My kids can : making math accessible to all learners, K–5

Becoming a Self-Reliant Learner

TEACHER: Good! What other ways can you find?

ELIZA:[finds the rest of the combinations] I think I’m done.

I felt so encouraged that Eliza kept trying until she felt she had all the combina-
tions (see Figure 18–2 on page 156).
During group time, when the class was sharing combinations of 10 red and
blue crayons, Eliza raised her hand.

ELIZA: 8 red and 2 blue.

TEACHER: How do you know?

ELIZA: I said 1, 2 [holds up fingers as she counts] 3, 4, 5, 6, 7, 8, 9, 10.

Several things happened during this assessment that showed me how far Eliza had
come in taking responsibility for her own learning.

1. Eliza listened to the instructions.


2. She knew the materials she needed to be successful with the activity.


3. She determined that she needed help and came to find me.


4. She persisted until she found all of the combinations.


5. She volunteered to share her work with the class.

Next Steps

Although I know my work with Eliza isn’t finished, I feel as if we have made good
first steps. I will continue to explicitly model strategies that work for her, keeping
in mind that I need to take my cues from the strategies that are already her own.
Trying to impose strategies might impede connections that she is making herself.
I will continue to work one-on-one with her, then scaffold her to partner work.
Past observations tell me that I need to vary her partners so that she learns to work
with a range of people and not become dependent on any one person. I am confi-
dent that eventually Eliza will be able to choose an appropriate partner herself.
I will work to make sure the activities are not too hard for Eliza, but push her
just beyond what she can do independently (her “zone of proximal development”
[Vygotsky 1978]). When playing games or learning a new concept, I will back up
to numbers that she is comfortable with and move from there. I’ve wondered, for
instance, what would have happened if I had started her off playing Counters in
a Cup with only 5 counters instead of 8. Would she have been able to develop her
own strategies with the smaller number of counters and then been able to move
on after developing a solid foundation? I am pleased that she has progressed to be
able to play the game with 10 counters, but I will think carefully about starting
with smaller numbers when the next challenge arises.