Understanding teachers’ noticing of children’s mathematical thinking in written work from different sources

Expertise in teacher noticing of children's thinking is central to a vision of responsive teaching in which teachers regularly elicit and build on children’s thinking during instruction (Richards & Robertson, 2016). In mathematics classrooms, this core instructional practice of noticing children’s mathematical thinking repeatedly occurs during instruction and involves attending to and making sense of children's mathematical thinking (Sherin, Jacobs, & Philipp, 2011). Teachers daily have opportunities to notice children’s mathematical thinking during their conversations with students and in students’ written work. However, expertise in noticing children’s mathematical thinking does not develop automatically or through years of teaching, and teachers need support developing noticing expertise. To help teachers develop noticing expertise, professional developers often employ artifacts of practice (e.g., video clips and student written work) from teachers’ own classrooms as well as strategically selected artifacts from classrooms taught by teachers unfamiliar to the PD participants. This study explored the potential differences in teachers’ noticing with written work from these two sources—teachers’ own classrooms and classrooms unfamiliar to the teachers. Drawing on the construct of framing (Goffman, 1974), particular attention was paid to the various frames (or lenses) teachers used during noticing. Using a context of professional development focused on children's mathematical thinking in the domain of fractions, this three-phase study explored teachers’ noticing and their use of frames by investigating the relationship between teachers' noticing of children's mathematical thinking in written work from their own classrooms versus unfamiliar classrooms. In the first phase, this study identified the frames individual teachers used when noticing children’s thinking in written work from their own classrooms. The second phase explored the frames that small groups of teachers used when collectively noticing children’s thinking in written work from unfamiliar classrooms during professional development. The third phase used in-depth interviews to investigate the relationship between the quality of teacher noticing and the use of frames of six teachers who were asked to notice children’s thinking in written work on the same problem from their own classrooms and from unfamiliar classrooms. Findings identified six frames teachers used while noticing children's mathematical thinking in written work from the two sources, and they fell into three broad categories: (a) noticing focused on the child’s current mathematical performance, (b) noticing focused on the child’s non-mathematical performance, and (c) noticing that compared the child’s performance to the expected performance based on the child’s past performance, the performance of the rest of the class, or curricular or testing guidelines. Confirmation of these frames in three data sets highlighted the variety of ways teachers reason during noticing, suggesting that frames are a useful construct for understanding the complexity of teachers’ noticing because frames capture the multiple and sometimes competing ideas that teachers need to coordinate. When comparing teachers’ noticing of children’s thinking in written work from their own classrooms versus unfamiliar classrooms, a lack of substantial evidence was found to distinguish the sources in terms of the use of particular frames, the prevalence of particular frames, or the quality of teachers’ noticing of children’s thinking. Further, there was evidence that teachers “imagined” insider knowledge of children from unfamiliar classrooms to assist with their noticing, which might explain why engaging with written work from either source did not seem to change the quality of teachers’ noticing. On the other hand, comparative analyses identified a distinction between teachers’ use of frames when they were considering one child’s strategy versus several children’s strategies regardless of whether the written work came from the teachers’ classrooms or unfamiliar classrooms. Specifically, when teachers’ noticing focused on more than one child, more frames and a greater variety of frames were invoked. Implications for professional development focus on the need to appreciate and address teachers’ coordination of multiple frames and the idea that the use of these frames depends less on the source of the written work and more on the number of children involved in the task