Watch one of the Japan videos from the Trends in International Mathematics and Science Study (TIMSS)--more specifically, mathematics video 3 on solving inequalities1--and you'll see that after giving his students a word problem to solve, the 8th grade math teacher strolls among the students' desks for almost 15 minutes, leaning over to see what each student is doing, making brief comments to each one, and noting on a chart how different students are solving the problem. Some are counting, some are making tables or charts, and some are writing equations. The teacher clarifies instructions for one student: "Yes, write your explanation on the paper next to the problem." He clarifies terms for another: "This 180-10x you wrote--whose money is this?" He nudges others forward: "So you counted all the way? Is there an easier method to find the answer?" And he supports and acknowledges more complex approaches: "If you try combining this and that, you can make a mathematical expression." "So you wrote a simultaneous equation--OK! "This process of roving among desks to monitor and assist students' independent or collaborative work is known as "kikan-shido" (between-desks instruction). The authors encountered this practice firsthand while teaching and coordinating professional development at a K-12 school in Saitama, Japan (Ermeling & Graff-Ermeling, 2014). This experience and subsequent observations of Japanese colleagues opened their eyes to the importance of "kikan-shido" as part of regular lesson preparation, as did their analysis of videos from their own classroom lessons. They saw that the unplanned, cursory exchanges with students when they were working on an assignment in class mostly reiterated previous instruction and seldom advanced student learning. From this observation, the authors came to understand that the teacher's role during student work time in class--what teachers chose to focus on, how long they spent with each team or individual, what teachers chose to say or not say--had crucial instructional value.