They seem used to paying attention to one another's ideas and to reasoning together. They also accept responsibility for helping others. A girl volunteers and carefully draws her graph on a large wipe-off grid board at the front of the room. As she does this, most students are watching closely, glancing down at their own graphs, checking for correspondence. A few students are seen helping others who had some difficulties producing the graph.
Students use a variety of tools to reason together about mathematics.
They do not rely on the teacher to initiate all ideas or to certify results. Another student suggests that they enter the function into the computer and watch it produce the graph. The first girl does this, and the class watches as the graph appears on the overhead screen. By directing them to think through comparisons, the teacher creates a context that is likely to promote students' reasoning and communication about these functions and their graphs. The students communicate with one another about mathematics without the teacher asking them questions or directing their comments.