Further investigation into the quality of teachers' noticing expertise: A proposed framework for evaluating teachers' models of students' mathematical thinking

Because teachers cannot directly access the processes by which students construct their mathematical knowledge, Teacher Noticing, an activity that involves observing students' work, interpreting students' mathematical thinking about a task based on their remarks or actions, and responding to their thinking, is important to grasp students' mathematical understanding. A possible way for teachers to develop noticing expertise is to engage in a situation focused on student thinking such as clinical interviews. However, noticing students' thinking productively through clinical interviews remains a challenge, especially for pre-service teachers, not only because it requires a broad range of knowledge but also because of the absence of a framework to inform and evaluate the process. This paper addresses the development of such a framework for evaluating the quality of pre-service teachers' noticing expertise in a context where students' thinking is emphasized by removing normal classroom interruptions. It then demonstrates how the framework can be used for this purpose through three empirical examples of pre-service teachers who engaged in an intervention that involved conducting clinical interviews and analyzing students' mathematical thinking by watching video-recordings of their clinical interviews.