Kyle had a bag of 8 chess pieces and a bag of 7 dominoes. He wrote an 8 and
drew one chess piece, and wrote a 7 and drew one domino. He said he knew that 8
was more because 7 comes before 8 when you are counting. This was a strategy that
some children used and shared to figure which number was higher when playing the
card game Compare, and Kyle applied the strategy to a different comparing task.
Latisha worked with Taryn. They had 6 Halloween pompoms and 5 crayons.
Taryn wrote the numbers and drew one of each object to show what they had,
and circled the 6. Latisha counted the pompoms over and over. She was accu-
rate every time. One time, Taryn interrupted her after 4, and Latisha answered
her and continued to count correctly, 5, 6. After each count she made marks on
her paper. She looked like a very young child playing Mommy or Teacher as she
spoke in a grown-up voice and mimicked how an adult writes on her clipboard.
Her writing is a collection of protonumbers and suggestions of letters, but she has
made significant progress in her willingness and ability to count quantities under
- I was pleased that she was persistent and understood what the task required.
Reflections
I will continue to think about how and when to be explicit about the mathemat-
ics we are working on with this and future classes. There are times when it is re-
ally helpful to tell the whole class, “This is the math idea in all these games,” or,
“If you are doing this activity the way I expect, I will see lots of so-and-so and hear
lots of such-and-such.” My experience with the Compare activities showed me
how important it is for me to direct my struggling learners to focus on an impor-
tant part of a math activity or an important behavior that will help them become
confident, independent learners. My experiences with this class, which needs so
much direction from me to have smooth and productive days in school, also
show me that being explicit doesn’t preclude those important chances for stu-
dents to make discoveries or think independently. My telling them to think
about a certain topic, or to try a certain strategy, actually helped my struggling
learners to have good ideas like comparing puppets’ sizes or using paper cube
strips to record and compare the lengths of classmates’ names. They needed me
to make the mathematical focus clear for them to play the games successfully.
The repeated practice then helped them gain the skills they needed to see con-
nections among the activities and learn the important mathematical concepts.
It has been very helpful to extend what I have learned about being very explicit
about desired behaviors to being very explicit about what math the students
should focus on. And really there is a way in which building a sand castle on
someone’s head is an interesting idea.
You Can’t Build a Sand Castle on a Classmate’s Head