they could refer back to these familiar strategies. I also discussed with the class
how to facilitate thinking with a partner so that each partner contributed ideas.
We talked about how to help a partner without giving answers and how to come
up with good questions we can ask when a partner is stuck.
The next day I observed Eliza successfully playing How Many Am I Hiding?
(Russell et al. 2008f), a similar game using the same strategy that had worked well
for her when she played Counters in a Cup.
AIDEN:[hides 3 cubes behind his back] How many am I hiding?
ELIZA:[counts cubes in view] 1, 2, 3, 4, 5, 6, 7 [then continues on fingers]... 8,
9, 10. Three are hiding!These initial steps with Eliza seemed to bring her increased understanding of the
mathematics and led her to begin to develop some responsibility for her own
learning. She began to come to me more frequently for help, and I often observed
her in a small-group setting using some strategies that I had made more explicit
for her. This seemed to also give her the confidence she needed to share her
strategies with the whole class. Her subsequent work on an assessment activity in
April provided further proof of the progress she was making.
Assessment Activity: Ten Crayons in All
I have 10 crayons. Some are red. Some are blue. How many of each could I have?
How many red? How many blue? Find as many combinations as you can. (Russell
et al. 2008i)Eliza listened to the instructions and then went to the manipulative shelf and got
10 red cubes and 10 blue cubes. She then came to me and asked for help. I read
the problem aloud and Eliza connected together the 10 red cubes.
TEACHER: I’ll read the problem again, and let’s check to see if we have all
the parts of the problem. “I have 10 crayons.” Do we have 10 crayons?
ELIZA:[counts 10 cubes]
TEACHER: “Some are red, some are blue.” Do we have red and blue crayons?
ELIZA:[takes off 2 red cubes and replaces them with 2 blue]
TEACHER: How can you show on paper what you have here?
ELIZA:[writes: 8 red 2 blue]
TEACHER: Is there another way?
ELIZA:[takes 1 blue cube off and replaces it with 1 red, records 9 red 1 blue]
TEACHER: You have two ways now. Do you think there is another way?
ELIZA: I can switch them around! [builds with cubes and records 2 red 8 blue
and 1 red 9 blue].TAKINGRESPONSIBILITY FORLEARNING