Teachers' perception  of and reflection on students' metacognitive knowledge in mathematical modelling processes

In mathematical modelling, there is general agreement that metacognitive modelling skills are indispensable. Metacognitive modelling competence is often divided into a knowledge aspect and a control aspect of metacognition (Schraw, 2001). However, it is not only relevant for learners but also for teachers. Apart from appropriate reflections on the activities of learners, teachers also focus on the area of appropriate action in relation to the perceived processes. Stillman (2011) has elaborated the concept of meta-metacognition. In this context, the teacher must monitor the metacognitive processes of usually several individual learning groups (Stillman & Galbraith, 2012) and thus reflect on a meta-meta level. The teacher must reflect to what extent students are using metacognitive strategies adequately, but also about the students’ metacognitive knowledge in order to support them. Due to little empirical studies examining how teachers consider their students’ metacognitive knowledge about tasks, persons and strategies, we will examine how, and to what extent, teachers pay attention to students’ metacognitive knowledge when observing and analysing modelling processes. In this chapter, we will present three case studies.