7

Assessing and Supporting Students

to Make Connections

Developing Flexibility with Counting

Ana Vaisenstein

Since 2003, I have focused my work on better understanding how to teach stu-
dents who struggle with math. Whether I work with students in general edu-
cation classrooms or students with special needs, I want all my students to
understand math and be efficient problem solvers. For students to understand
math, they need to make connections between what they already know and
new information. They also need to integrate knowledge they have from dif-
ferent contexts and use it in flexible ways—for example, applying information
they learn from playing a game when solving number or story problems and
vice versa.
Some children easily make these connections by themselves, and other stu-
dents need assistance from a teacher. My students challenge me to think deeply
about how to support them in making those connections. It is only when I com-
prehend how they are making sense of an idea through their words, actions, and
written work that I can identify how many of those ideas they are connecting
from one context to another and what connections they are not yet making. This
ongoing assessment guides my teaching. Instead of just following the sequence in
the curriculum, I make decisions about what to do based on what I know about
my students and the mathematical ideas they need to learn.
Children, like adults, make connections in different ways. Often my mistake
has been to think that by providing a specific activity, manipulative, mathemat-
ical model, or representation, the student will slowly “get it” by automatically
making the connections I expect them to make. What has become clearer to me
is that (1) no one activity, manipulative, mathematical model, or representation
guarantees understanding, but it is what students do with them over time that fa-
cilitates understanding, and (2) students will make connections in ways other
than the ones I expect.