Skip to main content
SpringerLink
Log in

Networking theoretical frames: the ReMath enterprise

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

In this article of the special issue devoted to the European project ReMath, we present and discuss the affordances of this project in terms of networking between theoretical frameworks. After clarifying the vision of theories and networking adopted in this project, we introduce the methodological constructs that have been developed and used in ReMath for performing the planned networking enterprise. We then present its outcomes, focusing on different facets of this networking activity: the identification of possible connections and complementarities between frameworks, the identification and elaboration of boundary objects between cultures, and the progressive building of a shared theoretical framework regarding semiotic representations. In the last part of this article, we review the whole networking enterprise from the perspective of research praxeology.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

Notes

  1. The Dynamic Digital Artifact (DDA), or some part of it, is distinguished from the instrument it becomes for someone through the elaboration and appropriation of schemes of use and instrumented action. The corresponding process is called instrumental genesis, and it affects both the artifact (instrumentalization process) and the user (instrumentation process).

  2. Star and Griesemer (1989) define boundary objects as “objects which are both plastic enough to adapt to local needs and the constraints of several parties employing them, yet robust enough to maintain a common identity across sites” (p. 393).

  3. A semiotic chain is meant as a chain of signification connecting highly contextualized signs, strictly related to the use of the artifact, to the mathematical signs that are objects of the teaching–learning activity (Bartolini Bussi and Mariotti, 2008, p.756).

References

  • 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. (Ed.) (2009a). Connecting approaches to technology enhanced learning in mathematics: The TELMA experience. International Journal of Computers for Mathematical Learning, 14(3).

  • Artigue, M. (2009b). Rapports et articulations entre cadres théoriques: Le cas de la théorie anthropologique du didactique [Relations and articulations between theoretical frameworks: The case of the anthropological theory of didactics]. Recherches en Didactique des Mathématiques, 29(3), 305–334.

    Google Scholar 

  • Artigue, M. (2013). Didactic engineering in mathematics education. In, S. Lerman (Ed.) Encyclopedia of Mathematics Education: Springer Reference (www.springerreference.com). Berlin: Springer.

  • Artigue M., Bosch, M., & Gascón J. (2011). Research praxeologies and networking theories. In, M. Pytlak, T. Rowlad, & E. Swoboda (Eds). Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (pp. 281–290). Rzeszów: University of Rzeszów.

  • Artigue, M. (coord.) (2006). Integrative theoretical framework. ReMath Deliverable 1. IST4-26751. http://www.remath.cti.gr. Accessed 26 Nov 2013.

  • Artigue, M. (coord.) (2009c). Integrative theoretical framework. ReMath Deliverable 18. IST4-26751. http://www.remath.cti.gr

  • Bartolini Bussi, M. G., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: Artifacts and signs after a Vygotskian perspective. In L. English, M. Bartolini Bussi, G. Jones, R. Lesh, & D. Tirosh (Eds.), Handbook of international research in mathematics education, second revised edition (pp. 746–805). Mahwah: Lawrence Erlbaum.

    Google Scholar 

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

  • Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  • Chevallard, Y. (1992). Concepts fondamentaux de la didactique. Perspectives apportées par une approche anthropologique. [Fundamental concepts of didactics. Perspectives provided by an anthropological approach]. Recherche en didactique des Mathématiques, 12(1), 73–112.

    Google Scholar 

  • Chevallard, Y. & Sensevy, G. (2013). Anthropological approaches in mathematics education, French perspectives. In S. Lerman (Ed.), Encyclopedia of mathematics education: springerreference (www.springerreference.com). Berlin: Springer

  • Duval, R. (1995). Sémiosis et pensée humaine [Semiosis and human thinking]. Bern: Peter Lang.

  • Engeström, Y. (1999). Activity theory and individual and social transformation. In Y. Engeström, R. Miettinen, & R.-L. Punamäki (Eds.), Perspectives on activity theory (pp. 19–38). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • Falcade, R (2006) Théorie des Situations, médiation sémiotique et discussions collectives dans des séquences d'enseignement qui utilisent Cabri-géomètre et qui visent à l'apprentissage des notions de fonction et graphe de fonction. [Theory of didactic situations, semiotic mediation and collective discussions in teaching sequences involving the use of Cabri-géomètre and aiming at the learning of function and graphs]. Thèse de doctorat. Université de Grenoble 1.

  • Halliday, M. A. K. (1978). Language as social semiotic: The social interpretation of language and meaning. London: Edward Arnold.

    Google Scholar 

  • Harel, G., & Papert, S. (Eds.). (1991). Constructionism. Norwood: Ablex.

    Google Scholar 

  • Kafai, Y., & Resnick, M. (Eds.). (1996). Constructionism in practice: Designing, thinking and learning in a digital world. Mahwah: Lawrence Erlbaum Associates.

    Google Scholar 

  • Lagrange, J. B. (2000). L’intégration d’instruments informatiques dans l’enseignement : Une approche par les techniques. [The integration of computer tools in education: An approach through techniques]. Educational Studies in Mathematics, 43(1), 1–30.

    Google Scholar 

  • Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. New York: Cambridge University Press.

    Book  Google Scholar 

  • Leont'ev, A. N. (1978). Activity, consciousness and personality. Englewood Cliffs: Prentice-Hall.

    Google Scholar 

  • Maracci M., Cazes, C., Vandebrouck, F., & Mariotti, M.A. (2009); Casyopée in the classroom: Two different theory-driven pedagogical approaches. In V. Durand-Guerrier, S. Soury-Lavergne & F. Arzarello (Eds) Proceedings of the 6th Conference of the European Society for Research in Mathematics Education. (pp. 1399–1408). Lyon: Service des publications, INRP.

  • Maracci, M., Cazes, C., Vandebrouck, F., & Mariotti, M. A. (2013). Synergies between theoretical approaches to mathematics education with technology: A case study through a cross-analysis methodology. Educational Studies in Mathematics, 84(3), 461–485.

    Article  Google Scholar 

  • Mariotti M. A. Maracci M. & Saberna (coords) (2007) Research design ReMath Deliverable 11. IST4-26751. http://www.remath.cti.gr. Accessed 26 Nov 2013.

  • Mariotti M.A. & Maracci M. (coords) (2007) Design-based research: Process and results ReMath Deliverable 13. IST4-26751. http://www.remath.cti.gr. Accessed 26 Nov 2013.

  • Niss, M. (2007). Reflections on the state and trends in research on mathematics teaching and learning: From here to utopia. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1293–1311). Greenwich, Connecticut: Information Age Publishing, Inc.

    Google Scholar 

  • Peirce, C.S. (1931/1958). Collected papers. Cambridge: Harvard University Press.

  • Prediger, S., Bikner-Ahsbahs, A., & Arzarello, F. (2008). 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 

  • Rabardel, P. (1995): Les hommes and les technologies. Approche cognitive des instruments contemporains.[Technologies and human beings. A cognitive approach to contemporary instruments]. Paris: A. Colin.

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

    Article  Google Scholar 

  • Sriraman, B., & English, L. (Eds.). (2010). Theories of mathematics education. Seeking new frontiers. New York: Springer.

    Google Scholar 

  • Star, S. L., & Griesemer, J. R. (1989). Institutional ecology, “translations” and boundary objects: Amateurs and professionals in Berkeley's museum of vertebrate zoology, 1907–39. Social Studies of Science, 19(3), 387–420.

    Article  Google Scholar 

  • TELMA ERT (2006). Developing a joint methodology for comparing the influence of different theoretical frameworks in technology enhanced learning in mathematics: The TELMA approach. In Le Hung Son, N. Sinclair, J.-B. Lagrange & C. Hoyles (eds.) Proceedings of the ICMI 17 Study Conference: Background papers for the ICMI 17 Study. (2, pp. 46–55). Hanoï: Hanoï University of Technology.

  • Vérillon, P., & Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrumented activity. European Journal of Psychology of Education, 10(1), 77–101.

    Article  Google Scholar 

  • Vygotsky, L. S. (1978). Mind in society. The development of higher psychological processes. Cambridge: Harvard University Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université Denis Diderot (Paris 7), Paris, France

    Michèle Artigue

  2. University of Siena, Siena, Italy

    Maria Alessandra Mariotti

Authors
  1. Michèle Artigue
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maria Alessandra Mariotti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Maria Alessandra Mariotti.

Appendix 1: Elements of the first ITF: key concerns and didactical functionalities

Appendix 1: Elements of the first ITF: key concerns and didactical functionalities

Integrative Theoretical Framework

Part 1: Contextual characteristics of the project under study

How are the following dimensions of context taken into consideration at a theoretical level in the project? What constructs are used for this purpose?

 - The situational context of the project

 - The institutional/cultural context of the project

Part 2: Didactical functionalities and design

For each dimension of didactical functionalities, a list of concerns is given. You are asked to grade them from 0 to 5, this grade reflects the level of priority given in design (0 not considered, 5 high priority). In a second phase, you are asked to say what are the theoretical frames you use, if any, when taking into account these concerns, and how you use these. Both representations and contexts are considered.

a) Characteristics of the ILE (or of the set of ILEs if several ILEs are concerned by design)

Are the following concerns given a high priority in your design (grade from 0 to 5: 0 not considered, 5 high priority):

 - Concerns about the ways mathematical objects and their interaction are represented?

 - Concerns about the ways didactic interactions are represented?

 - Concerns about the ways representations can be acted on?

 - Concerns about possible interactions, connections with other semiotic systems, including the representations provided by other DDAs?

 - Concerns about the relationships with institutional or cultural systems of representation?

 - Concerns about the rigidity/evolutive characteristics of representations?

For those considered, what are the theoretical frames and constructs, if any, which you refer to:

 - At the level of general principles and metaphors?

 - At an operational level?

b) Educational goals

When thinking about educational goals to be associated to the ILE or set of ILEs, in the design phase, what concerns are given a high priority (grade from 0 to 5):

 - Epistemological concerns?

 - Semiotic concerns?

 - Cognitive concerns?

 - Social concerns?

 - Cultural and institutional concerns?

Up to what point are those considered linked to representational characteristics of the ILE or set of ILEs (grade from 0 to 5: 0 no link, 5 strong link)?

For those linked, what are the theoretical frames and constructs, if any, used for this linkage:

 - At the level of general principles and metaphors?

 - At an operational level?

Up to what point do contextual concerns shape the vision of educational goals here (grade from 0 to 5: 0 does not shape, 5 strongly shapes):

 - Local concerns?

 - Global concerns?

What are the theoretical frames and constructs, if any, used:

 - At the level of general principles and metaphors?

 - At an operational level?

c) Modalities of use

When thinking about possible modalities of use in the design of this ILE or set of ILEs, what concerns were given a high priority (grade from 0 to 5):

 -Concerns about the mathematical tasks and their temporal organization?

 -Concerns about the functions to be given to the artifact and their possible evolution?

 -Concerns about semiotic issues?

 -Concerns about instrumentation processes?

 -Concerns about social organization and interactions?

-Institutional and cultural concerns?

Up to what point are those considered linked to representational characteristics of the ILE (grade from 0 to 5)?

For those linked, what are the theoretical frames and constructs, if any, used for this linkage

 - At the level of general principles and metaphors?

 - At an operational level?

Up to what point do contextual concerns shape the vision of modalities of use (grade from 0 to 5):

 - Local concerns?

 - Global concerns?

What are the theoretical frames and constructs, if any, used:

 - At the level of general principles and metaphors?

 - At an operational level?

Part 3: Analysis of use

Collection of data

How are concerns about representations and contexts taken into account in the collection of data as regards the use of ILEs?

What are the theoretical frames and constructs, if any, used for this:

 - At the level of general principles and metaphors?

 - At an operational level?

Analysis of data

How are concerns about representations and contexts taken into account in the analysis of data as regards the use of ILEs?

What are the theoretical frames and constructs, if any, used for this:

 - At the level of general principles and metaphors?

 - At an operational level?

Rights and permissions

Reprints and permissions

About this article

Cite this article

Artigue, M., Mariotti, M.A. Networking theoretical frames: the ReMath enterprise. Educ Stud Math 85, 329–355 (2014). https://doi.org/10.1007/s10649-013-9522-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10649-013-9522-2

Keywords

Search

Navigation