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.
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