her to become less dependent on her peers. I began spending one-on-one time with
her as she worked on some math story problems.
Solving Story Problems
One of the first story problems the class solved was: Rosa had 8 books. Max gave
her 3 more. How many books does she have now? (Russell et al. 2008f). Eliza’s
paper had random numbers written on the page (4, 1, 6, 3, 4, 5, 9, 7, 8). During
math workshop, I pulled her aside and asked her to tell me about her work. She
just stared at me blankly. She didn’t have a strategy. I asked her the same questions
that I routinely ask all of my students: “Can you tell me the story in your own
words?” “Will Rosa have more books or fewer books than when she started?”
I also helped Eliza act out the story with manipulatives. Then I asked her if
there was something she could draw that could help tell the story. Eliza drew a
line for each book and a number on top of each line (1–11). I continued to work
with her closely throughout September and October, repeating this scenario for
many other story problems. Figure 18–1 (on page 152) is a sample of Eliza’s work
from the end of our third unit in November. She was able to do this work inde-
pendently. Her work met the end-of-unit assessment benchmarks because she was
able to interpret the problem and combine the quantities accurately by drawing
the books, then counting each one.
I continued to work with Eliza and especially paid close attention when new
concepts were introduced. Partner work continued to be a challenge for Eliza. She
often depended on peers to do the thinking, particularly when playing games.
Games are introduced throughout our curriculum not only to engage children in
fun, meaningful mathematics but also to provide repeated practice for specific
concepts and skills. Counters in a Cup (Russell et al. 2008k) is a game in which
children explore relationships among combinations of numbers of up to 10 and
become exposed to the idea of a missing addend. In the game, children work with
a certain number of counters. One player hides some of the counters under a cup,
leaving the rest to show. The second player looks at the counters in view and fig-
ures out how many are in the cup.
Playing Counters in a Cup
I anticipated that this game might pose a challenge for Eliza. As expected, I saw her
partner doing most of the thinking for her and telling her what to write. At the first
opportunity, I sat down to play the game with Eliza to observe her strategies.
We played the game with 8 counters, and I began by hiding 7 counters under the
cup and leaving 1 in view.
Becoming a Self-Reliant Learner