Skip to main content
SpringerLink
Log in

Modeling empowered by information and communication technologies

  • Original Article
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

In this article, we describe our work with mathematical modeling (MM) at different educational levels and discuss how the use of information and communication technologies (ICTs) empowered such work. Characteristics of two trends in research which have influenced our work are presented: one is a Brazilian perspective of MM, and the other is the use of ICTs in mathematics classrooms seen through the lens of the theoretical construct “humans-with-media”. We introduce some key questions regarding the notion of mathematical model and the phases of the modeling process that were paramount for us. Finally, we describe and analyze two experiences using modeling in different educational contexts, and present some evidence of the empowering role of ICTs in such contexts.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Notes

  1. In order to avoid repetitions, sometimes we will just use the word modeling instead of mathematical modeling.

  2. The paper shows different spellings for some words (modeling/modelling, emphasize/emphasise, etc.) since, in the quotations, we decided to respect the original spelling from the authors.

  3. GPIMEM: Grupo de Pesquisa em Informática, outras mídias e Educação Matemática (Technology, other media and Mathematics Education Research Group) from the State University of São Paulo.

  4. NPMM: Núcleo de Pesquisas em Modelagem Matemática (Group of Research in Mathematical Modeling) from the State University of Feira de Santana, Brazil.

  5. The notion of humans-with-media has its roots in the theory of reorganization as posed by the Russian psychologist Tikhomirov (1981) and the ideas of collective thinking and technologies of the intelligence presented by the French philosopher Lévy (1993).

  6. From now on when we mention the word principles we will be referring to those stated in Sect. 2.

  7. This notion of mathematical model is consonant with that given by Biembengut and Hein (2000).

  8. The information included between brackets aims to clarify some of the students’ expressions.

  9. It is worth noting that this task may also be connected to the contextual modeling approach. Kaiser et al. (2007) inform that (at CERME 5) “it was difficult for some researchers to see the differences between educational and contextual modelling” (p. 2038).

Abbreviations

ICTs:

Information and communication technologies

MM:

Mathematical modeling

References

  • Araújo, J. (2002). Cálculo, tecnologias e modelagem matemática: as discussões dos alunos. Doctoral dissertation. Rio Claro, Brazil: Universidade Estadual Paulista.

  • Barbosa, J. (2001a). Modelagem matemática: concepções e experiências de futuros professores. Doctoral dissertation. Rio Claro, Brazil: Universidade Estadual Paulista.

  • Barbosa, J. (2001b) Modelagem na Educação Matemática: contribuições para o debate teórico. In Anais da 24 Reunião Anual da Anped. Caxambu: ANPED. 1 CD-ROM.

  • Barbosa, J. C. (2006). Mathematical modelling in classroom: A critical and discursive perspective. Zentralblatt für Didaktik der Mathematik, 38(3), 293–301.

    Article  Google Scholar 

  • Barbosa, J. C. (2007). Sobre a pesquisa em Modelagem Matemática no Brasil. In Anais da V Conferência Nacional sobre Modelagem na Educação Matemática (pp. 82–103). Ouro Preto: UFOP/UFMG.

  • Bassanezi, R. (1994). Modelling as a teaching–learning strategy. For the Learning of Mathematics, 14(2), 31–35.

    Google Scholar 

  • Bassanezi, R. (2002). Ensino-aprendizagem com modelagem matemática: uma nova estratégia. São Paulo: Contexto.

    Google Scholar 

  • Biembengut, M. (2007). Modelling and applications in primary education. In W. Blum, P. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education—The 14th ICMI Study (pp. 451–456). New York: Springer.

    Chapter  Google Scholar 

  • Biembengut, M., & Hein, N. (2000). Modelagem matemática no ensino. São Paulo: Editora Contexto.

    Google Scholar 

  • Blomhøj, M. (2004). Mathematical modeling: A theory for practice. In B. Clarke et al. (Eds) International perspectives on learning and teaching mathematics (pp. 145–159). Sweden: National Center for Mathematics Education.

  • Blomhøj, M., & Højgaard Jensen, T. (2003). Developing mathematical modeling competence: Conceptual clarification and educational planning. Teaching Mathematics and its Applications, 22(3), 123–138.

    Article  Google Scholar 

  • Blum, W., Galbraith, P., Henn, H., & Niss, M. (Ed.). (2007). Modelling and applications in mathematics education—The 14 th ICMI Study. New York: Springer.

  • Blum, W., et al. (2003). ICMI Study 14: Applications and modelling in mathematics education—Discussion Document. Educational Studies in Mathematics, 51, 149–171.

    Article  Google Scholar 

  • Borba, M., & Bovo, A. (2002). Modelagem em sala de aula de matemática: interdisciplinaridade e pesquisa em biologia. Revista de, 8(6–7), 27–33.

    Google Scholar 

  • Borba, M., Malheiros, A., & Zulatto, R. (2007). Educação a Distãncia Online. Belo Horizonte: Autêntica.

    Google Scholar 

  • Borba, M., & Penteado, M. (2001). Informática e Educação Matemática. Belo Horizonte: Autêntica.

  • Borba, M., & Villarreal, M. (2005). Humans-with-media and the reorganization of mathematical thinking: Information and communication technologies, modeling, experimentation and visualization. New York: Springer Science+business Media (Mathematics Education Library).

    Google Scholar 

  • Cristante, A., Esteley, C., Marguet, I., & Mina, M. (2007). Experiencia de modelización en aula con orientación en Economía y Gestión de las Organizaciones. In R. Abrate & M. Pochulu (Eds.), Experiencias, propuestas y reflexiones para la clase de Matemática (pp. 305–318). Córdoba: Universidad Nacional de Villa María.

    Google Scholar 

  • Diniz, L. (2007). O papel das tecnologias da informação e comunicação nos projectos de modelagem matemática. Master thesis. Rio Claro, Brazil: Universidade Estadual Paulista.

  • English, L., & Watters, J. (2004). Mathematical modeling in the early school years. Mathematics Education Research Journal, 16(3), 59–80.

    Google Scholar 

  • Esteley, C., Mina, M., Cristante, A., & Marguet, I. (2007). Innovaciones en el aula: desarrollo profesional y modelización. In R. Abrate & M. Pochulu (Eds.), Experiencias, propuestas y reflexiones para la clase de Matemática (pp. 281–294). Córdoba: Universidad Nacional de Villa María.

    Google Scholar 

  • Geiger, V. (2009). Factors affecting teachers’ adoption of innovative practices with technology and mathematical modelling. In Abstracts of the 14th international conference on the teaching of mathematical modelling and applications. Hamburg: University of Hamburg. http://www.ictma2009.de/media/files/ICTMA14_Abstracts_FINAL.pdf. Retrieved on December 9, 2009.

  • Greer, B., Verschaffel, L., & Mukhopadhyay, S. (2007). Modelling for life: Mathematics and children’s experience. In W. Blum, P. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education—The 14th ICMI Study (pp. 89–98). New York: Springer.

    Chapter  Google Scholar 

  • Haapasalo, L. (2009). Revitalizing sustainable heuristics through geometric modelling. In Abstracts of the 14th international conference on the teaching of mathematical modelling and applications. Hamburg: University of Hamburg. http://www.ictma2009.de/media/files/ICTMA14_Abstracts_FINAL.pdf. Retrieved on December 9, 2009.

  • Julie, C., & Mudaly, V. (2007). Mathematical modelling of social issues in school mathematics in South Africa. In W. Blum, P. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education—The 14th ICMI Study (pp. 503–510). New York: Springer.

    Chapter  Google Scholar 

  • Kaiser, G., Blomhøj, M., & Sriraman, B. (2006). Towards a didactical theory for mathematical modelling. Zentralblatt für Didaktik der Mathematik, 38(2), 82–85.

    Article  Google Scholar 

  • Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. Zentralblatt für Didaktik der Mathematik, 38(3), 302–310.

    Article  Google Scholar 

  • Kaiser, G., Sriraman, B., Blomhøj, M., & García, J. (2007). Modelling and applications—Differentiating perspectives and delineating commonalties. Papers presented at WG13 in the 5th congress of the European society for research in mathematics education. Larnaca: University of Cyprus. http://ermeweb.free.fr/CERME5b/WG13.pdf. Retrieved on December 7, 2009.

  • Kaiser-Messmer, G. (1991). Application-oriented mathematics teaching: A survey of the theoretical debate. In M. Niss, W. Blum, & I. Huntley, I. (Eds.), Teaching of mathematical modelling and applications (pp. 83–92). Chichester: Ellis Horwood.

  • Kenski, V. (2007). Educação e tecnologias. O novo ritmo da informação. Campinas: Papirus Editora.

    Google Scholar 

  • Lévy, P. (1993). As tecnologias da inteligência. O futuro do pensamento na era da informática. Translated by Costa, C. Translation of: Les technologies de l’intelligence. São Paulo: Editora 34.

  • Lingerfjärd, T. (2007). Mathematical modelling in teacher education–necessity or unnecessarily. In W. Blum, P. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education—The 14th ICMI Study (pp. 333–340). New York: Springer.

    Chapter  Google Scholar 

  • Malheiros, A. (2004). A produção matemática dos alunos em um ambiente de modelagem. Master thesis. Rio Claro, Brazil: Universidade Estadual Paulista.

  • Marguet, I., Esteley, C., Mina, M., & Cristante, A. (2007). Modelización como estrategia de enseñanza en un curso con orientación en ciencias naturales. In R. Abrate & M. Pochulu (Eds.), Experiencias, propuestas y reflexiones para la clase de Matemática (pp. 319–331). Córdoba: Universidad Nacional de Villa María.

    Google Scholar 

  • Mina, M., Esteley, C., Marguet, I., & Cristante, A. (2007). Experiencia de modelización con alumnos de 12–13 años. In R. Abrate & M. Pochulu (Eds.), Experiencias, propuestas y reflexiones para la clase de Matemática (pp. 295–304). Córdoba: Universidad Nacional de Villa María.

    Google Scholar 

  • Muller, E., & Burkhardt, H. (2007). Applications and modelling for mathematics. In W. Blum, P. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education—The 14th ICMI Study (pp. 267–274). New York: Springer.

    Chapter  Google Scholar 

  • Ndlovu, M., Wessels, D., & Devilliers, M. (2009). Modelling with sketchpad to enrich students’ concept image of the derivative. In Abstracts of the 14th international conference on the teaching of mathematical modelling and applications. Hamburg: University of Hamburg. http://www.ictma2009.de/media/files/ICTMA14_Abstracts_FINAL.pdf. Retrieved on December 9, 2009.

  • Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education—The 14th ICMI Study (pp. 3–32). New York: Springer.

    Chapter  Google Scholar 

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

    Google Scholar 

  • Oliveira, A. (2007). As análises dos futuros professores sobre suas primeiras experiências com Modelagem Matemática. In J. Barbosa, A. Caldeira, & J. Araújo (Eds.), Modelagem Matemática na Educação Matemática Brasileira: pesquisas e práticas educacionais (Vol. 3, pp. 233–254). Biblioteca do Educador Matemático. Recife: Coleção SBEM.

  • Pead, D., Ralph, B., & Muller, E. (2007). Use of technology in learning mathematics through modelling. In W. Blum, P. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 309–318). New York: Springer.

    Chapter  Google Scholar 

  • Skovsmose, O. (1994). Towards a philosophy of critical mathematics education. Dordrecht: Kluwer.

    Google Scholar 

  • Skovsmose, O. (2001). Landscapes of investigations. Zentralblatt für Didaktik der Mathematik, 33(4), 123–132.

    Article  Google Scholar 

  • Stillman, G. (2007). Upper secondary perspectives on applications and modelling. In W. Blum, P. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 463–468). New York: Springer.

    Chapter  Google Scholar 

  • Tikhomirov, O. K. (1981). The psychological consequences of computerization. In J. V. Wertsch (Ed.), The concept of activity in soviet psychology (pp. 256–278). New York: M.E. Sharpe Inc.

    Google Scholar 

  • Weitendorf, J. (2009). The role of technology in the modelling circle. In Abstracts of the 14th international conference on the teaching of mathematical modelling and applications. Hamburg: University of Hamburg. http://www.ictma2009.de/media/files/ICTMA14_Abstracts_FINAL.pdf. Retrieved on December 9, 2009.

Download references

Author information

Authors and Affiliations

  1. National Council of Scientific and Technical Research (CONICET), Faculty of Mathematics, University of Córdoba (FaMAF-UNC), Córdoba, Argentina

    Mónica E. Villarreal

  2. University of Villa María, Villa María, Argentina

    Cristina B. Esteley

  3. Colegio Gabriel Taborin, Córdoba, Argentina

    María V. Mina

Authors
  1. Mónica E. Villarreal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cristina B. Esteley
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. María V. Mina
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mónica E. Villarreal.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Villarreal, M.E., Esteley, C.B. & Mina, M.V. Modeling empowered by information and communication technologies. ZDM Mathematics Education 42, 405–419 (2010). https://doi.org/10.1007/s11858-010-0248-7

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-010-0248-7

Keywords

Search

Navigation