The FOCUS Framework: Snapshots of Mathematics Teacher Noticing

Abstract

This thesis investigates what, and how teachers notice as they plan, teach, and review lessons that support the development of students’ mathematical thinking. Teacher noticing refers to what teachers see and how they interpret these observations to decide their responses to classroom situations. More specifically, this study examines what makes noticing productive with regard to enhancing student reasoning. The conceptual framework for this study established the centrality of mathematical noticing for teachers to engage in productive practices that enhance student reasoning. An important premise for this research is the assumption that productive noticing is manifested when teachers respond to student thinking through these practices: designing a task that reveals student reasoning; listening and building on student reasoning to orchestrate a mathematically fruitful discussion in class; and analysing student reasoning in order to learn from their practice during post-lesson discussions. To address the twin challenges of developing theory and documenting productive noticing, a design research paradigm was adopted for this study. A modified Lesson Study protocol, designed to create an environment that would promote more educationally productive noticing, was the main methodology adopted for this research. Data generated from voice and video recordings were analysed using thematic analysis through a commognitive lens to uncover the characteristics of productive noticing. The FOCUS framework highlights the two key dimensions to promote productive noticing: the need for an explicit focus and the central role of reasoning. Following a photographic metaphor, the framework is used to develop models, which describe and analyse teachers’ noticing from two perspectives: A wide-angle view and a close-up view. The wide-angle view provides a portrayal of teachers’ noticing through the lesson cycle in relation to the productive practices for mathematical reasoning, whereas a close-up view can provide a lens to examine teacher noticing at each stage of the lesson cycle. The FOCUS framework was then applied to develop two portraits of teacher noticing, which demonstrate how a teacher’s noticing can be characterised. The findings suggest that the FOCUS framework is useful for teachers to improve their noticing expertise, and for researchers to analyse teacher noticing.