about their thinking and were able to offer explanations and listen to the strate-
gies of their classmates. Their progress was brought home to me during another
math club session when the group described a lesson taught by a guest teacher.
During the course of a lesson on rate of change, the guest teacher had written the
following: 3 5 5 5 5 5. My students wondered why she wrote
all of those 5s and explained to her that it would be more efficient to write 3
(55). I realized the guest teacher had written exactly what was in the teacher’s
edition, not realizing that these students could see 3 (55). The students told
me that she didn’t ask questions about what they were thinking, Heather added,
“It is just that when you or other kids ask questions, the questions help me think
about what I’m supposed to do. Sometimes I get started but can’t figure out what
to do next. You don’t tell us what to do but you ask us a question to help us think
about the problem.” Heather was describing how she becomes un-stuck.
Reflections
This was an enormous change from the small group of reluctant learners I had
worked with at the beginning of math club to the group who ended the school
year with more confidence and ability to use reasoning to solve problems. The
math club had a clear purpose that the students and I all shared: to help them
understand how they think, know what to use to help them when they are stuck,
build on their strengths while understanding their gaps, and use what they have
learned to determine entry points for the daily math work.
Before each session I was explicit about our mathematical goals. To accom-
plish these goals, I always reviewed the prior lessons, and together we worked
through examples that would provide connections to the current work. With
each example, we talked about not only what their solution was, but how they
arrived at it and what they needed to pay attention to.
Not only did Heather demonstrate growth in understanding number con-
cepts, she also helped me clarify and further develop the strategies I use to assess
learning, build understanding, and foster independence and confidence with all
my students. As my students said near the end of the year, “If we say we don’t
know, you don’t give up on us.” I hope never to give up on any student and
believe all have the ability to be mathematical thinkers.
TAKINGRESPONSIBILITY FORLEARNING