Among mathematics teacher educators, a consensus has emerged that exemplary teaching involves attention to students’ thinking. This consensus stems, in part, from theoretical and empirical work highlighting the importance of teachers’ being able to make thoughtful in-the-moment decisions, building on students’ ideas to adjust the ongoing lesson. Since this in-the-moment flexibility draws in large part on teachers’ noticing capabilities, mathematics education researchers have paid increasing attention over the past decade to key characteristics of teacher noticing and to ways to help teachers develop these skills and inclinations. In this paper, we explore how engaging teachers in annotating videos of mathematics classrooms can provide important insights into teacher noticing of students’ mathematical thinking. We argue that, when used in particular ways, video tagging affords researchers and teacher educators the ability to examine the relationship between what grabs a teacher’s attention and how teachers interpret the thinking displayed in those moments, and instructionally actionable feedback about how teachers are progressing in their attending to and interpreting of students’ thinking, two related skills that may or may not develop in sync.

中文翻译：

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视频标记是教师注意的窗口

在数学教师教育者中，已经出现了一种共识，即模范教学涉及对学生思维的关注。这种共识部分源于理论和经验工作，这些工作强调了教师能够根据学生的想法来调整进行中的课程，从而能够做出及时的，及时的决策的重要性。由于这种即时的灵活性在很大程度上取决于教师的注意能力，因此在过去的十年中，数学教育研究人员越来越关注教师注意的关键特征以及帮助教师发展这些技能和倾向的方法。在本文中，我们探讨了如何让教师参与注释数学课堂的视频如何为教师注意学生的数学思维提供重要的见解。我们认为，