Ways researchers can use teacher noticing to inform the conceptualization of a complex teaching practice

Abstract Prior research has examined teachers’ noticing in order to understand what factors affect teacher noticing and how mathematics teacher educators can support that noticing. We contend, however, that analyzing teachers’ noticing has the potential to be used for additional purposes. In this paper, we illustrate how we used teachers’ noticing as one tool for gaining insight into our conceptualization of a complex teaching practice—the practice of building on student mathematical thinking. We provide examples of how our analysis of instances of noticing enhanced our understanding of the practice of building by revealing aspects of the practice that we had never considered or were still underdeveloped. We also illustrate how instances of teacher noticing allowed us to gain insights into our own efforts to develop teachers’ understanding of the building practice, including areas where we thought we had been explicit but there was still evidence of incomplete understanding, areas where we needed to do something different or go deeper with the teachers, and areas where we had not been explicit about a critical aspect of the practice. The instances of noticing also revealed ways we needed to account for how important routines from the teachers’ own typical classroom teaching might interfere with aspects of building. Our findings illustrate how the study of teacher noticing can contribute to advancing researchers’ understanding not just of teachers’ noticing but also of the phenomena they are noticing.