Homework is a tool for school learning around the world. It is devised mainly for students to practice what is taught. In China, homework is also made for teachers; it is a teacher's job responsibility to mark student work and provide feedback to students in a timely manner. But teachers also analyze homework to inform their teaching. My observations of one teacher, Teacher (Tr.) Wang and her colleagues, a group of 8 th grade mathematics teachers in a middle school in Shanghai, reveal the prominence of homework in her daily work.

In this study, I investigate four major homework-related activities of Tr. Wang and describe and analyze what they each entailed and made possible for her teaching and student teaming. These four activities are: marking homework, explaining selected errors to the whole class, tutoring individual students on their errors and talking with colleagues about homework-related issues. Drawing on theory and methods from cultural-historic activity theory, cognitive psychology, ethnography and classroom discourse analysis, I collected and analyzed telephone interviews with mathematics teachers in Shanghai, focused observations of Tr. Wang's homework activities in her office and classrooms, audiotaped classroom and office observations, field notes, marked student work samples, and curriculum materials.

Analyses of the above data suggest several findings about how homework was used by Tr. Wang. (1) In marking homework, she created a communicative system of symbols and signs on student work to communicate teacher feedback; while marking, she was making sense of student problems of learning, selecting typical and important errors to explain and tutor. (2) In explaining selected homework errors to the class, Tr. Wang offered structured and detailed explanations of the important mathematics behind the errors from multiple perspectives. (3) In tutoring, she summoned students she identified to her office for individual assistance in which she diagnosed their learning issues and offered guidance for how to make corrections. (4) While marking homework together with her deskmate colleague, they shared student problems in homework and their stress from the challenges of helping all students learn. She and her math colleagues also informally deliberated on the problems arising from teaching and homework and figured out specific ways to resolve the problems. Such collective problem solving provided valuable learning opportunities for Tr. Wang and her colleagues.