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Modeling empowered by information and communication technologies

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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.

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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

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Correspondence to Mónica E. Villarreal.

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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

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