Skip to main content

Semiotic Representations: A Study of Dynamic Figural Register

  • Chapter
  • First Online:
Signs of Signification

Part of the book series: ICME-13 Monographs ((ICME13Mo))

Abstract

The aim of this chapter is to constitute the dynamic figural register. In order to do this, and based on the theory of Registers of Semiotic Representation and on the pertinence of the use of a Dynamic Representation Environment (DRE) for geometry teaching and learning, I revisit the three cognitive activities essential to every semiotic representation in the sense of Duval, which I call dynamic formation, dynamic treatment, and dynamic conversion, because it may be noticed that, when a person interacts with DRE, the three cognitive activities possess different features than when using pencil and paper.

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

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
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

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(3), 245–274. https://doi.org/10.1023/A:1022103903080.

    Article  Google Scholar 

  • da Silva, M. J. F., & Salazar, J. V. F. (2012). Cabri 3D na sala de aula. In VI Congreso Iberoamericano de IBEROCABRI (pp. 101–107). Lima, Peru: Ozlo.

    Google Scholar 

  • Dionizio, F. A., & Bandt, C. F. (2012). O caminho percorrido pela semiótica e a importância dos Registros de Representação Semiótica para a aprendizagem da matemática. Proceedings of the IX Seminário de pesquisa em Educação Matemática da região sul (pp. 2–15). Caxias do Sul, Brazil.

    Google Scholar 

  • Duval, R. (1993). Registres de représentation sémiotique et fonctionnement cognitif de la pensée. Annales de Didactique et de Sciences Cognitives Université Louis Pasteur (pp. 37–65). Strasbourg: IREM.

    Google Scholar 

  • Duval, R. (1995). Semiósis et pensée humaine. Registres sémiotiques et apprentissages intellectuelles. Paris, France: Peter Lang.

    Google Scholar 

  • Duval, R. (2004). Los problemas fundamentales en el aprendizaje de las matemáticas y las formas superiores en el desarrollo cognitivo. Cali, Colombia: Merlín.

    Google Scholar 

  • Duval, R. (2005). Les changements de regard nécessaires sur les figures. IREM, Grenoble, 76, 7–27. Available in: http://www-irem.ujf-grenoble.fr/revues/revue_n/fic/76/76n2.pdf.

  • Duval, R. (2011). Ver e Ensinar a Matemática de outra forma: entrar no modo de pensar, os registros de representação semiótica. São Paulo, Brazil: PROEM.

    Google Scholar 

  • Fortuny, J. M., Iranzo, N., & Morera, L. (2010). Geometría y tecnología. In M. M. Moreno, A. Estrada, J. Carrillo, & T. A. Sierra (Eds.), Investigación en Educación Matemática XIV (pp. 69–85). Lérida, Spain: SEIEM.

    Google Scholar 

  • García-Cuéllar, D. J. (2014). Simetría axial mediada por el GeoGebra: un estudio con estudiantes de primer grado de educación secundaria. Thesis (Mathematics Education Master). Pontificia Universidad Católica del Perú, Lima, Perú.

    Google Scholar 

  • Gómez, C. (2015). Proceso de visualización de cuadriláteros: un estudio con profesores de nivel secundario. Thesis (Mathematics Education Master). Pontificia Universidad Católica del Perú, Lima, Perú.

    Google Scholar 

  • Gómez, C., & Salazar, J. V. F. (2016). Visualización de cuadriláteros en el registro figural dinámico. In J. V. F. Salazar & F. Ugarte (Eds.), Investigaciones en Educación Matemática (pp. 189–204). Lima, Peru: PUCP.

    Google Scholar 

  • Gravina, M. (2001). Os ambientes de geometria dinâmica e o pensamento hipotético-dedutivo. Thesis (Mathematics Education Doctorate). Pontificia Universidade Federal do Rio Grande do Sul, Porto Alegre, Brasil.

    Google Scholar 

  • Gravina, M. A. (2008). Drawing in movement and insights for the proof process. International Journal of Continuing Engineering Education and Life-Long Learning, 18(5/6), 564–574.

    Article  Google Scholar 

  • Grinkraut, M. L. (2009). Formação de professores envolvendo a prova matemática: um olhar sobre o desenvolvimento profissional. Thesis (Mathematics Education Doctorate) Pontificia Universidad Católica de São Paulo, São Paulo, Brasil.

    Google Scholar 

  • Laborde, C. (2001). Integration of technology in the design of geometry tasks with Cabri-Geometry. International Journal of Computers for Mathematical Learning, 6(3), 283–317.

    Article  Google Scholar 

  • Laborde, C. (2005). Robust and soft constructions: Two sides of the use of dynamic geometry environments. In Proceedings of the 10th Asian Technology Conference in Mathematics (pp. 22–36). Seoul, South Korea.

    Google Scholar 

  • Marmolejo, G., & Vega, M. (2005). Geometría desde una perspectiva semiótica: visualización, figuras y áreas. In Proceedings of the XV Encuentro de Geometría y sus Aplicaciones y III Encuentro de Aritmética (pp. 661–693). Bogotá, Colombia: Universidad Pedagógica Nacional.

    Google Scholar 

  • Mendes, R. M. (2006). As potencialidades pedagógicas do jogo computacional. Simcity 4. Thesis (Education Master). Universidade de São Francisco, Itaba, Brazil.

    Google Scholar 

  • Miskulin, R. G. S., Moura, A. R. L., & Silva, M. R. C. (2003). Um estudo sobre a dimensão semiótica da tecnologia na educação e na educação matemática. In Proceedings of the II Seminario Internacional de pesquisa em Educação Matemática (pp. 57–89). Santos, Brazil.

    Google Scholar 

  • Mithalal, J. (2011). Vers la mobilisation d’une géométrie axiomatique et de la déconstruction dimensionnelle: intérêt de la géométrie dynamique tridimensionnelle. Proceedings of the séminaire national de didactique des mathématiques (pp. 113–126). Paris, France: IREM.

    Google Scholar 

  • Olivero, F. (2003). The proving process within a dynamic geometry environment. Thesis (Education Doctorate) University of Bristol, Graduate School of Education, England.

    Google Scholar 

  • Olivero, F., & Robutti, O. (2001). Measures in Cabri as a bridge between perception and theory. In Proceedings of the 25th Conference of the International Group for Psychology of Mathematics Education (pp. 9–16). Utrecht, Netherlands: Freudenthal Institute/Utrecht University.

    Google Scholar 

  • Pavanello, R. M. (2004). Por que Ensinar/aprender Geometria?. In VII Encontro Paulista de Educação Matemática. Available in: http://miltonborba.org/CD/Interdisciplinaridade/Anais_VII_EPEM/mesas_redondas/.

  • Peñaloza, T. (2016). Proceso de Visualización del Paraboloide en Estudiantes de Arquitectura mediado por el GeoGebra. Thesis (Mathematics Education Master). Pontificia Universidad Católica del Perú, Lima, Perú.

    Google Scholar 

  • Restrepo, M. A. (2008). Genèse Instrumentale du déplacement en Géométrie Dynamique chez des élèves de 6 e. Thesis (Mathematics and Computer Science Doctorate). Université Joseph Fourier, École Doctorale des Mathématiques, Sciences et Technologies de L’information, Informatique, France.

    Google Scholar 

  • Salazar, J. V. F. (2009). Génese instrumental na interação com Cabri 3D: um estudo de Transformações geométricas no espaço. Thesis (Mathematics Education Doctorate). Pontificia Universidad Católica de São Paulo, São Paulo, Brazil.

    Google Scholar 

  • Salazar, J. V. F. (2015). Génesis Instrumental: el caso de la función cuadrática. Revista Iberoamericana de Educación Matemática UNION, 1(41), 57–67.

    Google Scholar 

  • Salazar, J. V. F., & Almouloud, S. A. (2015). Registro figural no ambiente de geometria dinâmica. Educação Matemática e Pesquisa, 17(5), 927–932.

    Google Scholar 

  • Salazar, J. V. F., Gaita, C., Malaspina, U. J., & Ugarte, F. (2012). The use of technology and teacher training: An alternative for the teaching of spatial geometry. In 12th International congress on mathematical education (pp. 3774–3781). Seoul, South Korea: ICME-12.

    Google Scholar 

  • Silva, C. R. (2013). Signos peircianos e registros de representação semiótica: qual semiótica para a matemática e seu ensino?. Thesis (Mathematics Education Doctorate). Pontificia Universidad Católica de São Paulo, São Paulo, Brazil.

    Google Scholar 

  • Veloso, E. (2000). Geometria temas atuais materiais para professores (Desenvolvimento curricular no ensino secundário). Lisbon, Portugal: Instituto de Inovação Educacional.

    Google Scholar 

Download references

Acknowledgements

I thank Pontificia Universidad Católica del PerúMaestría en Enseñanza de las Matemáticas (group: Technologies and Visualization in Mathematics Education) for the support provided, which made this paper possible.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jesus Victoria Flores Salazar .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Salazar, J.V.F. (2018). Semiotic Representations: A Study of Dynamic Figural Register. In: Presmeg, N., Radford, L., Roth, WM., Kadunz, G. (eds) Signs of Signification. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-70287-2_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-70287-2_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70286-5

  • Online ISBN: 978-3-319-70287-2

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics