Another reason I have not always been very explicit with my students about
the math in an activity is that I believe that young students should be given the
opportunity to make their own discoveries. I have always thought that I should
not insert my own understanding of the math (or other subject matter), but rather
should let the students construct their own understanding. However, as I thought
about my struggling students, I decided to take steps to make the mathematics ex-
plicit for them.
Grab and Count
In the fall, my class spent a few weeks working on math activities that centered
around the idea of comparing. We started our work on comparing with an activ-
ity called Grab and Count: Compare (Russell et al. 2008a). In this activity, stu-
dents grab 2 separate handfuls of Unifix cubes and determine which handful has
more cubes. Students color in stacks of cubes on a paper to represent their 2 hand-
fuls and then indicate which stack has more cubes. This activity is a variation of
a game we played previously, Grab and Count (Russell et al. 2008a), that requires
students to grab handfuls of objects, count how many they got, and represent the
quantity on paper.
When I introduced the new version of Grab and Count, I decided to start out
with a conversation about the word compare.I asked the class if they had heard
the word before or if they had any idea what it meant, but none of the students
had any inkling. I told them that comparing can happen with a lot of different
things and that when we compared numbers or amounts, we were looking to see
which was more and which was less. We demonstrated the activity with student
volunteers. I reminded them that the point was to compare their 2 towers. I told
them, “If you choose this activity, you will be doing lots of counting and lots of
thinking about which number is bigger.”
Kyle
I knew it was important for me to check in right away with my struggling students
to make sure they understood what was required and that they had an entry point.
Kyle is a student who is very tentative about academic activities. He often asks
for help and reassurance, and he does not like trying new things. He counts ob-
jects up to 6 or 8 before losing one-to-one correspondence. I noticed Kyle would
play the entire game of Grab and Count without doing any actual counting. He
was successful at other steps of the activity; it is in fact possible to determine
which of your 2 towers is larger without doing any counting. Kyle would build his
stacks and then color his paper stacks by taking 1 cube off, coloring 1 cube, taking
You Can’t Build a Sand Castle on a Classmate’s Head