Speaking haltingly, Daniel elaborates. The teacher asks
whether he is referring to “Sean’s conjecture” (“when you
make, to make some number of pieces you cut one less”) and
he nods. Next, another student, Betsy, says that she can show
–4 and –4 on the number line. The teacher says that she would 48
like to see that but, recognizing that constructing this rep- resentation will take time, sets the child up to construct her number line while the rest of the class continues discussing other aspects of the problem.
The other children in the class listen with varying degrees of attentiveness while the teacher moves about the room. She occasionally leans over a pair of students, or straightens a pupil’s notebook, or places her hand on a child’s shoulder. She asks whether anyone else has a comment about Mei’s solution. Unexpectedly, Keith says he agrees, but that first he “did something different” and that it was “wrong.” The teacher asks whether he remembers what he did, and he explains:
Keith: First, I made the same thing that she did, then I made the other piece longer, so I thought they were supposed to be the same size.