When we gathered back together as a whole group, I asked the students from
the guided math pullout group to explain to the rest of the class how they figured
out their answers. We had already shared in our small group. All of the students
shared their answers confidently. Some students showed visual drawings of making
22 cones with 2 scoops and counting by 2. Others showed how they just added 22
and 22 together. None, however, used manipulatives to help explain their think-
ing. They seemed much more comfortable using the manipulatives within the
smaller group. Although the use of manipulatives is always an option for my stu-
dents, sometimes my struggling students want to do the problems mentally as they
see other classmates do. I don’t want to mandate that everyone use manipulatives
for every problem, because there are always students who can solve problems men-
tally and record their thinking. However, some students, especially those who
struggle, often start with manipulatives but when they try to finish by solving the
problems mentally, they get confused recording what they did. I want students to
use whatever problem-solving strategies work for them, and I want them to know
that manipulatives and drawings are valid approaches. I talk with the students
about how they might connect the manipulatives or representations to the math-
ematical equations and ideas in the problem. The manipulatives may help them
see the concept, but students must make sure they understand what is happening
and why.
I let my students know that manipulatives are also helpful in explaining
mathematical ideas to others. Doubling the cubes in the container is the per-
fect example. The cubes made the solution more accessible because students
used them to show the process of doubling, whether it was by doing 22 stacks
of 2, or 22 scoops, then another 22 scoops on top of those. Both of these
methods reinforced the action of doubling. Working with this group, I was
pleased that they could model the problem with manipulatives and explain
their work.
The students in the guided math group were able to work on the rest of
the problems from this lesson on their own, so I was free to check in with the
other students in the class. The guided math group students were now more
confident and stayed on task. I could tell that they felt successful. I checked
back in with them and reviewed some of the things they noticed about dou-
bling. Some of their statements included, “The numbers get bigger.” “You can
add the number to itself to find the answer.” “You can multiply the number
by 2.” I sent everyone back to their seats and, as a whole group, we discussed
what the students had noticed about doubling. My guided math students were
quick to raise their hands to respond, and I was thrilled that they felt
successful.
MAKINGMATHEMATICSEXPLICIT