Noticing students' mathematical thinking is a key element of effective instruction, but novice teachers do not naturally engage in this practice. Prospective secondary school mathematics teachers were engaged in an intervention grounded in analysis of minimally edited video from local secondary school mathematics classrooms; the goal was to support their ability to notice important student thinking within the complexity of instruction. Evidence of participants' learning in five iterations of the intervention is discussed, including their focus on student mathematical thinking, their ability to discuss the mathematics in that thinking, and their ability to notice particular high-leverage instances of student thinking.

This study investigates six university professors' reflections on the shift to remote instruction during the Spring 2020 semester in response to the COVID-19 global pandemic. The rapid shift in instructional platform presents an opportunity to learn from unresolved challenges that persisted through the semester.Here we present a qualitative study of how experienced (i.e., associate or full) chemistry professors report their teaching practices in light of the COVID-19 disruptions. We observed four major themes: personal factors, contextual factors of the structure and culture, teacher thinking, and teachers' practice. These themes revealed that the professors in this study adapted quickly using institutionally offered platforms, modified their courses as minimally as possible, struggled with assessment, and held diverging beliefs about teaching and students. The outcomes of this study have implications for ongoing efforts to reform instructional practices at the institutional and departmental level. Specifically, we recommend similar studies to ascertain current faculty beliefs and instructional practices in other departments in order to identify shared visions for change and effective supports for enacting that change.

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