back to the strategy chart to get ideas. I was hoping that by having these two
students point this out, others would be more likely to look back at the chart.
Ana shared how Stephanie moved the cards around to find her numbers.
Stephanie was able to follow up by saying that moving the cards helped her
see how close to 100 she could get, looking at the 10s first and then moving
over to the 1s. Verbalizing these important strategies represented real progress
for these girls. Perhaps the next game, Ana will attempt the strategy of mov-
ing the cards around as well as determining how many more she needs to get
to 100.
Growth Over Time
Through repeatedly interacting with my reluctant learners in small groups and
helping them prepare to share in the whole group, I usually notice growth in these
students’ abilities to express mathematical ideas. By the end of the year, I only
have to ask one or two questions before the students are able to keep the conver-
sation going on their own. When I ask one of my reluctant learners to share his
thinking, that student can usually tell the group why a particular strategy was cho-
sen and possibly even offer a second way to solve the problem. I may also ask the
rest of the class to explain in their own words(a difficult skill to develop) what was
shared, and to connect and compare students’ strategies.
The following is an excerpt from a conversation that took place at the end of
the school year as we reflected on our learning. It’s clear that the students are now
used to and comfortable with the math conversations we have in our classroom.
It takes a long time to get to this point.
June
TEACHER: Throughout this past year, we have done a lot of talking in math. I
remember how hard it was for you in the beginning of the year. How do you
feel about this now and why do you think we have these conversations?
DAQUAN: I think we talk so that we can talk through our math strategies. Like
if we didn’t know how to solve 7 8, we could just think about this out loud.
ANDREA: I thought that math in the third grade was hard, but we make a
lot of connections to what we did in the second grade. That’s what I like
about our talking.
ANTHONY: In second grade, I just did the math and I didn’t really know
why. Now I do math and get to explain my ideas and we talk about it to
understand it more. Everything has to do with math, we tell time, we can
measure how much we walk.Lightbulbs Happen