Teaching and Learning Mathematical Modelling

Abstract

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Research Trends in Digital Technologies and Modeling in Mathematics Education

“…The above mentioned facts show a close relationship between modeling and digital technologies and their impact on student learning that goes beyond the presentation of concepts, mathematical algorithms or training processes. In line with this, recent research recognizes the contributions, changes and reorganization of mathematics-teaching processes when modeling and technology are linked (Greefrath & Vorhölter, 2016;Soares & Borba, 2014;Villa-Ochoa et al, 2018).…”

“…Each document was assessed taking into account if: (a) the title was related to modeling topics, (b) the document included the use of digital technologies in its proposal (c) the abstract offered information about an empirical work reporting the use of technology and modeling in mathematics. To avoid publication bias (Jesson & Lacey, 2006), the first four volumes of the book series International Perspectives on the Teaching and Learning of Mathematical Modeling in Springer and ICME-13 Topical Survey on Modeling (Greefrath & Vorhölter, 2016) were included into the study. In those books, the selected chapters were identified through the word "Technology".…”

“…Digital technologies, on the other hand, play some roles in the modeling process associated with the possibility of developing experiments and simulations and promoting diverse kinds of participation of students in the construction of their own knowledge (Buteau, Muller, Marshall, Sacristán, & Mgombelo, 2016;Kaiser, 2005;Molina-Toro, 2013;Pons & Espinosa, 2015). Technologies also provide numerical solutions, visualization and graphic control tools, as well as access to information on the web (Greefrath & Vorhölter, 2016). The experiences that were presented in the work by Borba and Villarreal (2005) are a sample of how technologies reorganize the way of producing knowledge.…”

“…To do this, phases are described that intervene in the connection of two domains, one called mathematical and the other extra-mathematical, also called reality. Overall, the modeling process originates from a real-life problem Greefrath & Vorhölter, 2016;Perrenet & Zwaneveld, 2012). This problem, commonly located in an extramathematical domain or in the "real world", is simplified in such a way that it can be represented with a model in the mathematical domain.…”

“…Some differences between representations lie in the emphasis given to sub-processes or actions of students (Perrenet & Zwaneveld, 2012). Some examples of representations can be found in the works of Blum and Leiss (2007), Greefrath and Vorhölter (2016), Stillman and Brown (2014), and Perrenet and Zwaneveld (2012). In particular, the modeling cycle proposed Blum and Leiss (2007) has been used by other authors to investigate what type of variations occur when technologies are linked to modeling processes (Daher & Shahbari, 2015;Geiger, 2011;Greefrath, 2011) In the work of Greefrath, Siller and Weitendorf (2011), examples of situations that allow analyzing the influence of technology in the modeling cycle are presented.…”