Skip to main content

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

  • Chapter
  • First Online:
The Mathematics Teacher in the Digital Era

Part of the book series: Mathematics Education in the Digital Era ((MEDE,volume 2))

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).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

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.

    Article  Google 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.

    Article  Google 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.

    Article  Google 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.

    Article  Google 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.

    Article  Google 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.

    Article  Google 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.

    Chapter  Google 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.

    Chapter  Google 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.

    Article  Google 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.

    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). New York: Springer.

    Chapter  Google 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 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kenneth Ruthven .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Ruthven, K. (2014). Frameworks for Analysing the Expertise That Underpins Successful Integration of Digital Technologies into Everyday Teaching Practice. In: Clark-Wilson, A., Robutti, O., Sinclair, N. (eds) The Mathematics Teacher in the Digital Era. Mathematics Education in the Digital Era, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4638-1_16

Download citation

Publish with us

Policies and ethics