MARTA: We had sort of anticipated that they would hit a wall when they
had to split up the black and white.
KAREN: And we were right! Talking through the problem beforehand made
a major difference for me. Knowing what the kids have been exposed to
and the possibilities of the strategies that they might do, they might go to
fractions, they might do percents, or whatever. I felt like I was prepared, be-
cause there were several different ways that it could go, and I had an idea of
how to deal with that.
JOHN: Were their computation strategies ones that you were used to seeing?
I know we went over some of those in our earlier meeting.
KAREN: Well, I have gotten pretty used to them now. When they explain it
to me, it just reinforces that they understand what they are thinking. Even
if it’s not how I would solve it, the explaining just solidifies it for them. I
think it went really well.We proceeded to look over the student work, noticing the elements of each
child’s KWC chart. Karen was really pleased at one student’s reaction when he
said, “It looks really hard, but if you do a KWC it makes it easy!” I noted that one
child began to make a chart to represent the 2-to-3 ratio, but that after about the
twentieth step, it became too cumbersome. Karen noted that this was when that
child decided to use multiplication to work more efficiently.
Then we worked on creating a similar problem, but with a candy bar context,
rather than cars. The problem was a little more complicated, but we felt that the
students would be able to make connections from the previous work that would
help them tackle the similar problem.
Reflecting on Our Collaboration
The collaborative work for the lesson that we engaged in was invaluable for help-
ing us guide the students’ learning. We were able to share perspectives on the
children’s thinking while thoroughly exploring the many avenues on which the
students’ thoughts might travel. It was crucial that we met both before and after
each lesson and that the meeting beforehand included doing the problem to-
gether. Marta and I were able to help Karen anticipate some of the challenges
that students might face during the problem and suggest some questions and rep-
resentations that might be helpful.
After the lesson, Karen was able to reflect on what went well, how each stu-
dent approached the problem, and what parts of the lesson were challenging for
her. We then used what we learned from the lesson to plan future activities for
the students. Karen took what she learned from this collaboration to her training
WORKINGCOLLABORATIVELY