They also use mathematical language that they have developed through the discourse. The teacher listens to students carefully. A few other students look up. Ms. Chavez circulates through the class, listening to the students' discussions, asking questions, and offering suggestions. She notices one group has produced only one branch of the graphs.
Students initiate conjectures publicly.
They make connections between this graphing activity and transformational geometry. The students continue working, and the conversation is lowered to murmurs once again. Students present and explain solutions to the rest of the class. The teacher does not press for closure on these ideas simply because the period ends. These journals give the teacher insights into students' thinking.