Distinctive characteristics of mathematical thinking in non-modelling friendly environment

We first discern three different sources to describe the non-modelling-friendly environment in Taiwan: the background of mathematics teachers and students, examinations and textbooks. Under such unfriendly circumstances, how one can implement the teaching and learning of mathematical modelling is explored. In this paper, we focus on the analysis of distinctive characteristics of high school students' thinking of modelling. The changes required of the participating teacher and the evolution supporting these changes will be written in another article. Three kinds of Taiwanese students' modelling processes are identified, and the finding shows that the common feature of mathematical thinking of modelling is that, in practice, students do not solve mathematical models. We further conjecture that provoking students to explore mathematical solutions during modelling activities will benefit their situational reasoning, mathematizating, interpreting and communicating. On one hand, teachers can design model-exploring activities based on characteristics of students' thinking during modelling activities, and provide settings where conflicts between models and situations are confronted and the need to justify the validity of models and solutions is considered. On the other hand, students may elaborate their models and learn alternative approaches or tools for rethinking previously studied mathematical models during model-exploring activities.