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Networking Different Theoretical Perspectives

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The Didactics of Mathematics: Approaches and Issues

Abstract

During the last decade researchers in mathematics education have devoted efforts to understanding how theories can be connected successfully while respecting their underlying conceptual and methodological assumptions, a process called ‘networking theories’. Both authors of this chapter have had the privilege of collaborating with Michèle Artigue and colleagues where we explored ways of handling the diversity of theories in mathematics education. In this chapter, we describe this collaboration and explain the reasons for networking theories as well as the expected difficulties of the networking process. We characterise different cases of networking and describe methodological reflections on the difficulties and benefits that accompany the networking. We refer to Michèle Artigue’s contribution to the research on “networking theories” in general and in methodologies of the networking of theories in particular.

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References

  • Artigue, M. (1990). Épistémologie et didactique. Recherches en Didactique des Mathématiques, 10(2 3), 241–286.

    Google Scholar 

  • Artigue, M. (1994). Didactic engineering as a framework for the conception of teaching products. In R. Biehler, R. W. Scholz, R. Sträßer, & B. Winkelmann (Eds.), Didactics of mathematics as a scientific discipline (pp. 27–39). Dordrecht, The Netherlands: Kluwer Academic Publishers.

    Google Scholar 

  • Artigue, M. (1995). The role of epistemology in the analysis of teaching/learning relationships in mathematics education. In Y. M. Pothier (Ed.), Proceedings of the 1995 Annual Meeting of the Canadian Mathematics Education Study Group (pp. 7–21). Ontario: University of Western Ontario.

    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.

    Article  Google Scholar 

  • Artigue, M. (2007). Digital technologies: A window on theoretical issues in mathematics education. In D. Pitta-Pantazi, C. Philippou, & A. Gagatsis (Eds.), Proceedings of CERME 5 (pp. 68–82), Larnaca, Cyprus.

    Google Scholar 

  • Artigue, M. (2015). Perspectives on design research: The case of didactical engineering. In A. Bikner-Ahsbahs, Ch. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education: Examples of methodology and methods. Advances in mathematics education series (pp. 467–496). New York: Springer.

    Google Scholar 

  • Artigue, M., Bartolini-Bussi, M., Dreyfus, T., Gray, E., & Prediger, S. (2006). Different theoretical perspectives and approaches in research in mathematics education. In M. Bosch (Ed.), Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (pp. 1237–1399). Sant Feliu de Guíxols, Spain: Universitat Ramon Llull.

    Google Scholar 

  • Artigue, M., Bosch, M., & Gascón, J. (2012). Research praxeologies and networking theories. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education CERME7 (pp. 2381–2390). Rzeszów, Pologne: University of Rzeszów.

    Google Scholar 

  • Artigue, M., Haspekian, M., & Corblin-Lenfant, A. (2014). Introduction to the theory of didactical situations. In A. Bikner-Ahsbahs & S. Prediger (Eds.), Networking theories group networking of theories as a research practice in mathematics education. Advances in mathematics education series (pp. 47–65). New York: Springer.

    Google Scholar 

  • Artigue, M., & Mariotti, M. A. (2014). Networking theoretical frames: The ReMath enterprise. Educational studies in mathematics, 85, 329–355.

    Article  Google Scholar 

  • Arzarello, F., Bikner-Ahsbahs, A., & Sabena, C. (2009). Complementary networking: Enriching understanding. In Proceedings of the 6th Congress of the European Society for Research in Mathematics Education (pp. 1545–1554). Lyon, France: Université Claude Bernard. http://www.inrp.fr/editions/editions-electroniques/cerme6/. Accessed August 4, 2014.

  • Arzarello, F., Bosch, M., Lenfant, A., & Prediger, S. (2007). Different theoretical perspectives and approaches in research in mathematics education. In D. Pitta-Pantazi, C. Philippou, & A. Gagatsis (Eds.), Proceedings of the 5th Congress of the European Society for Research in Mathematics Education (pp. 1618–1627). Larnaca, Cyprus.

    Google Scholar 

  • Arzarello, F., & Sabena, C. (2014). Introduction to the approach of action, production and communication. In A. Bikner-Ahsbahs & S. Prediger (Eds.), Networking theories group, networking of theories as a research practice in mathematics education. Advances in mathematics education series (pp. 31–45). New York: Springer.

    Google Scholar 

  • Barquero, B. (2009). Ecología de la modelización matemática en la enseñanza universitaria de matemáticas [Ecology of mathematical modelling in mathematics teaching at university]. Doctoral Thesis, Universitat Autónoma de Barcelona, Barcelona.

    Google Scholar 

  • Bikner-Ahsbahs, A., Artigue, M., & Haspekian, M. (2014). Topaze effect: A case study on networking of IDS and TDS. In A. Bikner-Ahsbahs & S. Prediger (Eds.), Networking theories group, networking of theories as a research practice in mathematics education. Advances in mathematics education series (pp. 201–221). New York: Springer.

    Google Scholar 

  • Bikner-Ahsbahs, A., Dreyfus, T., Kidron, I., Arzarello, F., Radford, L., Artigue, M., et al. (2010). Networking of theories in mathematics education. In M. Pinto & T. F. Kawasaki (Eds.), Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 145–175). Belo Horizonte (Brazil): PME.

    Google Scholar 

  • Bikner-Ahsbahs, A., & Halverscheid, S. (2014). Introduction to the theory of interest-dense situations. In A. Bikner-Ahsbahs & S. Prediger (Eds.), Networking theories group networking of theories as a research practice in mathematics education. Advances in mathematics education series (pp. 97–103). New York: Springer.

    Google Scholar 

  • Bikner-Ahsbahs, A., & Kidron, I. (2015). A cross-methodology for the networking of theories: The general epistemic need (GEN) as a new concept at the boundary of two theories. In A. Bikner-Ahsbahs, Ch. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education: Examples of methodology and methods. Advances in mathematics education series (pp. 233–250). New York: Springer.

    Google Scholar 

  • Bikner-Ahsbahs, A., Prediger, S., & Networking Theories Group (2014). Networking of theories as a research practice in mathematics education. Book published in the Series Advances in Mathematics Education. New York: Springer.

    Google Scholar 

  • Bosch, M., & Chevallard, Y. (1999). La sensibilité de l’activité mathématique aux ostensifs. Objet d’étude et problématique. Recherches en Didactique des Mathématiques, 19(1), 77–124.

    Google Scholar 

  • Bosch, M., & Gascón, J. (2014). Introduction to the anthropological theory of the didactic. In A. Bikner-Ahsbahs & S. Prediger (Eds.), Networking theories group networking of theories as a research practice in mathematics education. Advances in mathematics education series (pp. 67–83). New York: Springer.

    Google Scholar 

  • Brousseau, G. (1986). Les fondements de la didactique des mathématiques. Doctoral dissertation, Université de Bordeaux I.

    Google Scholar 

  • Cerulli, M., Trgalova, J., Maracci, M., Psycharis, G., & Georget, J.-P. (2008). Comparing theoretical frameworks enacted in experimental research: TELMA experience. ZDM Mathematics Education, 40, 201–213.

    Article  Google Scholar 

  • Chevallard, Y. (1991). La transposition didactique (2nd ed.). Grenoble: La Pensée Suavage.

    Google Scholar 

  • Chevallard, Y. (1992). Concepts fondamentaux de la didactique: Perspectives apportèes par une perspective anthropologique. Recherches en Didactique des Mathematiques, 12(1), 73–112.

    Google Scholar 

  • Dreyfus, T., & Kidron, I. (2014). Introduction to abstraction in context. In A. Bikner-Ahsbahs & S. Prediger (Eds.), Networking theories group, networking of theories as a research practice in mathematics education. Advances in mathematics education series (pp. 85–95). New York: Springer.

    Google Scholar 

  • Haspekian, M., Bikner-Ahsbahs, A., & Artigue, M. (2013). When the fiction of learning is kept: A case of networking two theoretical views. In A. Heinze (Ed.) Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 9–16). Kiel: IPN.

    Google Scholar 

  • Hickman, M., & Monaghan, J. (2013). Networking methodologies: issues arising from a research study employing a multi-media artefact. In B. Ubuz, Ç. Haser, & M. A. Mariotti (Eds.), Proceedings of the 8th Congress of the European Society for Research in Mathematics Education (pp. 2820–2829). Ankara, Turkey: Middle East Technical University.

    Google Scholar 

  • Kidron, I. (2008). Abstraction and consolidation of the limit procept by means of instrumented schemes: the complementary role of three different frameworks. Educational Studies in Mathematics, 69(3), 197–216.

    Article  Google Scholar 

  • Kidron, I., Artigue, M., Bosch, M., Dreyfus, T., & Haspekian, M. (2014). Context, milieu and media-milieus dialectic: A case study on networking of AiC, TDS, and ATD. In A. Bikner-Ahsbahs & S. Prediger (Eds.), Networking theories group, networking of theories as a research practice in mathematics education. Advances in mathematics education series (pp. 153–177). New York: Springer.

    Google Scholar 

  • Kidron, I., & Bikner-Ahsbahs, A. (2015). Advancing research by means of the networking of theories. In A. Bikner-Ahsbahs, Ch. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education: Examples of methodology and methods. Advances in mathematics education series (pp. 221–232). New York: Springer.

    Google Scholar 

  • Kidron, I., Bikner-Ahsbahs, A., Monaghan, J., Radford, L., & Sensevy, G. (2012). Different theoretical perspectives and approaches in research in mathematics education. Research in Mathematics Education, 14(2), 213–214.

    Article  Google Scholar 

  • Kidron, I., Lenfant, A., Artigue, M., Bikner-Ahsbahs, A., & Dreyfus, T. (2008). Toward networking three theoretical approaches: the case of social interactions. Zentralblatt für Didaktik der Mathematik—The International Journal on Mathematics Education, 40(2), 247–264.

    Article  Google Scholar 

  • Kidron, I., & Monaghan, J. (2012). Complexity of dialogue between theories: Difficulties and benefits. In Pre-proceedings of the 12th International Congress on Mathematical Education (pp. 7078–7084). Paper presented in the Topic Study Group 37. COEX Seoul (Korea): ICME.

    Google Scholar 

  • Kynigos, C. (2012). Networking of theoretical frameworks and constructs: Artigue’s contributions to the case of using digital media for learning mathematics. International Colloquium. Plenary Paper Presented at the Conference, The Didactics of Mathematics: Approaches and Issues: A Hommage to Michèle Artigue. https://docs.google.com/file/d/0B7H9DyVUr48lVE9KUzFLSkwyRUE/edit?pli=1. Accessed September 21, 2013.

  • Kynigos, C., & Lagrange, J. B. (2014). Cross-analysis as a tool to forge connections amongst theoretical frames in using digital technologies in mathematical learning. Educational Studies in Mathematics, 85(3), 321–327.

    Article  Google Scholar 

  • Lagrange, J.-B., & Monaghan, J. (2010). On the adoption of a model to interpret teachers’ use of technology in mathematics lessons. In Proceedings of the 6th Congress of the European Society for Research in Mathematics Education (pp. 1605–1614), Lyon, France. Lyon (France): Université Claude Bernard. http://ife.ens-lyon.fr/editions/editions-electroniques/cerme6/. Accessed August 4, 2014.

  • Monaghan, J. (2010). People and theories. In Proceedings of the 6th Congress of the European Society for Research in Mathematics Education (pp. 16–23). Lyon (France): Université Claude Bernard. http://ife.ens-lyon.fr/publications/edition-electronique/cerme6/plenary-02-monaghan.pdf. Accessed August 4, 2014.

  • Perrin-Glorian, M. J. (2011). L’ingénierie didactique à l’interface de la recherche avec l’enseignement. Développement des ressources et formation des enseignants. In C. Margolinas, M. Abboud-Blanchard, L. Bueno-Ravel, N. Douek, A. Fluckiger, P. Gibel, et al. (Eds.), En amont et en aval des ingénieries didactiques. XVe école d’été de didactique des mathématiques (pp. 57–74). Grenoble: La Pensée Sauvage Editions.

    Google Scholar 

  • Prediger, S., Bikner-Ahsbahs, A., & Arzarello, F. (2008). Networking strategies and methods for connection theoretical approaches: First steps towards a conceptual framework. ZDM-International Journal on Mathematics Education, 40(2), 165–178.

    Article  Google Scholar 

  • Prediger, S., Bosch, M., Kidron, I., Monaghan, J., & Sensevy, G. (2010). Different theoretical perspectives and approaches in mathematics education research—strategies and difficulties when connecting theories. In Proceedings of the 6th Conference of the European Society for Research in Mathematics Education (pp. 1529–1534). Lyon, France: Université Claude Bernard. http://www.inrp.fr/editions/editions-electroniques/cerme6/. Accessed August 4, 2014.

  • Radford, L. (2008). Connecting theories in mathematics education: Challenges and possibilities. Zentralblatt für Didaktik der Mathematik—The International Journal on Mathematics Education, 40(2), 317–327.

    Article  Google Scholar 

  • Radford, L. (this book). Epistemology as a research category in mathematics teaching and learning. In B. R. Hodgson, A. Kuzniak, & J.-B. Lagrange (Eds.), The didactics of mathematics: approaches and issues. A homage to michèle artigue. Advances in Mathematics Education Series. New York: Springer.

    Google Scholar 

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Correspondence to Ivy Kidron .

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Kidron, I., Bikner-Ahsbahs, A. (2016). Networking Different Theoretical Perspectives. In: Hodgson, B., Kuzniak, A., Lagrange, JB. (eds) The Didactics of Mathematics: Approaches and Issues. Springer, Cham. https://doi.org/10.1007/978-3-319-26047-1_3

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  • DOI: https://doi.org/10.1007/978-3-319-26047-1_3

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