representation would support her in explaining her thinking. Our conversation
follows.
TEACHER: What about 6 and 7? Which is bigger?
TAMARA:7.
TEACHER: How do you know?
TAMARA: 7 is biggest and 6 is smaller.
TEACHER: Can you show me with the cubes?
TAMARA:[makes sticks of 6 and 7 and holds them up together] See?
TEACHER: How many bigger is 7 than 6?
TAMARA:7.
TEACHER: Hold them up together again. How many more is 7 than 6?
TAMARA: Oh! One more.
TEACHER: Yes, 7 is 6 plus 1 more.Planning an Intervention
Analyzing the interview, I was thrilled to have so much information about Tamara’s
mathematical thinking. It had taken months to gather the end-of-unit tests, but in
just fifteen minutes, I had learned so much more about her strategies. This individ-
ual interview provided me with a picture of her strengths as well as her needs. I saw
what she understood about comparing numbers and discovered that the number
line was an important foundation for this thinking. She did not seem to have in-
ternalized the idea that each number is quantitatively one more than the number
before it. This information gave me a place to start to plan appropriate instruction
for her. To help her further develop her number sense, she needed support in work-
ing on the 1 or “one more” pattern. Looking at our interview, I also decided to
work from the number line, because it was her strength, and to continue compar-
ing quantities using the concrete model of interlocking cubes. I thought that the
cubes would help her connect her understanding of the numbers in a number line
to a concrete model that we could use to highlight numbers as quantities.
I was eager to try out my plans, but as a first-year teacher, I was concerned
about how to manage the rest of the class during multiple one-on-one interven-
tion sessions. Timing was important. I wanted Tamara to participate in the
minilesson and sharing with the whole class, but, during independent practice, I
planned to work one-on-one with her. So, like the interview, the intervention
also took place while the rest of the class was practicing independently.
I gave Tamara a large piece of construction paper with a 0–10 number line
draw across the bottom and asked her to make sticks of cubes to show each num-
ber on this number line. She went right to it.
LINKINGASSESSMENT ANDTEACHING