11. Designing Powerful Environments to Examine and Support Teacher Competencies for Models and Modelling

The purpose of this chapter is to highlight how work focusing on student‐level modelling and idea development can also serve as a powerful context to investigate parallel and interacting modelling processes at the teacher level. We assert that expertise in teaching is partly reflected in how teachers interpret and respond to classroom situations—in what they see and recognize, as well as in what they do. To establish a setting for extended studies of teacher‐level modelling, different research groups have found it desirable to move beyond single‐activity implementations in one of several ways. We begin our description of this work by identifying several values or beliefs about the nature of mathematical thinking and learning and corresponding instructional practices, which comprise key teacher competencies for the teaching and learning of modelling that have been emphasized by these projects. Then, we describe three different extensions from previous reports of our ongoing research, each aimed at examining and supporting students’ and teachers’ models and modelling over long time‐scales, such as the level of an entire course. Our results suggest that, in course‐sized studies of student development, significant powerful changes can also occur in teacher‐level competencies for the teaching and learning of modelling. One reason for this teacher‐level development is that in our student‐level modelling activities, students naturally express important aspects of their thinking in forms that can be observed directly by both teachers and researchers. Insights about the nature of students’ thinking have proven to be a powerful impetus to encourage important aspects of teacher development. Furthermore, course‐sized research sites enable us to directly observe significant teacher competencies that cannot be seen in studies focusing on single modelling activities.