Abstract
This chapter describes a study that aims to illustrate how the interaction between mathematical modelling tasks and students’ mathematical thinking takes place. We based the study upon David Tall’s theory about mathematical thinking regarding mathematical modelling as a pedagogical way to teach mathematics. The research took place in the last year of a university course, with education students undertaking a mathematics degree. A qualitative approach was used with an interpretative analysis to infer points from data collected through audio recordings, video, quizzes, and written data. We have concluded that mathematical modelling can provide, and require the development of cognitive processes that promote interactions between “elementary” and “advanced” mathematical thinking through the cognitive processes of representation, abstraction and generalization.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Almeida, L. M. W., & Dias, M. R. (2004). A study on the use of mathematical modelling as a strategy for teaching and learning. BOLEMA – Boletim de Educação Matemática, 22, 19–35.
Almeida, L. M. W., & Ferruzzi, E. (2009). A socioepistemological approach to mathematical modelling. Alexandria Revista de Educação em Ciência e Tecnologia, 2(2), 117–134.
Bean, D. (2003). Modelling in the perspective of thought. Annals of the III national conference on modelling and mathematics education, 1–11. Piracicaba, SP.
Bogdan, R. C., & Biklen, S. K. (1994). Qualitative research in education. Porto: Porto Editora.
Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modeling process. Zentralblatt für Didaktik der Mathematik, 38(2), 86–95.
Dreyfus, T. (2002). Advanced mathematical thinking processes. In D. Tall (Ed.), Advanced mathematical thinking (pp. 25–41). Dordrecht: Kluwer.
Gray, E. M., & Tall, D. O. (1994). Duality, ambiguity, and flexibility: A “proceptual” view of simple arithmetic. Journal for Research in Mathematics Education, 25(2), 116–140.
Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM – The International Journal on Mathematics Education, 38(3), 302–310.
Palharini, B. N. (2010). Mathematical modelling and mathematical thinking: A study in the light of the three worlds of mathematics. Master's thesis, Universidade Estadual de Londrina, Londrina.
Sfard, A. (1991). On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1–36.
Tall, D. (1995). Cognitive growth in elementary and advanced mathematical thinking. In D. Carraher & L. Miera (Eds.), Proceedings of 19th international conference for the Psychology of Mathematics Education (Vol. 1, pp. 61–75). Recife: PME.
Tall, D. (2002). Advanced mathematical thinking. Cambridge: Kluwer.
Tall, D. (2004a). Introducing three worlds of mathematics. For the Learning of Mathematics, 23(3), 29–33.
Tall, D. (2004b). Thinking through three worlds of mathematics. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th conference of the international group for the Psychology of Mathematics Education (Vol. 4, pp. 281–288). Bergen: PME.
Tall, D. (2006). A theory of mathematical growth through embodiment, symbolism and proof. Annales de Didactique et de Sciences Cognitives, 11, 195–215.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Palharini, B., de Almeida, L.M.W. (2015). Mathematical Modelling Tasks and the Mathematical Thinking of Students. 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. https://doi.org/10.1007/978-3-319-18272-8_17
Download citation
DOI: https://doi.org/10.1007/978-3-319-18272-8_17
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18271-1
Online ISBN: 978-3-319-18272-8
eBook Packages: Humanities, Social Sciences and LawEducation (R0)