Box 9–1 The Instructional Triangle: instruction as the interaction Among Teachers, Students, and Mathematics, in Contexts SOURCE: Adapted from Cohen and Ball, 1999, 2000, in press.

cal task, ask different questions, and complete the work in different ways. Their interpretations and actions affect what becomes the enacted lesson. Teachers’ attention and responses to students further shape the course of instruction. Some teachers may not notice how students are interpreting the content, others may notice but not investigate further, and still others may notice and respond by reiterating their own interpretation.

Moreover, instruction takes place in contexts. By contexts we mean the wide range of environmental and situational elements that bear on instruction—for instance, educational policies, assessments of students and teachers,