TEACHER: So could you use the cubes to show that? How would you use the
cubes to show that? [Kristen counts 18 cubes.] Then what would you do after
that?
KRISTEN: Count more.
TEACHER: How many more?
KRISTEN: 18?
TEACHER: Go ahead. [Kristen counts 18 more cubes.] Then what would you
do?
KRISTEN: I would count them all together.
TEACHER: Why would you count them all together?
KRISTEN: To get the number? [She successfully counts to 36.]
TEACHER: So what’s the answer?
KRISTEN: 36.Although she ultimately arrived at the correct answer, I felt I was dragging the
math out of her. I didn’t have confidence that I was offering her a way to build
understanding. This problem was clearly too difficult for her, but it wasn’t com-
pletely clear to me what aspects of the problem were making it inaccessible. Was
it the size of the numbers or coming up with a strategy to solve it? Did she not
understand the concept of doubling or was it a combination of these?
Early Numeracy Assessment
I wanted to know more about what Kristen understood about numbers in general
and counting in particular. I used some of the tasks that I found in the Early
Numeracy Research Project assessment materials (Clarke 2001). I found these
tasks valuable in helping me develop a sharper picture of what Kristen knew
about counting and where her understanding was breaking down. While the rest
of the class was working on our daily Today’s Number routine,^1 I met with her for
three 5- to 10-minute interviews.
I began by asking Kristen to start counting from 1 and to continue until I
told her to stop. She counted successfully until I told her to stop at 32. Then I
asked her to start counting from 48. She counted 48, 49, then paused before con-
tinuing from 50. She counted from 50 to 59, then paused again: 50, 51, 52, 53,
54, 55, 56, 57, 58, 59... 30. She corrected herself; 60, and then continued suc-
cessfully to 65.
LINKINGASSESSMENT ANDTEACHING(^1) Today’s Number is a classroom routine during which students generate and discuss different
expressions that equal a given number to develop fluency with addition and subtraction (Russell
et al. 2008b).