3 white, so I didn’t even count the reds. I just saw them with my eyes.” When I
asked for 1 7, Stacy picked the correct train and said, “There’s 1 white and
7 red.” During the discussion, I was pleased that some of the students from the
intervention group were beginning to visualize and talk about the number com-
binations, while building on what other children in the class were sharing. For
example, Fernando said, “There’s 2 red so there has to be 6 whites to make 8.”
The practice in the small group, review in the large group, and the experience of
hearing their classmates’ ideas were helping to build their understanding of num-
ber combinations.
Reviewing Student Progress
After these lessons, Sarah and I sat down to review the progress of the interven-
tion group. I particularly wanted to help her analyze their contributions to the
large and small groups. The intervention group was, from our notes, participating
more confidently in the whole-group discussions. Mia’s progress, after just three
meetings, was good and she seemed ready to be phased out of this special group.
Nicole, Stacy, Fernando, Connor, Keith Allen, and Kelvin were progressing but
could continue to benefit from the additional intervention. We needed to capi-
talize on their gains and solidify their understanding so they could begin to see
patterns. Even though I had sequenced the equations to highlight a generalization
about addition, the children were not ready to see this. I decided to be patient and
not force the issue. It was important that this “aha” moment come from the stu-
dents themselves, after they had seen the patterns several more times and heard
the other children explain what they saw.
Working on Notations
During our discussions about the students, Sarah and I began to focus on how
Sarah would soon take over the small-group discussions and whole-group work
with the number books. From reviewing students’ work on the number books, we
decided on some additional themes she would emphasize. For example, we noted
that Nicole still had difficulty notating her work symbolically, often confusing the
plus and minus sign as well as the horizontal and vertical formats of addition and
subtraction. We decided that she needed more explicit instructions in these for-
mats and that perhaps other children in the class might benefit also. Sarah was
going to weave how to notate both vertical and horizontal equations into her
number discussions, asking children what to write next and talking about the
symbols. She planned to have the children respond on individual whiteboards so
BUILDINGUNDERSTANDINGTHROUGHTALK