Feedback provided by mathematics teachers usually addresses procedural skills and, to a much lesser extent, other competencies such as conceptual understanding or engagement in mathematical practices. As most previous literature has studied feedback provided on homework or video prompts, how teachers provide such feedback in the classroom is poorly understood. Here, sixteen lessons taught by five teachers were purposefully sampled from a larger video study (172 lessons) as lessons with high-quality feedback according to a standardized observation instrument. The analysis focused on the instructional situations in which teachers provided feedback. When teachers provided procedural feedback, the situations were orderly and effective. Feedback on conceptual understanding and mathematical practices was provided in situations when students were especially challenged, and entailed a series of complex decisions, thereby placing demands on the teachers to manage both the students’ understanding and behavior. We argue that researchers should focus on how teachers and students negotiate the instructional situation to allow for feedback on conceptual understanding or mathematical practices.

数学教师提供的反馈通常涉及程序技能，并在较小程度上涉及其他能力，例如概念理解或参与数学实践。由于以前的大多数文献都研究了对家庭作业或视频提示提供的反馈，因此对教师如何在课堂上提供此类反馈知之甚少。在这里，根据标准化的观察仪器，有目的地从更大的视频研究（172 节课）中抽取了由 5 位教师教授的 16 节课，作为具有高质量反馈的课程。分析侧重于教师提供反馈的教学情况。当教师提供程序反馈时，情况是有序和有效的。对概念理解和数学实践的反馈是在学生特别受到挑战的情况下提供的，并需要一系列复杂的决定，从而要求教师管理学生的理解和行为。我们认为，研究人员应该关注教师和学生如何协商教学情况，以便对概念理解或数学实践进行反馈。