he counted, to count out loud, and to explain how he used the number line to
help him. By sharing his work, Ricardo has an opportunity to think through and
articulate his strategies and practice communicating clearly his ideas to others. As
Ricardo shares his strategy, Lillian also repeats out loud what he did in each of his
steps, helping the other students get a clear picture of everything he did. The
other students benefit from hearing and looking at Ricardo’s work because it
might give them some new ideas about strategies for counting (for example, when
creating an equivalent set, he shows his strategy of taking one shell out of the jar
and then putting one object in the cup to match it) or it might affirm some of the
strategies they were already using.
Lillian next decides to have Janiris share her work. When Janiris shares her
work, it is clear she has made some counting mistakes. Each piece of her work
shows a different amount and those amounts do not match the quantity of objects
in the jar. When she counts out loud, she skips some numbers. Lillian does not
simply tell Janiris she made a mistake nor does she tell her what the mistake is.
Instead, she uses Janiris’ mistake as a learning opportunity for Janiris and for the
rest of the students. As Lillian says in the second interview, “If I helped her real-
ize she made a mistake, it would kind of get into her mind and she would think
about it next time she was working in the Counting Jar or anything else. If you
just tell them, then I think it becomes just a one-deal thing... it doesn’t become
their own. The ownership part of it... by her realizing her mistake... it was
more of her physically working through it.”
Lillian makes this a learning opportunity for all the students through the
questions she asks, the ideas she focuses on, and the way she supports Janiris in
working through her mistake. In the same way she asked Richardo, she asks
Janiris to show how she counted the shells. She does not just tell Janiris that she
made a mistake. Instead, Lillian has Janiris compare the amounts she recorded on
paper and the amount in her equivalent set to the amount she counted in the jar.
Lillian helps Janiris count again and then has all the class count. This gives every-
one practice counting and provides Janiris practice with the correct counting
sequence. Lillian asks others to share strategies they thought Janiris could use to
make sure she got the same amount. This involves other students in the discus-
sion, and it helps Janiris to hear strategies from her peers. Lillian also involves
students with a range of understanding of counting in the discussion of Janiris’
mistake. She asks the group how many more Janiris would need to have the correct
amount (a challenging question for a kindergartner) and asks the student who
responds to explain his strategy. Another student simply restates the mistake
Janiris made, perhaps trying to process it, and Lillian affirms his statement.
Because of the way Lillian structures the discussion of Janiris’ mistake, Janiris
and the other students are able to learn more about counting and their counting
BUILDINGUNDERSTANDINGTHROUGHTALK