A third-grade teacher and a teacher educator argue that, in an elementary mathematics class in which the teacher is encouraging the children to communicate and justify their mathematical ideas, the features of a mathematical task shape the mathematical discourse. They conjecture that divergent tasks, problems with many correct answers, may generate discourse in which students find it difficult to connect their classmates' ideas to their own and to listen to them with interest and respect. On the other hand, convergent tasks that point the students in the direction of a single answer appear to create an instructional context in which students may find it easier to connect to and care about other children's solutions and ideas. Two class lessons are discussed that illustrate the connections found between tasks and discourse in the mathematics classroom when teaching the concept of negative numbers. (NAV)