As the students discuss the repeated subtraction strategy, Dee carefully
records each step. Recording each step of the strategy may help students keep
track of what is being discussed even if they are not participating at that time.
Dee’s recording is a tangible record of what has been discussed and can be referred
to by students to remember what was said and to help them figure out an answer.
The recording particularly helps with repeated subtraction because sometimes
students find it challenging to figure out where the answer is with repeated sub-
traction (the number of groups taken away). As Dee records each step, she checks
in with the students to see if they are following the strategy by asking “Am I
finished?” She also repeatedly asks students what the specific numbers she has
recorded represent.
As the discussion continues, Dee uses the students’ ideas to try to help them
as a group and individually move forward in their ideas about and understanding
of division and specifically division with remainders. She does this by asking the
students very specific questions about what they are saying to make their ideas
clear to the other students and to themselves (whether they are correct or not),
by connecting students ideas, and by specifically asking a student about what
another student said. For example, when one student says the answer to 36 8
is thirty-two, Dee responds, “Is thirty-two really the answer?... So someone said
36 8 is how many 8s can we get out of 36. So are you saying we are getting
thirty-two 8s out of 36? 8 8 8 thirty-two times?” Later she asks this student
to listen to another student’s idea, which she then rephrases: “This 4 represents
the 4 buses, but the 4 also represents the four 8s, which according to Najat is 32,
4 8 is 32, so you are right it does land on 32, but 32 is not the answer.”
Participating in Discussions
At this time of year (October), the community in a math class is still develop-
ing and students are still figuring out how to be a part of that community. As
Dee says in one of the interviews, “In the beginning of the year, it’s very diffi-
cult to get all the students engaged in the conversation; they are coming from
different places. So it is important to do a lot of the modeling, put myself in
their shoes, even sometimes talk like them. And make arguments and have dis-
course back and forth about why this answer doesn’t work and so on and so
forth.” Her strategies—such as using humor, building the discussion from the
ideas coming from the students, responding positively to all students’ responses
and taking their responses seriously, and citing their words in her responses and
questions to others—all encourage students’ participation. At the end of the
discussion, Dee also makes sure to approach those who have not participated
and find out what they understood from the discussion. Consistently using these
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