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.

中文翻译：

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引出以不同符号记录表示的数学模型的建模过程的特征

通过建模活动构建的数学模型应该适合当前的情况。在这项研究中，我们试图监控不同学习者的建模路线以及他们的建模子能力，以了解这些与所得数学模型的符号学特征之间的关系。我们的数据来源包括六组职前和实习教师参与一项建模活动的视频记录、他们的工作草稿和他们的最终书面报告。六个小组构建的数学模型是用不同的符号记录（数字和代数）编写的，因此它们对情况需求的适当性不同。对这些建模过程的分析表明，在活动中构建的数学模型表明了小组的建模子能力及其建模路线。与生成数值模型的组的建模路径相比，代数模型产生于更复杂、顺序更少的建模路径。此外，产生效果较差的数值模型的群体在从情境模型到真实模型的转换以及从真实模型到数学模型的转换中缺乏某些子能力。