them all. I think about the range of learners when I analyze this conversation.
Which students already feel comfortable enough to share? Who is looking down
or away to avoid eye contact with me or with the student who is sharing? Which
students seem to be actively listening to each other and trying to build ideas off
of one another?
John and Darryl are both learners who are struggling with math. From this
brief conversation, I learn that they understand that sharing is considered impor-
tant and recognize that they benefit when they see how someone else has
approached a problem. However, they don’t typically share their thinking in the
larger group. Cody is quite the opposite. He is a confident math learner, but he
understands how other students feel. He too hesitates when he isn’t 100 percent
sure of himself because he doesn’t want others (including me) to know that he
doesn’t get it. His comment summed up many of the students’ feelings.
Facilitating Math Conversations
After our initial conversations in September, we jump right into the math and
address concerns as we encounter them. We don’t formally generate rules for
“math talk,” but there is an understanding of what is acceptable math conver-
sation. The students are encouraged to express what they are thinking about
the particular activities we are working on as well as to admit when they aren’t
sure and need some help. I carefully plan my actions and questions so that I am
making our discussion process explicit for the students. In the beginning of the
year, I will give the students a minute or so to think about their response. Then
I may say something such as “Do you need some help?” “Would you like to call
on someone to help you?” “Do you need more thinking time? I can come back
to you when you are ready, just be sure to raise your hand again.” Students can
then choose to call on someone to help them out or just pass. This strategy
helps build camaraderie, allowing an individual to share as much as she is com-
fortable with before calling on someone else for help. As the year goes on, I
find myself continuing to use these questions, but not as frequently. The stu-
dents take more ownership of their thinking and learning and will say things
such as “I’m not sure, can you come back to me?” or “Can I ask someone to
help me?”
When sharing, the students’ ability to articulate their responses changes over
time. In the beginning of the year, the students may just restate or repeat what
a classmate has said. Slowly, with my guidance, we evolve into rephrasing what
a classmate has said in a student’s own words. I may ask, “Can someone repeat
what Darryl just said?” in the fall, but by the winter, I may ask, “Can someone
explain Darryl’s thinking in their own words?” The students begin to find ways
Lightbulbs Happen