Skip to main content

Model Analysis with Digital Technology: A “Hybrid Approach”

  • Chapter
Mathematical Modelling in Education Research and Practice


The advent of informatics and its fast development has allowed for new ways of doing, thinking about, and applying mathematics. This chapter will address one role of the software, Modellus, in the development of a teaching approach based on Model Analysis, that proposes the analysis of a mathematical model for a phenomenon to discuss old and new mathematical concepts with students. The software gave access to graphical and numerical representations of model solutions, which allowed students to analyse the model, even though it involved mathematical concepts still advanced for them. Based on the notion of reorganization, the shift in the way of dealing with mathematical models in classrooms suggests that Model Analysis can be understood as a reorganization of modelling and applications.

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

Access this chapter

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

USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
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

Similar content being viewed by others


  1. 1.

    For more details about the teaching approach, refer to Borba and Soares (2011) and Soares (2012).

  2. 2.

    For more details about the model, refer to Basañez and Rodríguez (2004), Borba and Soares (2011) or Soares (2012).

  3. 3.

    Website: < >. Accessed on 15 June 2013.

  4. 4.

    Website: <>. Accessed on 7 Sep 2013.


  • Basañez, M.-G., & Rodríguez, D. J. (2004). Dinámica de transmisión y modelos matemáticos em enfermedades transmitidas por vectores. Entomotropica, 19(3), 113–134.

    Google Scholar 

  • Blomhøj, M., & Kjeldsen, T. H. (2011). Students’ reflections in mathematical modelling projects. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 385–396). New York: Springer.

    Chapter  Google Scholar 

  • Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling: Education, engineering and economic (pp. 222–231). Chichester: Horwood.

    Chapter  Google Scholar 

  • Borba, M. C., & Soares, D. S. (2011). Modeling in Brazil: A case involving biology. In W. Blum, R. Borromeo Ferri, & K. Maaß (Eds.), Mathematikunterricht im Komtext von Realität, Kultur und Lehererprofessionalität (pp. 53–61). New York: Springer.

    Google Scholar 

  • Borba, M. C., & Villarreal, M. E. (2005). Humans-with-media and the reorganization of mathematical thinking: Information and communication technologies, modeling, experimentation and visualization. New York: Springer.

    Google Scholar 

  • Doerr, H., & Pratt, D. (2008). The learning of mathematics and mathematical modeling. In M. K. Heid & G. W. Blume (Eds.), Research on technology and the teaching and learning of mathematics (Research Syntheses, Vol. 1, pp. 18–23). New York: Information Age Publishing.

    Google Scholar 

  • Doerr, H., & Wood, T. (2006). Pesquisa-Projeto (design research): aprendendo a ensinar Matemática. In M. C. Borba (Ed.), Tendências Internacionais em Formação de Professores de Matemática (pp. 113–130). Belo Horizonte: Autêntica.

    Google Scholar 

  • Maaβ, K. (2006). What are modelling competences? ZDM, 38(2), 113–142.

    Article  Google Scholar 

  • Napoletani, D., Panzo, M., & Struppa, D. C. (2014). Is big data enough? A reflection on the changing role of mathematics in applications. Notices of the AMS, 61(5), 485–490.

    Article  Google Scholar 

  • Niss, M. (2015). Prescriptive modelling – challenges and opportunities. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice: Cultural, social, and cognitive influences (pp. 67–80). Cham: Springer.

    Google Scholar 

  • Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. 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 

  • Soares, D. S. (2012). Uma abordagem pedagógica baseada na Análise de Modelos para alunos de Biologia: qual o papel do software? Unpublished doctoral dissertation, Universidade Estadual Paulista, Rio Claro.

    Google Scholar 

  • Soares, D. S., & Javaroni, S. L. (2013). Análise de Modelos: possibilidades de trabalho com modelos matemáticos em sala de aula. In M. C. Borba & A. Chiari (Eds.), Tecnologias Digitais e Educação Matemática (pp. 195–219). São Paulo: Editora Livraria da Física.

    Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Débora da Silva Soares .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

da Silva Soares, D. (2015). Model Analysis with Digital Technology: A “Hybrid Approach”. In: Stillman, G., Blum, W., Salett Biembengut, M. (eds) Mathematical Modelling in Education Research and Practice. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer, Cham.

Download citation

Publish with us

Policies and ethics