their understandings—fragile though they may be—and to be able to have dis-
course with their peers in a manner that provides further understanding of concepts
that may be tenuous. The first step is encouraging them to express themselves in the
small group. Once I can get them to say what they are thinking, it gives me a start-
ing place as a teacher to assess what they know, what questions to ask, and what
representations and examples to offer. My notes (mental or otherwise) from these
small-group conversations allow me to plan how to include these students when we
have the large-group discussions. I can refer to ideas they talked about in the small
group. For example, I could ask Kendrick, “Do you remember when you talked what
you know about 81? Do you remember what you said?”
If we are talking about something that I think is still confusing to them, I can
make sure to rephrase the ideas with words and representations that will help clar-
ify the ideas/concepts. Because we have established a community where students
feel safe, I can say something like, “Chelsea, did you understand what Kenny was
saying?” or “Malia and Dante, make sure you pay attention to what Larnelle is say-
ing. He’s talking about how you can decide if a number is a square number. This
is something you weren’t sure about. Remember?”
I try to facilitate conversation so that students make connections among the
strategies that their classmates are sharing. I also know that students will support
each other when they get stuck. When we solved multiplication problems, I vali-
dated skip counting as one method we can use because I knew that Kendrick and
a few others were comfortable solving problems that way. During one class con-
versation, we were trying to solve the problem 38 21. Kendrick was trying to
come up with a shorter way to solve the problem without writing all of the multi-
ples of 38. He understood that the 10th multiple would help him, but thought that
he could continue skip counting from there, instead of making the connection that
he could do another 10th multiple and have the 20th multiple of 38. Marcus asked
Kendrick, “Remember yesterday’s before-school work assignment? When we had
to find the 10th multiple of 15? Well, if you know the 10th multiple of 38, then
you can figure out to solve 38 21. You know the 10th multiple of 38, right? Then
you know the 20th multiple because of how 10 is related to 20... right? 10 is half
of 20, right?” When Kendrick didn’t respond, we paused and used an example of
something he already knew—10 10.
TEACHER: If you know 10 10, how will you find out 10 20?
KENDRICK: Oh, that’s just another 10 10, then you put them together...
so that’s 10 10 100 and another 10 10, which is 100, so all together
that’s 200.
TEACHER: Right! So now use that idea to think about what Marcus said
about the 20th multiple?BUILDINGUNDERSTANDINGTHROUGHTALK