TEACHER: So—
TAMARA:[interrupts without looking up from her paper] I want to keep going.As I watched, she repeated each equation aloud to herself and then wrote it
down. She worked diligently, carefully looking at the number above in each col-
umn to assure she was continuing the pattern. Although I was thrilled she noticed
a pattern and was eager to extend it, I still didn’t think she recognized that any
number plus 1 is the next counting number. When she came to the end of the pa-
per, at 1 11 12, she looked up at her large 0–10 number line (where we were
earlier placing the sticks of cubes).
TAMARA: We should do longer. [I jump up to get her another large piece of pa-
per and quickly tape it to her other number line. She draws the line and marks and
writes up to 23.]
TEACHER: So if you move from 9 to 10 how many do you move?
TAMARA:[looks at number line] 1.
TEACHER: What about 6 to 7?
TAMARA:1.
TEACHER: Any number plus 1 is the next number. After 6 is 7.
TAMARA:[taking ownership of the language, she follows along the number line
chanting.] After 7 is 8... After 8 is 9... After 9 is 10... [Hoping she will trans-
fer this to the dice, I ask her to roll the dice again. She takes the dice and rolls a 4 and
a 1. Before she can count all, I ask her what comes after 4. She responds 5.]
TEACHER: How do you know?
TAMARA: Because you can see the number line. [She begins to roll the dice and
rapidly call out in a rhythmic tone.]
TAMARA: After 6 is 7... after 3 is 4... after 5 is 6... [I am delightedly cheering
her on. In response, she quickens her pace, equally excited by her discovery. I stop her
one last time to ask how she knows each sum so fast without counting the numbers up.]
TAMARA: After one [number] is the next.I felt that Tamara was recognizing that what she already knew from counting and
the number line (i.e., after 7 is 8), the same thing as adding 1 or plus 1. Even
though she already knew that “after __ is __,” she was still counting all
when asked to add 1 to any number. I wanted her to realize that she knew what
came next and that was what “adding 1 more” meant.
Reflections
Since that day, Tamara has frequently requested that we “play that game with 1”
and we have. Empowered by her understanding, she even proudly demonstrated
After One Number Is the Next!