The teacher and the tool: Instrumental orchestrations in the technology-rich mathematics classroom

Educational Studies in Mathematics

Volumn 75, Issue 2, 2010, Pages 213-234

  Drijvers, Paul ^a   Doorman, Michiel ^a   Boon, Peter ^a   Reed, Helen ^a   Gravemeijer, Koeno ^b  

^a UTRECHT UNIVERSITY   (Netherlands)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Applet; Classroom teaching practice; Digital technology integration; Instrumental orchestration; Teachers' views; Technology

Indexed keywords

EID: 77957906116     PISSN: 00131954     EISSN: 15730816     Source Type: Journal    
DOI: 10.1007/s10649-010-9254-5     Document Type: Article

References (41)

1. 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.
2. Artigue, M., Drijvers, P., Lagrange, J-b, Mariotti, M. A., & Ruthven, K. (2009). Technologies numériques dans l'enseignement des mathématiques, où en est-on dans les recherches et dans leur intégration? [Technology in mathematics education: how about research and its integration?] In C. Ouvrier-Buffet & M.-J. Perrin-Glorian (Eds.), Approches plurielles en didactique des mathématiques; Apprendre à faire des mathématiques du primaire au supérieur: quoi de neuf? [Multiple approaches to the didactics of mathematics; learning mathematics from primary to tertiary level: what's new?] (pp. 185-207). Paris: Université Paris Diderot Paris 7.
3. Bartolini Bussi, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: artefacts and signs after a Vygotskian perspective. In L. English, M. Bartolini Bussi, G. Jones, R. Lesh, & D. Tirosh (Eds.), Handbook of International Research in Mathematics Education (2nd ed., pp. 746-805). Mahwah: Lawrence Erlbaum.
4. Billington, M. (2009). Establishing didactical praxeologies: teachers using digital tools in upper secondary mathematics classrooms. Paper presented in WG9, Cerme6 conference, 28 January-1 February 2009, Lyon, France.
5. Bretscher, N. (2009). Dynamic geometry software: The teacher's role in facilitating instrumental genesis. Paper presented in WG9, Cerme6 conference, 28 January-1 February 2009, Lyon, France.
6. Bueno-Ravel, L., & Gueudet, G. (2007). Online resources in mathematics: teachers' genesis of use? In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the V Congress of the European Society for Research in Mathematics Education CERME5 (pp. 1369-1378). Cyprus: Larnaca.
7. Doerr, H. M., & Zangor, R. (2000). Creating meaning for and with the graphing calculator. Educational Studies in Mathematics, 41, 143-163.
8. Doorman, M., Boon, P., Drijvers, P., van Gisbergen, S., Gravemeijer, K., & Reed, H. (2009). Tool use and functional thinking: An example of a form-function-shift. In M. Tzekaki, M. Kaldrimidou, & H. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 449-456). Thessaloniki, Greece: PME.
9. Drijvers, P., & Trouche, L. (2008). From artefacts 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.
10. Drijvers, P., Doorman, M., Boon, P., van Gisbergen, S., & Gravemeijer, K. (2007). Tool use in a technology-rich learning arrangement for the concept of function. In D. Pitta-Pantazi & G. Philipou (Eds.), Proceedings of the V Congress of the European Society for Research in Mathematics Education CERME5 (pp. 1389-1398). Cyprus: Larnaca.
11. Drijvers, P., Kieran, C., & Mariotti, M. A. (2010). Integrating technology into mathematics education: Theoretical perspectives. In C. Hoyles & J.-B. Lagrange (Eds.), Mathematics education and technology-rethinking the terrain (pp. 89-132). New York: Springer.
12. Forman, E. A., & Ansell, E. (2002). Orchestrating the multiple voices and inscriptions of a mathematics classroom. Journal of the Learning Sciences, 11(2-3), 251-274.
13. Gravemeijer, K. (1994). Developing realistic mathematics education. Utrecht: CD-β Press.
14. Gueudet, G., & Trouche, L. (2009). Towards new documentation systems for mathematics teachers? Educational Studies in Mathematics, 71(3), 199-218.
15. Kendal, M., & Stacey, K. (2002). Teachers in transition: Moving towards CAS-supported classrooms. ZDM, The International Journal on Mathematics Education, 34(5), 196-203.
16. Kendal, M., Stacey, K., & Pierce, R. (2004). The influence of a computer algebra environment on teachers' practice. In D. Guin, K. Ruthven, & L. Trouche (Eds.), The didactical challenge of symbolic calculators: Turning an computational device into a mathematical instrument (pp. 83-112). Dordrecht: Kluwer Academic Publishers.
17. Kieran, C., & Drijvers, P. (2006). The co-emergence of machine techniques, paper-and-pencil techniques, and theoretical reflection: A study of CAS use in secondary school algebra. International Journal of Computers for Mathematical Learning, 11, 205-263.
18. Lagrange, J. B., & Caliskan-Dedeoglu, N. (2009). Usages de la technologie dans des conditions ordinaires: le cas de la géométrie dynamique au collège. [The use of technology in ordinary conditions: the case of dynamic geometry in lower secondary education.] Recherches en Didactique des Mathématiques, 29(2), 189-226.
19. Lagrange, J.-B., & Monaghan, J. (2009). On the adoption of a model to interpret teachers' use of technology in mathematics lessons. Paper presented in WG7, Cerme6 conference, 28 January-1 February 2009, Lyon, France.
20. Lagrange, J.-B., & Ozdemir Erdogan, E. (2009). Teachers' emergent goals in spreadsheet-based lessons: analyzing the complexity of technology integration. Educational Studies in Mathematics, 71(1), 65-84.
21. Lagrange, J.-B., Artigue, M., Laborde, C., & Trouche, L. (2003). Technology and mathematics education: A multidimensional study of the evolution of research and innovation. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education (Vol. 1, pp. 237-269). Dordrecht: Kluwer.
22. Maracci, M., & Mariotti, M.-A. (2009). The teacher's use of ICT tools in the classroom after a semiotic mediation approach. Paper presented in WG9, Cerme6 conference, 28 January-1 February 2009, Lyon, France.
23. Mariotti, M. A. (2002). Influence of technologies advances in students' math learning. In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 757-786). Mahwah: Lawrence Erlbaum.
24. McKenzie, J. (2001). How teachers learn technology best. The Educational Technology Journal, 10(6). Available at: http://www. fno. org/mar01/howlearn. html. Accessed 20 Oct 2009.
25. Monaghan, J. (2001). Teachers' classroom interactions in ICT-based mathematics lessons. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 383-390). Utrecht: Freudenthal Institute.
26. Monaghan, J. (2004). Teachers' activities in technology-based mathematics lessons. International Journal of Computers for Mathematical Learning, 9, 327-357.
27. Pierce, R., & Ball, L. (2009). Perceptions that may affect teachers' intention to use technology in secondary mathematics classes. Educational Studies in Mathematics, 71(3), 299-317.
28. Reed, H. C., Drijvers, P., & Kirschner, P. A. (2010). Effects of attitudes and behaviours on learning mathematics with computer tools. Computers and Education, 55(1), 1-15.
29. Robert, A., & Rogalski, J. (2005). A cross-analysis of the mathematics teacher's activity. An example in a French 10th-grade class. Educational Studies in Mathematics, 59, 269-298.
30. Ruthven, K. (2007). Teachers, technologies and the structures of schooling. In D. Pitta-Pantazi & G. Philipou (Eds.), Proceedings of the V Congress of the European Society for Research in Mathematics Education CERME5 (pp. 52-67). Cyprus: Larnaca.
31. Ruthven, K. (2009). An investigative lesson with dynamic geometry: A case study of key structuring features of technology integration in classroom practice. Paper presented in WG9, Cerme6 conference, 28 January-1 February 2009, Lyon, France.
32. Ruthven, K., & Hennessy, S. (2002). A practitioner model of the use of computer-based tools and resources to support mathematics teaching and learning. Educational Studies in Mathematics, 49(1), 47-88.
33. Ruthven, K., Deaney, R., & Hennessy, S. (2009). Using graphing software to teach about algebraic forms: A study of technology-supported practice in secondary-school mathematics. Educational Studies in Mathematics, 71(3), 279-297.
34. 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, 297-317.
35. Saxe, G. B. (1991). Culture and Cognitive Development: Studies in Mathematical Understanding. Hillsdale: Laurence Erlbaum Associates.
36. Sensevy, G., Schubauer-Leoni, M. L., Mercier, A., Ligozat, F., & Perrot, G. (2005). An Attempt to Model the Teacher's Action in the Mathematics Class. Educational Studies in Mathematics, 59(1-3), 153-181.
37. Sherin, M. G. (2002). A balancing act: Developing a discourse community in a mathematics classroom. Journal of Mathematics Teacher Education, 5(3), 205-233.
38. Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26, 114-145.
39. Slavit, D. (1997). An alternate route to the reification of function. Educational Studies in Mathematics, 33, 259-281.
40. Trouche, L. (2004). Managing complexity of human/machine interactions in computerized learning environments: Guiding students' command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9, 281-307.
41. Vergnaud, G. (1996). Au fond de l'apprentissage, la conceptualisation. [At the basis of learning, the conceptualization.] In R. Noirfalise & M.-J. Perrin (Eds.), Actes de l'école d'été de didactique des mathématiques [Proceedings of the summer school on didactics of mathematics.] (pp. 174-185). Clermont-Ferrand: IREM.