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.
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References
Arnold, M., & Fischer, R. (Eds.) (2004). Disziplinierungen. Kulturen der Wissenschaft im Vergleich [Disciplines. Sciences as cultures in comparison]. Wien: Turia & Kant.
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.
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.
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.
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.
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.
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.
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.
Bikner-Ahsbahs, A. (2005). Mathematikinteresse zwischen Subjekt und Situation [Interest in mathematics between subject and situation]. Hildesheim: Verlag Franzbecker.
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.
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.
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.
Brousseau, G. (1997). The Theory of Didactical Situations in Mathematics. Dordrecht: Kluwer.
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.
Chevallard, Y. (1992). Concepts fondamentaux de la didactique: Perspectives apportées par une approche anthropologique. Recherches en Didactique des Mathématiques, 12(1), 73–112.
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.
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.
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.
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.
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.
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.
Gravemeijer, K. (1994). Educational development and developmental research. Journal for Research in Mathematics Education, 25, 443–471.
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.
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.
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.
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.
Krummheuer, G. (2001). Paraphrase und Traduktion. Weinheim: Beltz Verlag.
Kuhn, T. S. (1969). Die Struktur wissenschaftlicher Revolution [The Structure of Scientific Revolutions]. Frankfurt a.M.: Suhrkamp.
Lamnek, S. (1995). Qualitative Sozialforschung [Qualitative Social Research]. Weinheim, Basel: Beltz Verlag.
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.
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.
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.
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.
Prediger, S. (2004). Intercultural perspectives on mathematics learning—Developing a theoretical framework. International Journal of Science and Mathematics Education, 2(3), 377–406.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Steen, L. A. (1999). Review of mathematics education as research domain. Journal for Research in Mathematics Education, 30(2), 235–241.
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.
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.
Voigt, J. (1994). Negotiation of mathematical meaning and learning mathematics. Educational Studies in Mathematics, 26, 275–298.
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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
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