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

eurasia journal of mathematics science and technology education

Further Investigation into the Quality of Teachers’ Noticing Expertise: A Proposed Framework for Evaluating Teachers’ Models of Students’ Mathematical Thinking