Skip to main content

Networking of Theories—An Approach for Exploiting the Diversity of Theoretical Approaches

  • Chapter
  • First Online:
Theories of Mathematics Education

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

Internationally, mathematics education research is shaped by a diversity of theories. This contribution suggests an approach for exploiting this diversity as a resource for richness by the so-called networking of theories. For being able to include different traditions, this approach is based on a tolerant and dynamic understanding of theories that conceptualizes theories in their dual character as frame and as result of research practices. Networking strategies are presented in a landscape, linearly ordered according to their degree of integration. These networking strategies can contribute to the development of theories and their connectivity and, hence, offer an interesting research strategy for the didactics of mathematics as scientific discipline.

This article is built upon a synthesis of two articles that formerly appeared in ZDM: Bikner-Ahsbahs, A., & Prediger, S. (2006). Diversity of theories in mathematics education—How can we deal with it?, ZDM, 38(1), 52–57, and Prediger, S., et al. (2008b). Networking strategies and methods for connecting theoretical approaches—First steps towards a conceptual framework, ZDM, 40(2), 165–178.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Arnold, M., & Fischer, R. (Eds.) (2004). Disziplinierungen. Kulturen der Wissenschaft im Vergleich [Disciplines. Sciences as cultures in comparison]. Wien: Turia & Kant.

    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 4th Congress of the European Society for Research in Mathematics Education (pp. 1239–1244). Barcelona: Fundemi IQS.

    Google Scholar 

  • Arzarello, F., Bosch, M., Lenfant, A., & Prediger, S. (2008a). Different theoretical perspectives in research from teaching problems to research problems. In D. Pitta-Pantazi & G. Phillipou et al. (Eds.), Proceedings of the 5 th Congress of the European Society for Research in Mathematics Education (CERME 5) (pp. 1618–1627). Cyprus: ERME.

    Google Scholar 

  • Arzarello, F., Bosch, M., Gascón, J., & Sabena, C. (2008b). The ostensive dimension through the lenses of two didactic approaches. ZDM—The International Journal on Mathematics Education, 40(2), 179–188.

    Article  Google Scholar 

  • Assude, T., Boero, P., Herbst, P., Lerman, S., & Radford, L. (2008). The notions and roles of theory in mathematics education research. Paper presented by the Survey Team at ICME 11. Mexico, 2008.

    Google Scholar 

  • Bauersfeld, H. (1988). Interaction, construction, and knowledge—Alternatives for mathematics education. In T. Cooney & D. Grouws (Eds.), Effective Mathematics Teaching (pp. 27–46). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Bergsten, C. (2008). How do theories influence the research on teaching and learning limits of functions. ZDM—The International Journal on Mathematics Education, 40(2), 189–199.

    Article  Google Scholar 

  • Bigalke, H.-G. (1984). Thesen zur Theoriediskussion in der Mathematikdidaktik. [Contributions to the discussion about theories in mathematics education.] Journal für Mathematik-Didaktik, 5, 133–165.

    Google Scholar 

  • Bikner-Ahsbahs, A. (2005). Mathematikinteresse zwischen Subjekt und Situation [Interest in mathematics between subject and situation]. Hildesheim: Verlag Franzbecker.

    Google Scholar 

  • Bikner-Ahsbahs, A. (2007). “Sensitizing concepts” as heuristics to compare and connect different theories. Contribution to the symposium: Networking a variety of theories within a scientific domain—The case of mathematics education. In B. ö Csapó & C. Csikos (Eds.), Developing Potentials for Learning, 12 th Biennial Conference for Research on Learning and Instruction. Budapest: University of Szeged.

    Google Scholar 

  • Bikner-Ahsbahs, A. (2008). Erkenntnisprozesse. Rekonstruktion ihrer Struktur durch Idealtypenbildung. [Epistemic processes. Reconstruction of its structure by building ideal types.] In H. Jungwirth & G. Krummheuer (Eds.), Der Blick nach innen: Aspekte der alltäglichen Lebenswelt Mathematikunterricht. [The view inside: aspects of the everyday life in mathematics classrooms] (pp. 105–144). Münster et al.: Waxmann.

    Google Scholar 

  • Bikner-Ahsbahs, A., & Prediger, S. (2006). Diversity of theories in mathematics education—How can we deal with it? (ZDM) Zentralblatt für Didaktik der Mathematik, 38(1), 52–57.

    Article  Google Scholar 

  • Brousseau, G. (1997). The Theory of Didactical Situations in Mathematics. Dordrecht: Kluwer.

    Google Scholar 

  • Cerulli, M., Trgalova, J., Maracci, M., Psycharis, G., & Geirget, J.-P. (2008). Comparing theoretical frameworks enacted in experimental research: TELMA experience. ZDM—The International Journal on Mathematics Education, 40(2), 201–213.

    Article  Google Scholar 

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

    Google Scholar 

  • Cobb, P. (2007). Putting philosophy to work. Coping with multiple theoretical perspectives. In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 3–38). Reston: NCTM.

    Google Scholar 

  • Dreyfus, T. (2006). Linking theories in mathematics education. In A. Simpson (Ed.), Retirement as Process and as Concept (pp. 77–82). Festschrift for Eddie Gray and David Tall, presented at Charles University, Prague.

    Google Scholar 

  • Eisenhart, M. (1991). Conceptual frameworks for research. Ideas from a cultural anthropologist; implications for mathematics education researchers. In R. Underhill (Ed.), Proceedings of the Thirteenth Annual Meeting of Psychology of Mathematics Education—North America. Blaksburg, VA: Psychology of Mathematics Education.

    Google Scholar 

  • Ernest, P. (1998). A postmodern perspective on research in mathematics education. In A. Sierpinska & J. Kilpatrick (Eds.), Mathematics Education as a Research Domain: A Search for Identity (Vol. 1, pp. 71–85). Dordrecht: Kluwer.

    Google Scholar 

  • Fischer, R. (1993). Wissenschaft, Argumentation und Widerspruch [Science, argumentation and contradiction]. In R. Fischer et al. (Eds.), Argumentation und Entscheidung. Zur Idee und Organisation von Wissenschaft [Towards the idea and organization of science] (pp. 29–43). Wien-München: Profil.

    Google Scholar 

  • Gellert, U. (2008). Validity and relevance: Comparing and combining two sociological perspectives on mathematics classroom practice. ZDM—The International Journal on Mathematics Education, 40(2), 215–224.

    Article  Google Scholar 

  • Gravemeijer, K. (1994). Educational development and developmental research. Journal for Research in Mathematics Education, 25, 443–471.

    Article  Google Scholar 

  • Halverscheid, S. (2008). Building a local conceptual framework for epistemic actions in a modelling environment with experiments. ZDM—The International Journal on Mathematics Education, 40(2), 225–234.

    Article  Google Scholar 

  • Harel, G., & Lim, K. H. (2004). Mathematics teacher’s knowledge base: Preliminary results. In M. Johnsen Høines & A. B. Fuglestad (Eds.), Proceedings of the 28 th Conference on the International Group for the Psychology of Mathematik Education (pp. 25–32). Bergen: University College.

    Google Scholar 

  • Jungwirth, H. (1996). Symbolic interactionism and ethnomethodology as a theoretical framework for the research on gender and mathematics. In G. Hanna (Ed.), Towards Gender Equity in Mathematics Education. An ICMI Study (pp. 49–70). Dordrecht: Kluwer.

    Google Scholar 

  • Kidron, I., Lenfant, A., Artigue, M., Bikner-Ahsbahs, A., & Dreyfus, T. (2008). Toward networking three theoretical approaches: The case of social interaction. ZDM—The International Journal on Mathematics Education, 40(2), 247–267.

    Article  Google Scholar 

  • Krummheuer, G. (2001). Paraphrase und Traduktion. Weinheim: Beltz Verlag.

    Google Scholar 

  • Kuhn, T. S. (1969). Die Struktur wissenschaftlicher Revolution [The Structure of Scientific Revolutions]. Frankfurt a.M.: Suhrkamp.

    Google Scholar 

  • Lamnek, S. (1995). Qualitative Sozialforschung [Qualitative Social Research]. Weinheim, Basel: Beltz Verlag.

    Google Scholar 

  • Maier, H., & Beck, C. (2001). Zur Theoriebildung in der interpretativen mathematikdidaktischen Forschung. [Towards building theories in the interpretative research of mathematics education]. Journal für Mathematik-Didaktik, 22(1), 29–50.

    Google Scholar 

  • Maracci, M. (2008). Combining different theoretical perspectives for analyzing students’ difficulties in vector spaces theory. ZDM—The International Journal on Mathematics Education, 40(2), 265–276.

    Article  Google Scholar 

  • Mason, J., & Waywood, A. (1996). The role of theory in mathematics education and research. In A. J. Bishop et al. (Eds.), International Handbook of Mathematics Education (pp. 1055–1089). Dordrecht: Kluwer.

    Google Scholar 

  • Niss, M. (2007). Reflections on the state of and trends in research in mathematics teaching and learning. From here to utopia. In F. K. Lester & K. Frank (Eds.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 1293–1312). Reston: NCTM.

    Google Scholar 

  • Prediger, S. (2004). Intercultural perspectives on mathematics learning—Developing a theoretical framework. International Journal of Science and Mathematics Education, 2(3), 377–406.

    Article  Google Scholar 

  • Prediger, S. (2008). How are theoretical approaches expressed in research practices? A report on an experience in comparing theoretical approaches with respect to the construction of research problems. ZDM—The International Journal on Mathematics Education, 40(2), 277–286.

    Article  Google Scholar 

  • Prediger, S., Arzarello, F., Bosch, M., & Lenfant, A. (Eds.) (2008a). Comparing, combining, coordinating—Networking strategies for connecting theoretical approaches. Thematic Issue of ZDM—The International Journal on Mathematics Education, 40(2), 163–327.

    Google Scholar 

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

    Article  Google Scholar 

  • Prediger, S., Viggiani-Bicudo, M., & Ernest, P. (2008c). Philosophy of mathematics education—Strands and issues. In M. Niss, E. Emborg (Eds.), Proceedings of the 10th International Congress on Mathematical Education (pp. 438–442). Copenhagen 2004; Roskilde University.

    Google Scholar 

  • Prediger, S., Bosch, M., Kidron, I., Monaghan, J., & Sensevy, G. (2009, in preparation). Different theoretical perspectives and approaches in mathematics education research—Strategies and difficulties when connecting theories. In Proceedings of CERME 6, Lyon.

    Google Scholar 

  • Rodriguez, E., Bosch, M., & Gascón, J. (2008). A networking method to compare theories: Metacognition in problem solving reformulated within the anthropological theory of the didactic. ZDM—The International Journal on Mathematics Education, 40(2), 287–301.

    Article  Google Scholar 

  • Schoenfeld, A. H. (2002). Research methods in (mathematics) education. In L. D. English (Ed.), Handbook of International Research in Mathematics Education (pp. 435–487). Mahwah: Lawrence Erlbaum Associates.

    Google Scholar 

  • Silver, E. A., & Herbst, P. G. (2007). Theory in mathematics education scholarship. In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 39–68). Reston: NCTM.

    Google Scholar 

  • Sriraman, B., & English, L. (2005). Theories of mathematics education: A global survey of theoretical frameworks/trends in mathematics education research. (ZDM) Zentralblatt für Didaktik der Mathematik, 37(6), 450–456.

    Article  Google Scholar 

  • Steen, L. A. (1999). Review of mathematics education as research domain. Journal for Research in Mathematics Education, 30(2), 235–241.

    Article  Google Scholar 

  • Steinbring, H. (2005). In Mathematics Education Library : Vol. 38. The Construction of New Mathematical Knowledge in Classroom Interaction—An Epistemological Perspective. Berlin, New York: Springer.

    Google Scholar 

  • Steinbring, H. (2008). Changed views on mathematical knowledge in the course of didactical theory development. ZDM—The International Journal on Mathematics Education, 40(2), 303–316.

    Article  Google Scholar 

  • Voigt, J. (1994). Negotiation of mathematical meaning and learning mathematics. Educational Studies in Mathematics, 26, 275–298.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Angelika Bikner-Ahsbahs .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Bikner-Ahsbahs, A., Prediger, S. (2010). Networking of Theories—An Approach for Exploiting the Diversity of Theoretical Approaches. In: Sriraman, B., English, L. (eds) Theories of Mathematics Education. Advances in Mathematics Education. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00742-2_46

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-00742-2_46

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00741-5

  • Online ISBN: 978-3-642-00742-2

  • eBook Packages: Humanities, Social Sciences and LawEducation (R0)

Publish with us

Policies and ethics