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Prospective mathematics teachers’ (PMT) abilities to notice a range of important aspects of classroom instruction can be developed through interventions within teacher education programs (e.g., Author, 2017; Ivars et al., 2019; McDuffie et al., 2014; Schack et al., 2013). Little is known, however, about whether noticing skills developed in this context transfer to support PMTs’ noticing during their own instruction. This study addresses this issue by focusing on how the in-the-moment noticing when teaching a lesson compares between PMTs who participated in a targeted noticing invention and those who did not.
The noticing intervention in the larger study focused on noticing student mathematical thinking (SMT) because of its centrality to ambitious teaching (Lampert et al., 2010). Consistent with others (e.g., Choy 2014), we take the perspective that not all SMT is equally valuable in terms of its potential to enhance student learning and thus—informed by Author et al.’s (2015) construct of MOSTs—focus on noticing instances of SMT that have significant potential to support the learning of important mathematics.
The participants were PMTs enrolled in a secondary level teacher preparation program at a US university. The nine experimental group PMTs (E-PMTs) participated in an intervention that focused on noticing high-leverage instances of SMT using classroom videos (see Author, 2017 for details). The seven comparison PMTs (C-PMTs) did not participate in the intervention, but otherwise completed all of the same teacher preparation coursework.
During the study, all 16 PMTs were observed and video-recorded teaching a mathematics lesson three or four times during their student teaching internship. The PMTs documented important instances they noticed while teaching the lesson by wearing a self-mounted camera. Following the lesson, the PMT engaged in a recorded interview to discuss each self-documented instance. Two rounds of coding classified each self-documented instance. One round classified each instance according to whether it was a high-leverage instance of SMT. The other classified each instance according to who or what was the object of noticing (agent), the way the mathematics of an instance was discussed (specificity), and, when a student agent was assigned to the instance, the focus of the PMT’s noticing of the student(s).
Substantial differences between the noticing of the two groups were documented. For agent, the C-PMTs’s noticed students 59.1% of the time, while the E-PMTs did so 97.2% of the time. The specificity analysis revealed the E-PMTs more often focused on specific mathematics in the lesson than the C-PMTs (95.8% versus 69.7% of instances, respectively). For focus, the E-PMTs noticed students’ ideas in 95.7% of their student-focused instances compared to 46.4% for the C-PMTs. The analysis of whether the PMTs were focused on high-potential instances of SMT revealed this was the case only 24% of the time for the C-PMTs compared to 61% for the E-PMTs. Thus, the results provide evidence that the noticing skills developed in the E-PMTs during a noticing intervention (see Author, 2017) did seem to transfer to support the PMTs’ in-the-moment noticing while teaching a lesson.