- discussing possible order of clues that narrow the search quickly (for ex-
ample, after recognizing the range, is it more efficient to list all the odd
numbers or list the multiples of 9 or the square numbers?) - reviewing definitions of words such as multiple, factor, prime, even, square
numbers - providing supplemental work with multiples, factors, and squares
Gradually, Tasha began to participate in discussions and was often able to supply
reasonable answers using some of the strategies listed here. As she experienced
more success, she gained confidence and began attempting to explain her math-
ematical work, which in turn built her understanding of mathematics.
Makes Connections to Prior Knowledge
It was also important for me to learn about Tasha’s strengths and find ways to help
her apply those when encountering a new problem. For example, Tasha often
used money as a tool to solve problems. When I wanted to introduce her to dou-
bling and halving as a strategy, I started with a context involving money. I knew
that Tasha and her sister often went shopping together, so I presented the fol-
lowing problem: If I gave you $2.50, how would you share this equally with your
sister? At first Tasha used actual coins, but eventually she was able to solve more
problems like this mentally. Tasha was then able to make connections to the
doubling and halving strategy in other problem contexts.
Another strength of Tasha’s seemed to be visual representation. The array
model appeared to make sense to her. Reminding her of this strategy helped her
get started on and solve multiplication problems (see Figure 20–5). When Tasha
was unsure about how to start a problem, I prompted her to remember concepts
from previous lessons that could provide an entry point, for example, “Do you re-
member how you made a list of factors of 100? How could those factors help you
find the factors of 300?” I often reminded Tasha and her group, “What have we
done before that was like this?” Another strategy I used to stress the importance of
making connections to prior knowledge included posting strategy charts around
the room. These charts highlighted problem-solving strategies that students came
up with. I even developed a miniature version of a strategy chart that students
could use at their desks. Eventually, Tasha used these resources to help her with
her work. For example, Figure 20–6 represents Tasha’s solution to the following di-
vision problem: How many groups of 4 pencils can you make with 720 pencils? Not
only were the methods she used from the strategy chart, but she was able to show
her work and explain her thinking. (She used an algorithm that my students called
the “Forgiving Method” and a second method using clusters to check her work.)
TAKINGRESPONSIBILITY FORLEARNING