tests as the only form of assessment was dangerous in the same way because I
was highlighting only her areas of need and then feeling overwhelmed by the
amount.
After I had spent nearly a week mulling over the list of Tamara’s strengths
and needs, I was still unsure what to do next. On my morning commute, I was
leafing through my new issue of Teaching Children Mathematicswhen I came across
the article, “Focal Points—Pre-K to Kindergarten” (Clements and Sarama 2008).
In this article, Douglas Clements and Julie Sarama explicitly identify and analyze
the components of building early number sense. Both the detailed way in which
number sense was broken down and the developmental sequence that the authors
illuminate allowed me to see not only whereTamara fit in, but also thatTamara
fit in. Knowing where she fit in would help guide my interventions with her be-
cause I could be more precise about what areas of her mathematical understand-
ing she most needed support with to move forward. Knowing that she fit in made
me feel more confident that the work I was doing with her was worthwhile, valu-
able, and sensible.
The Interview
I was curious about Tamara’s ability to compare values and, yet, her need to count
up from 1 each time I asked her how many there were in a set. To understand her
thinking, I needed to ask her about it. I returned to my graduate school work of
conducting math interviews with students. These interviews are built from one
question you have about a child’s understanding. Interviews are short sessions
that present increasingly challenging tasks aiming to reveal a child’s thinking on
a topic. The teacher records the exchange (notebook, audio recorder, or video)
and analyzes the thinking.
So, my assessment of Tamara’s understanding continued with an interview.
It took place in the fifteen to twenty minutes of independent practice time for
the rest of the class. My question was: How does she compare numbers 0–15?
In the frame of reference of a card game, at which she demonstrated success, I
asked her to compare different pairs of cards and explain how she knew which
number was greater. Although she did not articulate that a certain number
comes after another when you count, it was clear that she was thinking about
the number line when making comparisons. Discussing which number, 13 or
15, was larger she noted, “This [pointing to 15] is the front and this [pointing
to 13] is behind,” referring to their placement on the number line. Again,
comparing 5 and 8, her explanation was in reference to the number line: “7
separates them. 8 is far away from 5.” After comparing 5 and 8, I specifically
asked her to compare 6 and 7 because there was no whole number separating
them. This time I encouraged her to use interlocking cubes to see if the visual
After One Number Is the Next!