TEACHER: How many counters do you think are in the cup?
ELIZA: I think there is 6. I really don’t know.
TEACHER: How many counters did we start with all together?
ELIZA:8.
TEACHER: Show me 8 fingers.This was my attempt to show her with her own fingers that 7 and 1 make 8. She
couldn’t show me 8 fingers, so I physically helped her hold up 8 fingers and
together we counted the 8 fingers.
TEACHER: Let’s say that this finger [points to 8th finger] is the counter that
we can see, and the other fingers are like the counters that are in the cup.
ELIZA:[counts remaining fingers slowly] 7 in the cup?
TEACHER: How can we find out?
ELIZA: Let’s check in the cup. [Together, we count the counters in the cup.]
There are 7.
TEACHER: Let’s try again. [hides 1 in the cup, 7 counters are showing]
ELIZA: One in the cup?
TEACHER: How did you know?
ELIZA: It’s hard to explain. My daddy taught me there is 1 in the cup.
TEACHER:[hides 3 in the cup, 5 are showing]
ELIZA:[counts the counters that are showing] 1, 2, 3, 4, 5. [recounts] 6? 7? I
don’t know. [Together, we count the counters that are showing.] 1, 2, 3, 4, 5.
[Holding up 1 finger at a time, we continue counting.]... 6, 7, 8.
Teacher: How many fingers are showing?
ELIZA:3.
TEACHER: How many counters do you think are in the cup?
ELIZA:3!I continued working with Eliza, teaching her to count the counters that were
showing, then continue on her fingers until she got to 8. After many repetitions,
she was successful part of the time on her own.
As Eliza began to have success with these strategies during one-on-one situa-
tions with me, I began to scaffold her work with me to her work with a peer. I did
this by staying close to her as she worked and shared strategies with a partner,
sometimes helping her verbalize her thoughts. I gradually encouraged her to be
less dependent upon my support and rely more on her own words. When she was
stuck, I asked guiding questions to get her back on track: “How did you know
that?” “What did you think about next?” I also made sure to post all of my
students’ problem-solving strategies as they shared them. This provided students
with a place to start working more independently. As they solved new problems,
Becoming a Self-Reliant Learner