the overhead forced light onto everything the teacher wrote. A strategically placed sheet of paper, meanwhile, covered up everything but the latest problem. Guiding students step by step, teachers brought all eyes to the immediate idea—and prevented any reflection on what came before. In Japan, where teachers cared more about the attention students paid to the ideas as they unfolded, a chalkboard that could hold the full trajectory of forty-five minutes’ worth of insights served teachers better.
