My kids can : making math accessible to all learners, K–5

WORKINGCOLLABORATIVELY

denominators with Jhali and her small group. Diane and I both noted that Jhali
was applying comparison strategies consistently. One day, Diane shared that Jhali
had volunteered several times to explain to the group how she had “stories” that
she could tell that would explain how she knew which fraction was greater. We
were pleased that she connected the work I was doing with her to the sequence
of tasks that she worked with in Diane’s room. The consistent practice helped
Jhali begin to make sense of fractional relationships. Numeratoranddenominator
were no longer just words. Jhali was able to represent and tell stories to describe
relationships. Diane shared one of Jhali’s stories about comparing and :

You see, there is this rich man that has a big car. When 4 people get in, they have

lots of space but when 6 people get in, they are all squished because the space gets

split up into 6 parts. So more people is less space so you only get a little piece, it is

only a 1 little piece of 6 spaces. That’s why is bigger, those people have 4 spaces

in the car and they get 1 of the 4 spaces.

Although Jhali’s story did not take into account whether or not the people were
of equal size, she was able to describe the relationship that more people would
mean less space for each, that each would only have a smaller fraction of space
available.

Reflections

An important aspect of working with Jhali was working through this assessment-
teaching cycle in close collaboration with Diane. This collaboration ensured that
Jhali’s mathematical experiences were consistent and provided her with multiple
opportunities to practice the same concepts over time in a variety of contexts.
Because Diane had participated in mathematical professional development with
the classroom teachers, she and I shared a common language and approach. Diane
did not simply offer Jhali a set of manipulatives, but she varied the representations
and focused on Jhali’s expression of the fractional relationships. Because of
Diane’s support, Jhali could continue to participate in the work that the rest of
her class was doing while still receiving the support she needed to build her skills.
I am convinced that Jhali benefited both from listening to our classroom discourse
and from having the additional practice with Diane. Providing these consistent
experiences for Jhali took a great deal of planning by Diane and me.
It was essential that Diane and I made the time to meet together. She was ea-
ger to hear about the information I gathered about Jhali from seeing her in class
every day and about the mathematical goals I had identified for the unit of study.
I found her reporting of Jhali’s mathematics in the pullout group to be very valu-
able in my planning for Jhali during the regular mathematics block. For example,

1

4

1

6

1

4