This study aims to systematically explore and define the concept of “巡回指導” (Sunhoe-jido), often referred to as “circulating” in mathematics classrooms, and to categorize its types. Circulating involves teachers moving around the classroom during individual or group activities to interact with students. Through the analysis of 32 mathematics lesson videos of 16 teachers, seven categories of circulating were identified: helping students understand a given task, facilitating a small-group discussion, guiding and supporting exploration, providing specific information and remediating, verificating student work, tracking progress and preparing for whole-group, and management. Circulating in mathematics instruction refers to the interactions that primarily occur when a teacher moves around the classroom while students work individually or in groups on mathematical tasks, during which the teacher monitors students' ideas in real time, adjusts the flow of instruction, and provides timely support and feedback. This interaction not only helps students overcome obstacles in exploring tasks but also allows the teacher to observe their thinking process, refine mathematical ideas, and address misconceptions. Circulating involves more than just physical movement in the classroom; it represents a meaningful interaction in which the teacher intervenes at key moments to facilitate learning and help students meet the lesson's objectives, whether working individually or collaboratively. This study highlights the need for developing training programs that help teachers effectively utilize circulating guidance in their practice and suggests further research to more broadly verify the effectiveness of each type of circulating in various contexts.
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