Over the past three decades, research and policy in many geographic regions has promoted a shift from direct, lecture-oriented mathematics instruction to inquiry-based, dialogic forms of instruction. While theory and research support dialogic instructional approaches, some have noted that the complexities of dialogic teaching make it difficult for teachers to implement. One mechanism by which teachers can improve their decision-making practices in dialogic classrooms is learning to notice (i.e. becoming aware of learners’ processes). While research has contributed frameworks for understanding how teachers notice individual learners’ mathematical thinking, there is little conceptualization regarding how teachers notice group processes in mathematics classrooms, which is integral to dialogic instruction. We offer a noticing framework termed professional noticing of coordinated mathematical thinking that describes how teachers notice group activity in mathematics classrooms. Professional noticing of coordinated mathematical thinking is conceptualized as a bi-dimensional process: noticing groups’ mathematical activity and noticing groups’ coordinated activity. Teachers must become aware of how groups approach the mathematical and collaborative nature of a task, since both of these aspects inform whether learners develop opportunities to learn in groups. The framework describes noticing practices integral to dialogic instruction and promotes inquiry for future research related to teaching moves in dialogic classrooms.

中文翻译：

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专业注意协调数学思维

在过去的三十年里，许多地理区域的研究和政策推动了从直接的、以讲座为导向的数学教学向以探究为基础的、对话式的转变。教学形式。虽然理论和研究支持对话式教学方法，但有些人注意到对话式教学的复杂性使教师难以实施。教师在对话课堂中改进决策实践的一种机制是学习注意（即了解学习者的过程）。虽然研究为理解教师如何注意到个别学习者的数学思维提供了框架，但关于教师如何注意到数学课堂中的小组过程却几乎没有概念化，这对于对话教学来说是不可或缺的。我们提供了一个称为协调数学思维的专业注意的注意框架这描述了教师如何注意到数学课堂上的小组活动。协调数学思维的专业注意被概念化为一个二维过程：注意小组的数学活动和注意小组的协调活动。教师必须意识到小组如何处理任务的数学和协作性质，因为这两个方面都可以告知学习者是否有机会在小组中学习。该框架描述了对话教学不可或缺的注意实践，并促进了对与对话课堂教学活动相关的未来研究的探究。