vives: le travail documentaire des professeurs en mathématiques (pp. 201–216). Rennes/Lyon: INRP/PUR.Google Scholar
- Rocha, K. (2018). Uses of online resources and documentational trajectories: The case of Sésamath. In L. Fan, L. Trouche, C. Qi, S. Rezat, J. & Visnovska (Eds.), Research on mathematics textbooks and teachers’ resources: Advances and issues. ICME-13 monograph (pp. 235–258). Cham: Springer.Google Scholar
- Rodrigues, A., Baltar, P., & Bellemain, F. (2018). Analysis of a Task in three Environments: paper and pencils, manipulative materials and Apprenti Géomètre 2∗. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury–Lavergne, & L. Trouche (Eds.), Proceedings of the Re(s)source 2018 International Conference (pp. 223–226). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563
- Rudd, T. (2007). Interactive whiteboards in the classroom. Bristol: Futurelab Report – IWBs.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 (pp. 373–393). Dordrecht: Springer.CrossRefGoogle Scholar
- Ruthven, K., Hennessy, S., & Deaney, R. (2008). Constructions of dynamic geometry: A study of the interpretative flexibility of educational software in classroom practice. Computers and Education, 51(1), 297–317.CrossRefGoogle Scholar
- Scherrer, J., & Stein, M. K. (2013). Effects of a coding intervention on what teachers learn to notice during whole–group discussion. Journal of Mathematics Teacher Education, 16(2), 105–124.CrossRefGoogle Scholar
- Schoenfeld, A. H. (2010). How we think: A theory of goal–oriented decision making and its educational applications. New York: Routledge.CrossRefGoogle Scholar
- Sensevy, G. (2011). Le Sens du Savoir. Éléments pour une théorie de l’action conjointe en didactique. Bruxelles: De Boeck.Google Scholar
- Sherman, M. F., & Cayton, C. (2015). Using appropriate tools strategically for instruction. Mathematics Teacher, 109(4), 306–310.CrossRefGoogle Scholar
- Sherman, M. F., Cayton, C., & Chandler, K. (2017). Supporting PSTs in using appropriate tools strategically: A learning sequence for developing technology tasks that support students’ mathematical thinking. Mathematics Teacher Educator, 5(2), 122–157.CrossRefGoogle Scholar
- Silva, A. (2018). Concepção de um suporte para a elaboração de webdocumentos destinados ao ensino da geometria: o caso das curvas cônicas. Dissertação do mestrado. Programa de Pós-graduação em Educação Matemática e Tecnológica. UFPE, Recife.Google Scholar
- Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114–145.CrossRefGoogle Scholar
- Simon, M. A., & Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning, 6(2), 91–104.CrossRefGoogle Scholar
- Siqueira, J. E. M., & Bellemain, F. (2018). A dynamic multirepresentational resource for conics. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)source 2018 international conference (pp. 359–361). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Stein, M. K., & Smith, M. S. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics Teaching in the Middle School, 3(4), 268–275.Google Scholar
- Stockero, S. L., & Van Zoest, L. R. (2013). Characterizing pivotal teaching moments in beginning mathematics teachers’ practice. Journal of Mathematics Teacher Education, 16(2), 125–147.CrossRefGoogle Scholar
- Swidan, O., Arzarello, F., & Sabena, C. (2018). Teachers’ interventions to foster inquiry-based learning in a dynamic technological environment. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)source 2018 international conference (pp. 332–335). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Tabach, M. (2011). A mathematics teacher’s practice in a technological environment: A case study analysis using two complementary theories. Technology, Knowledge and Learning, 16(3), 247–265.Google Scholar
- Tabach, M. (2013). Developing a general framework for instrumental orchestration. In B. Ubuz, Ç. Haser, & M. A. Mariotti (Eds.), Proceedings of the Eighth Congress of the European Society for Research in Mathematics Education (pp. 2744–2753). Ankara: Middle East Technical University and ERME.Google Scholar
- Taranto, E., Arzarello, F., & Robutti, O. (2018). MOOC as a resource for teachers’ collaboration in educational program. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)source 2018 international conference (pp. 167–170). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Tchounikine, P. (2011). Computer science and educational software design—A resource for multidisciplinary work in technology enhanced learning. New York: Springer.CrossRefGoogle Scholar
- Thomas, A., & Edson, A. J. (2018). An examination of teacher-generated definitions of digital instructional materials in mathematics. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)source 2018 international conference (pp. 340–343). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Thomas, M. O. J., & Hong, Y. Y. (2005). Teacher factors in integration of graphic calculators into mathematics learning. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th conference of the International Group for the Psychology of mathematics education (Vol. 4, pp. 257–264). Melbourne: University of Melbourne.Google Scholar
- Tiburcio, R., & Bellemain, F. (2018). Computational engineering, didactical, educational software, software engineering. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)source 2018 international conference (pp. 262–264). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Trocki, A., & Hollebrands, K. (2018). The development of a framework for assessing dynamic geometry task quality. Digital Experiences in Mathematics Education, 4(2–3), 110–138.CrossRefGoogle Scholar
- Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized learning environment: Guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematics Learning, 9(3), 281–307.CrossRefGoogle Scholar
- Trouche, L. (2005). Construction et conduite des instruments dans les apprentissages mathématiques : Nécessité des orchestrations. Recherches en Didactique des Mathématiques, 25, 91–138.Google Scholar
- Trouche, L., & Drijvers, P. (2010). Handheld technology: Flashback into the future. ZDM – Mathematics Education, 42(7), 667–681.CrossRefGoogle Scholar
- Trouche, L., & Drijvers, P. (2014). Webbing and orchestration; two interrelated views on digital tools in mathematics education. Teaching Mathematics and its Applications, 33(3), 193–209.CrossRefGoogle Scholar
- Trouche, L., Gueudet, G., & Pepin, B. (2018, Online First). Documentational approach to didactics. In S. Lerman (Ed.), Encyclopedia of mathematics education. New York: Springer. doi: https://doi.org/10.1007/978-3-319-77487-9_100011-1.Google Scholar
- van Dijke-Droogers, M., Drijvers, P., & Bakker, A. (2018). From sample to population: A hypothetical learning trajectory for informal statistical inference. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)source 2018 international conference (pp. 348–351). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Vergnaud, G. (1996). The theory of conceptual fields. In. L.P. Steffe, P.Nesher, P. cobb, G.a. Goldin, & B. Greer (Eds.), Theories of Mathematical Learning (pp. 210–239). Mahwah: Laurence Erilbaum.Google Scholar
- Vergnaud, G. (2011). Au fond de l’action, la conceptualisation. In J. M. Barbier (Ed.), Savoirs théoriques et savoirs d’action (pp. 275–292). Paris: Presses Universitaires de France.CrossRefGoogle Scholar
- Villamizar, F., Cuevas, C., & Martinez, M. (2018). A proposal of instrumental orchestration to integrate the teaching of physics and mathematics. In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the re(s)source 2018 international conference (pp. 352–355). Lyon: ENS de Lyon. Retrieved on November 8th, 2018, at https://hal.archives-ouvertes.fr/hal-01764563.Google Scholar
- Voltolini, A. (2018). Duo of digital and material artefacts dedicated to the learning of geometry at primary school. In L. Ball, P. Drijvers, S. Ladel, H. Siller, M. Tabach, & C. Vale (Eds.), Uses of technology in primary and secondary mathematics education (pp. 83–99). Cham: Springer.CrossRefGoogle Scholar
- Wenger, E. (1998). Communities of practice: Learning, meaning, and identity. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
- Zbiek, R.M., & Hollebrands, K. (2008). A research-informed view of the process of incorporating mathematics technology into classroom practice by inservice and prospective teachers. In M. K. Heid & G. Blume (Eds.), Research on technology in the learning and teaching of mathematics: Syntheses and perspectives. Charlotte: Information Age Publishers.Google Scholar
- Zbiek, R. M., Heid, M. K., Blume, G. W., & Dick, T. P. (2007). Research on technology in mathematics education: A perspective of constructs. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 1169–1207). Charlotte: Information Age.Google Scholar