Skip to main content

Advertisement

Log in

Pre-service teachers’ experiences within modelling scenarios enriched by digital technologies

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

Abstract

This paper presents issues related to the use of technology by secondary school pre-service mathematics teachers engaged in open mathematical modelling projects. Pre-service teachers developed these projects within a regular mathematics education course during the teacher education program at the university concerned. This environment, called a modelling scenario, is the context for our study, which is based on the analysis of projects produced by seven consecutive cohorts of pre-service teachers beginning in 2010. The research questions guiding our study seek to determine which technologies pre-service teachers chose, for which modelling purposes they chose them, and in which phases of the modelling process they were significantly used. During the modelling process, pre-service teachers used the Internet, spreadsheets, mathematical software and programming languages. The Internet, the most utilized technology, was used to find information or data, to select variables, or to formulate problems. The other three technologies significantly influenced the processes of mathematical solution and validation. The in-depth analysis of a single project shows an original use of visual affordances of technologies and a dialectical relationship between problem posing and technology use. The study enables us to conclude the necessity for coordinated action between mathematics educators and mathematicians to generate a deeper understanding of modelling as a pedagogical proposal and mathematical activity.

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.

Fig. 1

(adapted with permission from Bassanezi 2002, p. 27)

Fig. 2
Fig. 3

Similar content being viewed by others

Notes

  1. To avoid repetition, at times we will use “modelling” in place of “mathematical modelling”.

  2. To avoid repetition, at times we will use “technologies” in place of “digital technologies”.

  3. From now on, if nothing else is specified, “students” will refer to “pre-service teachers”.

References

  • Anhalt, C., & Cortez, R. (2016). Developing understanding of mathematical modelling in secondary teacher preparation. Journal of Mathematics Teacher Education, 19(6), 523–545.

    Article  Google Scholar 

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

    Google Scholar 

  • Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In S. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education (pp. 73–96). Cham: Springer.

  • 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.

    Google Scholar 

  • Borba, M., Villarreal, M., & Soares, D. (2016). Modeling using data available on the internet. In C. Hirsch & E. McDuffie (Eds.), Annual perspectives in mathematics education 2016: Mathematical modeling and modeling mathematics (pp. 143–152). Reston: NCTM.

    Google Scholar 

  • Britzman, D. (2003). Practice makes practice. Albany, NY: State University of New York Press.

    Google Scholar 

  • Brown, J. (2015). Visualisation tactics for solving real world tasks. In G. Stillman, W. Blum & M. Biembengut (Eds.), Mathematical modelling in education research and practice: Cultural, social and cognitive influences (pp. 431–442). Cham: Springer.

    Chapter  Google Scholar 

  • Confrey, J., Hoyles, C., Jones, D., Kahn, K., Maloney, A., Nguyen, K., Noss, R., & Pratt, D. (2010). Designing software for mathematical engagement through modeling. In C. Hoyles & J.-B. Lagrange (Eds.), Mathematics education and technology: Rethinking the terrain (pp. 19–45). New York: Springer.

    Google Scholar 

  • Daher, W., & Shahbari, J. (2015). Pre-service teachers’ modelling processes through engagement with model eliciting activities with a technological tool. International Journal of Science and Mathematics Education, 13(1), 25–46.

    Article  Google Scholar 

  • Doerr, H. (2007). What knowledge do teachers need for teaching mathematics through applications and modelling? In W. Blum, P. Galbraith, H.-W. Henn & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 69–78). New York: Springer.

    Chapter  Google Scholar 

  • Doerr, H., Ärlebäck, J., & Misfeldt, M. (2017). Representations of modelling in mathematics education. In G. Stillman, W. Blum & G. Kaiser (Eds.), Mathematical modelling and applications: Crossing and researching boundaries in mathematics education (pp. 71–82). Cham: Springer.

    Chapter  Google Scholar 

  • Esteley, C. (2014). Desarrollo profesional en escenarios de modelización matemática: Voces y sentidos. (Doctoral Thesis). Facultad de Filosofía y Humanidades–Universidad Nacional de Córdoba, Argentina.

  • Gastón, J., & Lawrence, B. (2015). Supporting teachers’ learning about mathematical modeling. Journal of Mathematics Research, 7(4), 1–11.

    Article  Google Scholar 

  • Greefrath, G. (2011). Using technologies: new possibilities of teaching and learning modelling–Overview. In G. Kaiser, W. Blum, R. Borromeo Ferri & G. Stillman (Eds.), Trends in the teaching and learning of mathematical modelling (pp. 301–304). Dordrecht: Springer.

    Chapter  Google Scholar 

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

    Chapter  Google Scholar 

  • Kaiser, G. (2014). Mathematical modelling and applications in education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 396–403). New York: Springer.

    Google Scholar 

  • Larrosa, J. (2002). Notas sobre a experiência e o saber de experiência. Revista Brasileira de Educação, 19, 20–28.

    Google Scholar 

  • Larrosa, J. (2003). La experiencia de la lectura. México: Fondo de Cultura Económica.

    Google Scholar 

  • Lave, J. (1988). Cognition in practice: Mind, mathematics and culture in everyday life. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Lingefjärd, T. (2007). Modelling in teacher education. In W. Blum, P. Galbraith, H.-W. Henn & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 475–482). New York: Springer.

    Chapter  Google Scholar 

  • Lingefjärd, T. (2013). Teaching mathematical modeling in teacher education: Efforts and results. In X.-S. Yang (Ed.), Mathematical modeling with multidisciplinary applications (pp. 57–80). Hoboken, NJ: John Wiley & Sons, Inc.

    Chapter  Google Scholar 

  • Ministerio de Educación de la Provincia de Córdoba. (2012). Diseño curricular de educación secundaria. Orientación Ciencias Naturales 2012–2015. Tomo 4. http://www.igualdadycalidadcba.gov.ar/SIPEC-CBA/publicaciones/EducacionSecundaria/LISTO%20PDF/orientacion%20naturales28-03-12.pdf. Accessed 22 Sept 2017.

  • 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 (pp. 3–32). New York: Springer.

    Chapter  Google Scholar 

  • Rodríguez, R., & Quiroz, S. (2015). Developing modelling competences through the use of technology. In G. Stillman, W. Blum & M. Biembengut (Eds.), Mathematical modelling in education research and practice: Cultural, social and cognitive influences (pp. 443–452). Cham: Springer.

    Chapter  Google Scholar 

  • Soares, D. (2015). Model analysis with digital technology: A “hybrid approach”. In G. Stillman, W. Blum & M. Biembengut (Eds.), Mathematical modelling in education research and practice: Cultural, social and cognitive influences (pp. 453–463). Cham: Springer.

    Chapter  Google Scholar 

  • Stillman, G., Blum, W., & Biembengut, M. (Eds.). (2015). Mathematical modelling in education research and practice: Cultural, social and cognitive influences. Cham: Springer.

    Google Scholar 

  • Stillman, G. A., Kaiser, G., Blum, W., & Brown, J. P. (Eds.). (2013). Teaching mathematical modelling: Connecting to research and practice. Dordrecht: Springer.

    Google Scholar 

  • Villarreal, M., Esteley, C., & Mina, M. (2010). Modeling empowered by information and communication technologies. ZDM, 42(3–4), 405–419.

    Article  Google Scholar 

  • Villarreal, M., Esteley, C., & Smith, S. (2015). Pre-service mathematics teachers’ experiences in modelling projects from a socio-critical modelling perspective. In G. Stillman, W. Blum & M. Biembengut (Eds.), Mathematical modelling in education research and practice: Cultural, social and cognitive influences (pp. 567–578). Cham: Springer.

    Chapter  Google Scholar 

  • Widjaja, W. (2013). Building awareness of mathematical modelling in teacher education: A case study in Indonesia. In G. Stillman, G. Kaiser, W. Blum & J. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 583–593). Dordrecht: Springer.

    Chapter  Google Scholar 

Download references

Acknowledgements

This research was carried out with the financial support of the Secretaría de Ciencia y Técnica–Universidad Nacional de Córdoba. We would like to thank the meaningful and insightful suggestions of the reviewers in previous versions of this paper. Finally, we would like to thank our students Felipe, Gastón and Otto for their help in providing us with images and data corresponding to their modeling project.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mónica E. Villarreal.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Villarreal, M.E., Esteley, C.B. & Smith, S. Pre-service teachers’ experiences within modelling scenarios enriched by digital technologies. ZDM Mathematics Education 50, 327–341 (2018). https://doi.org/10.1007/s11858-018-0925-5

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-018-0925-5

Keywords

Navigation