Skip to main content

Advertisement

Log in

Brazilian research on modelling in mathematics education

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

Abstract

The objective of this article is to present a current panorama of research on mathematical modelling in Brazilian mathematics education by approaching it from three perspectives. The first addresses the historical roots of this field of knowledge in Brazil, highlighting the relationship with the international community, masters and doctoral research, and some important forums dedicated to modelling in Brazil. The second is a synthesis of some existing works also dedicated to the discussion of Brazilian research and publications related to modelling in mathematics education. The third perspective consists of description and analysis of research, in terms of the authors’ proposed objectives, presented in recent national scientific events, seeking to characterize and comprehend current interests that move research in this field. Based on this panorama, I offer some cautionary notes to Brazilian researchers regarding care to be taken when proposing new research in modelling in mathematics education, and I present a proposal for future studies.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /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.

Similar content being viewed by others

Notes

  1. The main findings of these studies will be presented in the next two sections.

  2. Translated from the original Portuguese text.

  3. Issues 2 and 3, volume 38, 2006.

  4. More information is available at http://www.sbem.com.br/gt10.

  5. Although I know of other groups in the country dedicated to this theme, I selected several that are well represented at national events, such as the CNMEM and SIPEM and the National Meeting of Mathematics Education (ENEM), and which illustrate well the geographical expansion of modelling in Brazilian mathematics education.

  6. More information is available at: http://www.furb.br/cremm/portugues/index.php.

  7. More information is available at: http://www.rc.unesp.br/igce/pgem/gpimem.html.

  8. More information is available at: http://www.uefs.br/nupemm/.

  9. More information is available at: http://www.ufpa.br/npadc/gemm/grupo.htm.

  10. Brazil is a federative republic formed of 26 states plus the Federal District, and São Paulo is one of the states.

  11. There were no events in Brazil in 2008 with significant participation of the community involved in modelling in mathematics education. The SIPEM and CNMEM that followed the ones analysed here took place in 2009, after this article was written. The next ENEM is scheduled to take place in July 2010.

References

  • Andresen, M. (2009). Teaching to reinforced bonds between modelling and reflecting. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics: Proceedings from TSG21 at the ICME11 (pp. 73–83). IMFUFA-text no. 461, Department of Science, Systems and Models, Roskilde University.

  • Araújo, J. L. (2002). Cálculo, tecnologias e modelagem matemática: As discussões dos alunos. Unpublished Doctoral Theses. Rio Claro: Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista.

  • Araújo, J. L. (2009). Formatting real data in mathematical modelling projects. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics: Proceedings from TSG21 at the ICME11 (pp. 229–239). IMFUFA-text no. 461, Department of Science, Systems and Models, Roskilde University.

  • Araújo, J. L., & Borba, M. C. (2004). Construindo pesquisas coletivamente em educação matemática. In M. C. Borba & J. L. Araújo (Orgs.), Pesquisa qualitativa em educação matemática (pp. 25–45). Belo Horizonte: Autêntica Editora.

  • Araújo, J. L., & Corrêa, R. A. (Eds.). (2007). Proceedings from V CNMEM: V Conferência Nacional sobre Modelagem na Educação Matemática [CD ROM]. Ouro Preto: Universidade Federal de Ouro Preto/Universidade Federal de Minas Gerais.

  • Aravena, M. D., & Caamaño, C. E. (2009). Mathematical models in the secondary Chilean education. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics: Proceedings from TSG21 at the ICME11 (pp. 159–176). IMFUFA-text no. 461, Department of Science, Systems and Models, Roskilde University.

  • Barbosa, J. C. (2001). Modelagem matemática: Concepções e experiências de futuros professores. Unpublished Doctoral Theses. Rio Claro: Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista.

  • Barbosa, J. C. (2006). Mathematical modelling in classroom: A socio-critical and discursive perspective. The International Journal on Mathematics Education, 38(3), 293–301. http://subs.emis.de/journals/ZDM/zdm063a8.pdf. Accessed 22 December 2009.

  • Barbosa, J. C. (2007). Sobre a pesquisa em modelagem matemática no Brasil. In J. L. Araújo & R. A. Corrêa (Eds.). Proceedings from V Conferência Nacional sobre Modelagem na Educação Matemática [CD ROM] (pp. 82–103). Ouro Preto: Universidade Federal de Ouro Preto/Universidade Federal de Minas Gerais.

  • Barbosa, J. C. (2009). Mathematical modelling, the socio-critical perspective and the reflexive discussions. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics: Proceedings from TSG21 at the ICME11 (pp. 133–143). IMFUFA-text no. 461, Department of Science, Systems and Models, Roskilde University.

  • Barbosa, J. C., Caldeira, A. D., & Araújo, J. L. (Eds.). (2007). Modelagem matemática na educação matemática brasileira: Pesquisas e práticas educacionais. Recife: Sociedade Brasileira de Educação Matemática.

  • Biembengut, M. S., Hein, N., & Dorow, K. C. (2007). Mapeamento das pesquisas sobre modelagem matemática no ensino brasileiro: Análise das dissertações e teses desenvolvidas no Brasil. In J. L. Araújo & R. A. Corrêa (Eds.). Proceedings from V Conferência Nacional sobre Modelagem na Educação Matemática [CD ROM] (pp. 466–479). Ouro Preto: Universidade Federal de Ouro Preto/Universidade Federal de Minas Gerais.

  • Blomhøj, M. (2009). Different perspectives in research on the teaching and learning mathematical modelling—Categorising the TSG21 papers. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics: Proceedings from TSG21 at the ICME11 (pp. 1–17). IMFUFA-text no. 461, Department of Science, Systems and Models, Roskilde University.

  • Blum, W., Galbraith, P. L., Henn, H.-W., & Niss, M. (2007). Preface. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. xi–xiv). New York: Springer.

    Chapter  Google Scholar 

  • Caldeira, A. D. (2009). Mathematical modelling and environmental education. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics: Proceedings from TSG21 at the ICME11 (pp. 145–157). IMFUFA-text no. 461, Department of Science, Systems and Models, Roskilde University.

  • D’Ambrosio, U. (1999). Literacy, matheracy and technocracy: A trivium for today. Mathematical Thinking and Learning, 1(2), 131–153.

    Article  Google Scholar 

  • Ernest, P. (1997). A postmodern perspective on research in mathematics education. In A. Sierpinska & J. Kilpatrick (Eds.), Mathematics education as a research domain: A search for identity: An ICMI Study (pp. 71–85). Dordrecht: Kluwer.

    Google Scholar 

  • Ferreira, N. S. A. (2002). As pesquisas denominadas “estado da arte”. Educação & Sociedade, 79, 257–272. http://www.scielo.br/pdf/es/v23n79/10857.pdf. Accessed 31 January 2009.

  • Ferreira, D. H. L., & Jacobini, O. R. (2009). Mathematical modelling: From classroom to the real world. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics: Proceedings from TSG21 at the ICME11 (pp. 35–46). IMFUFA-text no. 461, Department of Science, Systems and Models, Roskilde University.

  • Fiorentini, D. (1996). Brazilian research in mathematical modelling. Sevilla: ICME, 1996. Paper presented in the GT-17 at 8th International Congress on Mathematical Education, Sevilla.

  • Gallardo, P. C. (2009). Mathematical models in the context of sciences. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics: Proceedings from TSG21 at the ICME11 (pp. 117–131). IMFUFA-text no. 461, Department of Science, Systems and Models, Roskilde University.

  • Gallegos, R. R. (2009). Differential equations as a tool for mathematical modelling in physics and mathematics courses—A study of high school textbooks and the modelling processes of senior high students. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics: Proceedings from TSG21 at the ICME11 (pp. 19–34). IMFUFA-text no. 461, Department of Science, Systems and Models, Roskilde University.

  • Kadijevich, D. (2009). Simple spreadsheet modelling by first-year business undergraduate students: Difficulties in the transitions from real-world problem statement to mathematical model. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics: Proceedings from TSG21 at the ICME11 (pp. 241–248). IMFUFA-text no. 461, Department of Science, Systems and Models, Roskilde University.

  • Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. The International Journal on Mathematics Education, 38(3), 302–310. http://subs.emis.de/journals/ZDM/zdm063a9.pdf. Accessed 10 September 2006.

  • Lester, F. K., & Lambdin, D. V. (1997). The ship to Theseus and other metaphors for thinking about what we value in mathematics education research. In A. Sierpinska & J. Kilpatrick (Eds.), Mathematics education as a research domain: A search for identity: An ICMI Study (pp. 415–425). Dordrecht: Kluwer.

    Google Scholar 

  • Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. California: Sage Publications, Inc.

    Google Scholar 

  • Ludwig, M., & Xu, B. (2009). A comparative study on mathematical modelling competences with German and Chinese students. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics: Proceedings from TSG21 at the ICME11 (pp. 197–206). IMFUFA-text no. 461, Department of Science, Systems and Models, Roskilde University.

  • Meier, S. (2009). Mathematical modelling in a European context—A European network project. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics: Proceedings from TSG21 at the ICME11 (pp. 207-216). IMFUFA-text no. 461, Department of Science, Systems and Models, Roskilde University.

  • Niss, M. (2001). Issues and problems of research on the teaching and learning of applications and modelling. In J. F. Matos, W. Blum, S. K. Houston, & S. P. Carreira (Eds.), Modelling and mathematics education—ICTMA 9: Applications in science and technology (pp. 72–88). Chichester: Horwood Publishing.

    Google Scholar 

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

    Chapter  Google Scholar 

  • Oliveira, A. M. P., & Barbosa, J. C. (2009). The teachers’ tensions in mathematical modelling practice. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics: Proceedings from TSG21 at the ICME11 (pp. 61–71). IMFUFA-text no. 461, Department of Science, Systems and Models, Roskilde University.

  • Siller, H-S. (2009). A “new” type of diagram to support functional modelling – PROGRAPH diagrams. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics: Proceedings from TSG21 at the ICME11 (pp. 101–115). IMFUFA-text no. 461, Department of Science, Systems and Models, Roskilde University.

  • Silveira, E. (2007). Modelagem matemática em educação no Brasil: Entendendo o universo de teses e dissertações. Unpublished Master’s Dissertation. Curitiba: Setor de Educação, Universidade Federal do Paraná.

  • Skovsmose, O., & Borba, M. C. (2004). Research methodology and critical mathematics education. In P. Valero & R. Zevenbergen (Eds.), Researching the socio-political dimensions of mathematics education: Issues of power in theory and methodology (pp. 207–226). Dordrecht: Kluwer.

    Chapter  Google Scholar 

  • Sociedade Brasileira de Educação Matemática (SBEM). (2006). Proceedings from III SIPEM: III Seminário Internacional de Pesquisa em Educação Matemática [CD ROM]. Águas de Lindóia: SBEM.

  • Sociedade Brasileira de Educação Matemática (SBEM). (2007). Proceedings from IX ENEM: IX Encontro Nacional de Educação Matemática [CD ROM]. Belo Horizonte: SBEM.

  • Tarp, A. (2009). Applying pastoral metamatism or re-applying grounded mathematics. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics: Proceedings from TSG21 at the ICME11 (pp. 85–100). IMFUFA-text no. 461, Department of Science, Systems and Models, Roskilde University.

  • vom Hofe, R., Jordan, A., Hafner, T., Stölting, P., Blum, W., & Pekrun, R. (2009). On the development of mathematical modelling competencies—The PALMA longitudinal study. In M. Blomhøj & S. Carreira (Eds.), Mathematical applications and modelling in the teaching and learning of mathematics: Proceedings from TSG21 at the ICME11 (pp. 47–60). IMFUFA-text no. 461, Department of Science, Systems and Models, Roskilde University.

Download references

Acknowledgments

I would like to thank Marcelo Borba and Ubiratan D’Ambrosio for the invitation to participate in this special issue of ZDM, Gabriele Kaiser for her support during the process of review, Jonei Barbosa for comments made on earlier versions of the paper, the reviewers of ZDM for their comments and Marcos Oliveira for the comprehension and support whilst this paper was being written. I am grateful to the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), of the Ministry of Education of Brazil, for the financial support to the post-doctoral research.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jussara de Loiola Araújo.

Additional information

Work developed during the author’s post-doctoral studies at the University of Lisbon, with the support of the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) of the Ministry of Education of Brazil (Process no. 0799/08-4). Text translated to English from the original in Portuguese by Anne Kepple.

Rights and permissions

Reprints and permissions

About this article

Cite this article

de Loiola Araújo, J. Brazilian research on modelling in mathematics education. ZDM Mathematics Education 42, 337–348 (2010). https://doi.org/10.1007/s11858-010-0238-9

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-010-0238-9

Keywords

Navigation