counting the total number. When I asked Kristen to tell me what each row on the
table meant, she was able to generate a sentence that related the number of floors
to the corresponding number of rooms (“When the building has 2 floors, there are
6 rooms”). (See Figure 10–3.)
Once she was solid with the 5 floors, I worked with her to extend the rela-
tionships to 10 floors, something the rest of the class was able to do on their own.
Kristen faltered when the total number of rooms grew greater than 20. However,
I was pleased that she was able to persist and recognize the relationships that were
generated up to 5 floors. Having the cubes to count helped her solve this prob-
lem. Without the counters, her understanding was still fragile when working with
a number as large as 30 rooms.
Reflections
Working with Kristen has been difficult at times, but it has forced me to think
more deeply about the mathematics I teach. It has been an opportunity for me to
deepen my understanding of how early counting and number sense lay the foun-
dation for the counting work and development of number sense that we focus on
in second grade. I spend so much time with second-grade activities that I don’t al-
ways have the opportunity to spend time thinking about how number sense devel-
ops before second grade. I learned that it is important to have the understanding of
how number sense develops at the forefront, instead of planning one accommoda-
tion at a time. Once I deepened my own understanding, I was able to begin to in-
tegrate the early counting and number sense experiences into my planning for
LINKINGASSESSMENT ANDTEACHINGTotal Number
of FloorsTotal Number
of Rooms
13263 94 12515Figure 10–3.