Abstract
This chapter considers mathematics teachers’ appropriation and classroom use of digital tools. The first section considers teachers—who are they, how are they conceived in the literature and what aspects of teachers have been studied? The second section examines twenty-first century research on mathematics teachers using digital tools. This sheds light on the complexity of mathematics teachers’ appropriation and classroom use of digital tools but what we find is that our focus is too narrow and we need to consider digital tools within the range of resources use in planning and realising their lessons, which leads us to the third section, mathematics teachers using resources. We end with a review of the current state of understanding and an agenda for future research.
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- 1.
‘Reasons’ may not be the best term if it suggests some explicit logic behind actions; ‘agencies at play’ in an institutional setting may be a better term, suggesting a range of factors influencing teachers’ actions.
- 2.
Actually a set of praxeologies realised in different institutions.
- 3.
Mishra and Koehler (2006), like many authors, use the term ‘technology’ (short for ‘digital technology’). We prefer, in this book, the term ‘digital tool’ but realise that we are ‘nit picking’. We adopt the following usage in this chapter: when we are developing our own line of thought we shall use the term ‘digital tool’ but when we are discussing literature that uses the term ‘technology’, then we shall use the term ‘technology’.
- 4.
This was outlined in Chap. 14. A brief resume is: the parameters activity structures, social interactions, conventions and artefacts and prior understandings interact and influence, and can interrupt, emergent goals arising in practice.
- 5.
Pragmatic values which concern the range of application of a technique and epistemic values which concern the role of techniques in promoting mathematical understanding.
- 6.
Networking theoretical approaches is a term used by the Congress of European Research on Mathematics Education (CERME), see, for example, Kidron, Bikner-Ahsbahs, Monaghan, Radford, and Sensevy (2012).
- 7.
The photograph is available on https://iamliterate.wikispaces.com/Social+Studies+IRP.
- 8.
Comments such as this are provided as possible comments which can be provided, not as exemplar comments.
- 9.
Pairform@nce stands for ‘training (formation in French) based on collaborations with colleagues (pairs in French)’. The symbol @ evokes the importance of Internet in this program.
References
Adler, J. (2000). Conceptualising resources as a theme for teacher education. Journal of Mathematics Teacher Education, 3, 205–224.
Allen, R., Wallace, M., Cederberg, J., & Pearson, D. (1996). Teachers empowering teachers: Vertically-integrated, inquiry-based geometry in school classrooms. Mathematics Teacher, 90(3), 254–255.
Artigue, M. (1998). Teacher training as a key issue for the integration of computer technologies. In J. D. Tinsley, & D. C. Johnson (Eds.), Information and communication in school mathematics (pp. 121–129). London: Chapman and Hall.
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(3), 245–274.
Assude, T. (2005). Time management in the work economy of a class. A case study: Integration of Cabri in primary school mathematics teaching. Educational Studies in Mathematics, 59(1–3), 183–203.
Chevallard, Y., & Bosch, M. (2014). Didactic transposition in mathematics. In S. Lerman (Ed.), Encyclopedia of mathematics education. Dordrecht, The Netherlands: Springer.
Cuban, L. (1986). Teachers and machines: The classroom use of technology since 1920. New York: Teachers College Press.
Cuban, L. (1989). Neoprogressive visions and organizational realities. Harvard Educational Review, 59, 217–222.
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, 213–234.
Etzioni, A. (1969). The semi-professions and their organization: Teachers, nurses, social workers. New York: The Free Press.
Goos, M. (2005). A sociocultural analysis of the development of pre-service and beginning teachers’ pedagogical identities as users of technology. Journal of Mathematics Teacher Education, 8, 35–59.
Gueudet, G., Buteau, C., Mesa, V., & Misfeldt, M. (2014). Instrumental and documentational approaches: From technology use to documentation systems in university mathematics education. Research in Mathematics Education, 16(2), 139–155.
Gueudet, G., Pepin, B., & Trouche, L. (2013), Collective work with resources: An essential dimension for teacher documentation, ZDM, The International Journal on Mathematics Education, 45(7), 1003–1016. doi:10.1007/s11858-013-0527-1
Gueudet, G., & Trouche, L. (2009). Towards new documentation systems for mathematics teachers? Educational Studies in Mathematics, 71(3), 199–218.
Gueudet, G., & Trouche, L. (2011). Mathematics teacher education advanced methods: An example in dynamic geometry. ZDM: The International Journal on Mathematics Education, 43(3), 399–411.
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.
Hannula, M. S. (2012). Exploring new dimensions of mathematics-related affect: Embodied and social theories. Research in Mathematics Education, 14(2), 137–161.
Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 372–400.
Kendal, M., & Stacey, K. (2001). The impact of teacher privileging on learning differentiation with technology. International Journal of Computers for Mathematical Learning, 6(2), 143–165.
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, 101–116.
Kidron, I., Bikner-Ahsbahs, A., Monaghan, J., Radford, L., & Sensevy, G. (2012). CERME7 Working Group 16: Different theoretical perspectives and approaches in research in mathematics education. Research in Mathematics Education, 14(2), 213–214.
Laborde, C. (2001). Integration of technology in the design of geometry tasks with Cabri-Geometry. International Journal of Computers for Mathematical Learning, 6(3), 283–317.
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 (pp. 39–271). Dordrecht, The Netherlands: Kluwer.
Lagrange, J.-B., & Erdogan, E. O. (2009). Teachers’ emergent goals in spreadsheet-based lessons: Analyzing the complexity of technology integration. Educational Studies in Mathematics, 71(1), 65–84.
Lagrange, J. B., & Monaghan, J. (2009). On the adoption of a model to interpret teachers’ use of technology in mathematics lessons. In Proceedings of the sixth Conference of the European Society for Research in Mathematics Education (pp. 1605–1614).
Mathematical Association. (1992). In W. Mann, & D. Tall (Eds.), Computers in the mathematics curriculum: A report of the mathematical association. Leicester, England: The Mathematical Association.
Mishra, P., & Koehler, M. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. The Teachers College Record, 108(6), 1017–1054.
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 Groups for the Psychology of Mathematics Education (Vol. 3 pp. 383–390).
Monaghan, J. (2004). Teachers’ activities in technology-based mathematics lessons. International Journal of Computers for Mathematical Learning, 9(3), 327–357.
Moreira, C., & Noss, R. (1995). Understanding teachers’ attitudes to change in a logomathematics environment. Educational Studies in Mathematics, 28, 155–176.
Noss, R. (2001). For a learnable mathematics in the digital culture. Educational Studies in Mathematics, 48, 21–46.
Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings: Learning cultures and computers. Dordrecht, The Netherlands: Kluwer.
Olson, J. (1992). Understanding teaching: Beyond expertise. Milton Keynes, England: OU Press.
Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. Brighton, England: The Harvester Press.
Pedauque, R. T. (Ed.). (2006). Le document à la lumière du numérique (Document under digital light). Caen, France: C & F éditions.
Pepin, B., Gueudet, G., Yerushalmy, M., Trouche, L., & Chazan, D. (to appear). E-textbooks in/for teaching and learning mathematics: A potentially transformative educational technology. In English, L., & Kirschner, D. (Eds.), Handbook of international research on mathematics education. Taylor & Francis.
Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75(2), 211–246.
Rowland, T., & Ruthven, K. (2011). Mathematical knowledge in teaching (Vol. 50). Dordrecht, The Netherlands: Springer.
Ruthven, K. (2012). Constituting digital tools and materials as classroom resources: The example of dynamic geometry. In G. Gueudet, B. Pepin, & L. Trouche (Eds.), From text to ‘Lived’ resources: Mathematics curriculum materials and teacher development. New York: Springer.
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, The Netherlands: Springer.
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.
Sabra, H., & Trouche, L. (2011). Collective design of an online math textbook: When individual and collective documentation works meet. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of CERME 7, 9–13 February 2011 (pp. 2356–2366). Rzesów, Poland.
Saxe, G. (1991). Culture and cognitive development: Studies in mathematical understanding (pp. 15–18). Hillsdale, NJ: Lawrence Erlbaum. Chapter 2.
Schwartz, J. L. (1989). Intellectual mirrors: A step in the direction of making schools knowledge-making places. Harvard Educational Review, 59(1), 51–62.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 2, 4–14.
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–23.
Trouche, L. (2004). Managing the 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.
Trouche, L., & Drijvers, P. (2010). Handheld technology for mathematics education, flashback to the future. ZDM, The International Journal on Mathematics Education, 42(7), 667–681.
Trouche, L., Drijvers, P., Gueudet, G., & Sacristan, A. I. (2013). Technology-driven developments and policy implications for mathematics education. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Third international handbook of mathematics education (pp. 753–790). New York: Springer.
Valsiner, J. (1987). Culture and the development of children's action: A cultural-historical theory of developmental psychology. John Wiley & Sons.
Vergnaud, G. (1998). Toward a cognitive theory of practice. In A. Sierpinska & J. Kilpatrick (Eds.), Mathematics education as a research domain: A search for identity (pp. 227–241). Dordrecht, The Netherlands: Kluwer.
Watson, A. (2008, March 18). Developing and deepening mathematical knowledge in teaching: being and knowing. In MKiT 6, Nuffield Seminar Series. University of Loughborough.
Wertsch, J. V. (1991). Voices of the mind: A sociological approach to mediated action. Cambridge MA: Harvard University Press.
Williams, J. (2011). Audit and evaluation of pedagogy: Towards a cultural-historical perspective. In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching (pp. 161–178). Dordrecht, The Netherlands: Springer.
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Monaghan, J., Trouche, L. (2016). Mathematics Teachers and Digital Tools. In: Tools and Mathematics. Mathematics Education Library, vol 110. Springer, Cham. https://doi.org/10.1007/978-3-319-02396-0_15
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