The Planning
Karen began coming into our rooms for the small-group math instruction a few
months into the year. At the time, all of the classroom teachers were using the
same, nonroutine word problems, which students worked in homogenous groups
to solve. The students we focused on were in a group with the literacy specialist
(Karen, in our cases) while the classroom teacher rotated among the other few
small groups in the room. (This kind of grouping is how Title I reading groups are
organized, so we decided to stay with this familiar structure.)
We realized that it was crucial for the three of us to meet to plan the word
problems we would be focusing on, to work on the mathematics in the problems
together, and to discuss what comprehension strategies would support students’
understanding of those particular problems. We decided that Karen would start
out working with a group from Marta’s classroom, then we would debrief, and she
would use what she learned to adjust her teaching for the group in my classroom.
We wanted to choose a problem that involved the application of the ideas
surrounding the number work we had done with students with the operations of
multiplication and division, as well as fractions. We also wanted to choose a prob-
lem that would require the students to navigate a significant amount of language
to understand the problem. The problem we chose was:
One day, the Lugnut Car Factory produced 315 cars. The cars were silver, black, or
white. One-ninth of all the cars were silver. For every 3 black cars made, 2 were
white. How many of each color did they produce? (Wheatley 2002)During our discussion, we talked about what Karen should focus on during the
lesson.
- strategies for unpacking the problem to figure out what it is asking
- possible representations to support students’ visualization of the problem
- possible strategies for computing the solution
- places where students might be confused
Unpacking the Problem
It was important that we took the time to unpack the problem and solve it our-
selves. This allowed us to “think like the students” and gave Karen the opportu-
nity to learn about the different kinds of math thinking our students were doing
and where their comprehension might break down.
We began with a discussion of how to use a KWC chart to help our students
slow down and think carefully about the information in the problem, one sen-
tence at a time. After the first sentence of the problem, we agreed that we wanted
WORKINGCOLLABORATIVELY