Skip to main content
SpringerLink
Log in

Digital artefacts as representations: forging connections between a constructionist and a social semiotic perspective

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

Abstract

This paper uses the methodology of cross-case analysis to clarify connections and differences between two specific conceptual frameworks, multimodal social semiotics and constructionism, in particular in the ways they each deal with the idea of representation. It builds especially upon the idea of “distance” of digital representations with respect to usual representations, stressing the multidimensionality of this notion and possibilities for progress towards a shared framework for research about representations. The paper focuses on the cross-case analysis study of a “middle distance” dynamic digital artefact, MoPiX, by two teams sharing a common reference framework (constructionism), but with distinct views with regard to representations. The research yielded a distinction in the ways connections between representations are valued by the two approaches and their respective interpretations of meaning generation.

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.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Notes

  1. ReMath was co-funded by the European Commission FP6-IST4-26751. Related resources can be found at http://remath.cti.gr.

  2. MoPiX can be found at http://remath.cti.gr/ and will run in any browser with Flash.

  3. MoPix was designed to run on tablet computers in order to facilitate face-to-face communication among students as well as the sharing of digital models on-line.

  4. Student names used here are all pseudonyms.

References

  • Ainsworth, S. E., Bibby, P. A., & Wood, D. J. (1997). Information technology and multiple representations: New opportunities–new problems. Technology, Pedagogy and Education, 6(1), 93–105.

    Google Scholar 

  • Artigue, M., Cerulli, M., Haspekian, M., & Maracci, M. (2009). Connecting and integrating theoretical frames: The TELMA contribution. International Journal of Computers for Mathematical Learning, 14, 217–240.

    Article  Google Scholar 

  • Bezemer, J., & Kress, G. (2008). Writing in multimodal texts: A special semiotic account of designs for learning. Written Communication, 25(2), 166–195.

    Article  Google Scholar 

  • Borba, M. C., & Villarreal, M. E. (2006). Humans-with-media and the reorganization of mathematical thinking: Information and communication technologies, modelling, experimentation and visualization. New York: Springer.

    Google Scholar 

  • Bottino, R. M., & Kynigos, C. (2009). Mathematics education & digital technologies: Facing the challenge of networking European research teams. International Journal of Computers for Mathematical Learning, 14, 203–215.

    Article  Google Scholar 

  • Carreira, S., Evans, J., Lerman, S., & Morgan, C. (2002). Mathematical thinking: Studying the notion of ‘transfer’. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 185–192). Norwich: School of Education and Professional Development, University of East Anglia.

  • Cobb, P. (2000). From representations to symbolizing: Introductory comments on semiotics and mathematical learning. In P. Cobb, E. Yackel, & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools and instructional design (pp. 17–36). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Dreyfus, T. (1994). The role of cognitive tools in mathematics education. In R. Biehler (Ed.), Didactics of mathematics as a scientific discipline (pp. 201–211). Dordrecht: Kluwer.

    Google Scholar 

  • Duval, R. (1999). Representation, vision and visualization: Cognitive functions in mathematical thinking. Basic issues for learning Proceedings of the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 3–26). Cuernavaca, Morelos, Mexico.

  • Duval, R. (2006). A cognitive analysis of problems of comprehension in the learning of mathematics. Educational Studies in Mathematics, 61(1–2), 103–131.

    Article  Google Scholar 

  • Edwards, L. D. (1998). Embodying mathematics and science: Microworlds as representations. The Journal of Mathematical Behavior, 17(1), 53–78.

    Article  Google Scholar 

  • Falcade, R., Laborde, C., & Mariotti, M. (2007). Approaching functions: Cabri tools as instruments of semiotic mediation. Educational Studies in Mathematics, 66(3), 317–333.

    Article  Google Scholar 

  • Font, V., Godino, J. D., & D’Amore, B. (2007). An onto-semiotic approach to representations in mathematics education. For the Learning of Mathematics, 27(2), 2–7.

    Google Scholar 

  • Goldin, G. A. (1998). Representational systems, learning, and problem solving in mathematics. The Journal of Mathematical Behavior, 17(2), 137–165.

    Article  Google Scholar 

  • 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, NJ: Ablex.

    Google Scholar 

  • Hodge, R., & Kress, G. (1988). Social semiotics. Cambridge: Polity Press.

    Google Scholar 

  • Janvier, C. (1987). Problems of representation in the teaching and learning of mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

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

    Google Scholar 

  • Kaput, J. J. (1991). Notations and representations as mediators in constructive processes. In E. van Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 53–74). Dordrecht: Kluwer.

    Google Scholar 

  • Kress, G., & Selander, S. (2012). Multimodal design, learning and cultures of recognition. The Internet and Higher Education, 15(4), 265–268.

    Article  Google Scholar 

  • Kress, G., & van Leeuwen, T. (2001). Multimodal discourse: The modes and media of contemporary communication. London: Arnold.

  • Kynigos, C. (2007). Half-baked microworlds as boundary objects in integrated design. Informatics in Education, 6(2), 335–359.

    Google Scholar 

  • Kynigos, C. (2012). Constructionism: Theory of learning or theory of design? Proceedings of the 12th International Congress on Mathematics Education. Seoul, S. Korea.

  • Kynigos, C., Psycharis, G., & Moustaki, F. (2010). Meanings generated while using algebraic-like formalism to construct and control animated models. International Journal for Technology in Mathematics Education, 17(1), 17–32.

    Google Scholar 

  • Morgan, C., & Alshwaikh, J. (2009). Mathematical activity in a multi-semiotic environment. Sixth Congress of the European Society for Research in Mathematics Education, Working Group 6 Language and Mathematics, 993–1002. Retrieved from http://www.inrp.fr/editions/cerme6.

  • Morgan, C., Mariotti, M. A., & Maffei, L. (2009). Representation in computational environments: Epistemological and social distance. International Journal of Computers for Mathematical Learning, 14(3), 241–263.

    Article  Google Scholar 

  • Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings: Learning cultures and computers. Dordrecht: Kluwer.

    Google Scholar 

  • O’Halloran, K. L. (2005). Mathematical discourse: Language, symbolism and visual images. London: Continuum.

  • 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

  • Radford, L. (2009). Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings. Educational Studies in Mathematics, 70(2), 111–126.

    Article  Google Scholar 

  • Strohecker, C., & Slaughter, A. (2000). Kits for learning and a kit for kitmaking. CHI ‘00 Extended Abstracts on Human Factors in Computing Systems, 149–150.

  • Vergnaud, G. (1998). A comprehensive theory of representation for mathematics education. Journal of Mathematical Behaviour, 17(2), 167–181.

    Article  Google Scholar 

  • Vérillon, P., & Rabardel, P. (1995). Cognition and artefacts: 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 

  • Yerushalmy, M. (2005). Functions of interactive visual representations in interactive mathematical textbooks. International Journal of Computers for Mathematical Learning, 10, 217–249.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Education, University of London, 20 Bedford Way, London, WC1H 0AL, UK

    Candia Morgan

  2. Educational Technology Lab, National Kapodistrian University of Athens, Athens, Greece

    Chronis Kynigos

Authors
  1. Candia Morgan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chronis Kynigos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Candia Morgan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Morgan, C., Kynigos, C. Digital artefacts as representations: forging connections between a constructionist and a social semiotic perspective. Educ Stud Math 85, 357–379 (2014). https://doi.org/10.1007/s10649-013-9523-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10649-013-9523-1

Keywords

Search

Navigation