The Mathematics Teacher in the Digital Era pp 373-393 | Cite as

# Frameworks for Analysing the Expertise That Underpins Successful Integration of Digital Technologies into Everyday Teaching Practice

## Abstract

This chapter examines contemporary frameworks for analysing teacher expertise which are relevant to the integration of digital technologies into everyday teaching practice. It outlines three such frameworks, offering a critical appreciation of each, and then explores some commonalities, complementarities and contrasts between them: the Technological, Pedagogical and Content Knowledge (TPACK) framework (Koehler & Mishra, *Contemporary Issues in Technology and Teacher Education, 9*(1), 2009); the Instrumental Orchestration framework (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). New York: Springer.); and the Structuring Features of Classroom Practice framework (Ruthven, *Education* & *Didactique, 3*(1), 2009). To concretise the discussion, the use of digital technologies for algebraic graphing, a now well established form of technology use in secondary school mathematics, serves as an exemplary reference situation: each of the frameworks is illustrated through its application in a study of teacher expertise relating to this topic (respectively Richardson, *Contemporary Issues in Technology and Teacher Education, 9*(2), 2009; Drijvers, Doorman, Boon, Reed, & Gravemeijer, *Educational Studies in Mathematics, 75*(2), 213–234, 2010; Ruthven, Deaney, & Hennessy, *Educational Studies in Mathematics, 71*(3), 279–297, 2009).

## Keywords

Instrumental orchestration TPACK Structuring features of classroom practice## References

- Association of Mathematics Teacher Educators. (AMTE). (2009).
*Mathematics TPACK (Technological Pedagogical Content Knowledge) Framework.*Retrieved February 8, 2012 from http://www.amte.net/sites/all/themes/amte/resources/AMTETechnologyPositionStatement.pdf - 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.CrossRefGoogle Scholar - Cuban, L. (1989). Neoprogressive visions and organizational realities.
*Harvard Educational Review, 59*(2), 217–222.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.CrossRefGoogle Scholar - Groth, R., Spickler, D., Bergner, J., & Bardzell, M. (2009). A qualitative approach to assessing technological pedagogical content knowledge.
*Contemporary Issues in Technology and Teacher Education, 9*(4). Retrieved February 8, 2012, from http://www.citejournal.org/vol9/iss4/mathematics/article1.cfm - Guin, D., Ruthven, K., & Trouche, L. (Eds.). (2005).
*The didactical challenge of symbolic calculators: Turning a computational device into a mathematical instrument*. New York: Springer.Google Scholar - Guin, D., & Trouche, L. (2002). Mastering by the teacher of the instrumental genesis in CAS environments: Necessity of instrumental orchestrations.
*Zentralblatt für Didaktik der Mathematik, 34*(5), 204–211.CrossRefGoogle Scholar - Koehler, M. J., & Mishra, P. (2009). What is technological pedagogical content knowledge?
*Contemporary Issues in Technology and Teacher Education, 9*(1). Retrieved February 8, 2012 from http://www.citejournal.org/vol9/iss1/general/article1.cfm - 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.CrossRefGoogle Scholar - Rabardel, P. (2002).
*People and Technology: a cognitive approach to contemporary instruments.*Retrieved February 8, 2012 from http://ergoserv.psy.univ-paris8.fr/ - Richardson, S. (2009). Mathematics teachers’ development, exploration, and advancement of technological pedagogical content knowledge in the teaching and learning of algebra.
*Contemporary Issues in Technology and Teacher Education, 9*(2). Retrieved February 8, 2012 from http://www.citejournal.org/vol9/iss2/mathematics/article1.cfm - Ruthven, K. (2002). Instrumenting mathematical activity: Reflections on key studies of the educational use of computer algebra systems.
*International Journal of Computers for Mathematical Learning, 7*(3), 275–291.CrossRefGoogle Scholar - Ruthven, K. (2009). Towards a naturalistic conceptualisation of technology integration in classroom practice: The example of school mathematics.
*Education & Didactique, 3*(1), 131–149.CrossRefGoogle Scholar - Ruthven, K. (2011a). Conceptualising mathematical knowledge in teaching. In T. Rowland & K. Ruthven (Eds.),
*Mathematical knowledge in teaching*(pp. 83–96). New York: Springer.CrossRefGoogle Scholar - Ruthven, K. (2011b). 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*(pp. 83–103). New York: Springer.CrossRefGoogle Scholar - 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.CrossRefGoogle Scholar - 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*(3), 281–307.CrossRefGoogle 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). New York: Springer.CrossRefGoogle Scholar - Wilson, S., Shulman, L., & Richert, A. (1987). ‘150 different ways’ of knowing: Representations of knowledge in teaching. In J. Calderhead (Ed.),
*Exploring teacher thinking*(pp. 104–124). London: Cassell.Google Scholar