Features of modeling processes that elicit mathematical models represented at different semiotic registers
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Features of modeling processes that elicit mathematical models represented at different semiotic registers Juhaina Awawdeh Shahbari 1
& Michal Tabach
2
Published online: 25 September 2020 # Springer Nature B.V. 2020
Abstract
Mathematical models that are constructed through modeling activities should be appropriate for the situation at hand. In this study, we seek to monitor the modeling routes of different learners as well as their modeling sub-competencies in order to learn how these are related to the semiotic characteristics of the resulting mathematical models. Our data sources include video recordings of six groups of pre-service and practicing teachers engaging with one modeling activity, their working drafts, and their final written reports. The mathematical models constructed by the six groups were written in different semiotic registers (numeric and algebraic) and hence differ in their appropriateness to the situation demands. The analyses of these modeling processes suggest that the mathematical models constructed in the activity are indicative both of the groups’ modeling sub-competencies and of their modeling routes. Algebraic models emerged from more complicated and less sequential modeling routes compared with the modeling routes of the groups that produced numeric models. In addition, the groups that produced the less effective numeric models lacked certain sub-competencies in the transition from the situation model to the real model and in the transition from the real model to the mathematical model. Keywords Mathematical model . Modeling process . Modeling cycle . Modeling route . Semiotic register
1 Introduction Mathematical modeling is a two-directional process of translation between the real world and mathematics (Blum & Borromeo Ferri, 2009). This process begins with a real situation and ends with a solution that meets the demands of the situation. In solving modeling problems,
* Juhaina Awawdeh Shahbari [email protected]
1
Al- Qasemi Academy College, Baqa-El-Gharbia, Israel
2
Tel-Aviv University, Tel-Aviv, Israel
116
Shahbari J.A., Tabach M.
learners go through multiple cycles of modeling processes. In carrying out these modeling processes, learners need to apply modeling competencies (English & Fox, 2005). Some researchers have described the solution process in terms of modeling cycles (e.g., Maaß, 2006; Daher & Shahbari, 2015). Modeling processes have been the focus of much research. Some studies examined learner engagement with one or more modeling activities, while others described the modeling process as a whole (e.g., Galbraith, Stillman, Brown, & Edwards, 2005) or focused on the transitions between each phase of the modeling process (e.g., Hankeln, 2020; Shahbari & Peled, 2017). Other studies examined the features of various solutions or the final models created for specific activities, but did not discuss the related modeling process (e.g., Dorier, 2005; Shahbari & Daher, 2016; Yanagimoto & Yoshimura, 2013). Indeed, very few studies (e.g., Ludwig & Reit, 2013) have focuse
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