By John Golden, Posted September 29, 2014 –
Is it okay to blog about something that is not my
innovation or lesson idea? Certainly! Blogging includes sharing your practices and things you’ve learned from other
teachers. In the Math Twitter Blog-o-Sphere (#MTBoS), I
love reading how teachers share and implement one another’s ideas.
At Twitter Math Camp 14, I blogged
about my desire to implement Counting Circles. I learned it from Sadie Estrella
who has blogged
about it (read the Blame
Game first) and shared her
materials. As Sadie points out, the Counting Circles activity connects to
Jo Boaler’s Number Talks; she, in turn, cites Ruth Parker and Kathy
Richardson.
A more few posts to read about Counting Circles:
What Is a Counting
Circle?
Image: John Golden
I introduced Counting Circles to my preservice
teachers and emphasized the following:
- We’re going to count up or down by a specified amount from a given starting
value.
- You have plenty of time; there’s no rush.
- Please don’t comment on other people’s counts.
- If you make a mistake, it’s not a problem. We’ll go from what you say.
- When we stop, I’ll ask you a question about what would happen if we had counted
on. When you’ve got an answer to the question, put your thumb up by your chest.
I’ll ask for volunteers to share their thinking.
My first Counting Circle with college math students was
pretty stiff: up by 97, starting at 235. It wound up being a little
uncomfortable for a few people: up by 99 might have been better. (If you ask
her on Twitter, Sadie will help you figure out a good counting amount and
starting point for your students.) After 1.3 times around the circle, at 2175,
I paused and asked, “What would Amanda say?” (5 people farther around the
circle). When all students indicated that they had an answer, I asked for volunteers
to share their thinking, recorded it as they spoke, and elicited details. The
shared strategies included noticing that the units place went down 3 each time,
from adding 100 and multiplying 97 ´ 5 and adding it to 2175. Even the computation can be
interesting: 97 ´ 5
used partial products to get 485, and then one individual added the 5, the 400,
and then the 80. My advice for the Number Talk at the end: push for elaboration
on thinking and details. It’s rich material, helpful to students, and ripe for
representation.
I recently asked if students wanted to squeeze in a
counting circle. An enthusiastic yes ensued. With just a few minutes, it was
worthwhile to highlight number sense, thinking, verbalizing, and noticing. The
count: up by 3/4, starting at 11.
“Can we use improper fractions?” Sure. Other students
went back to mixed numbers, where more interesting thinking occurred. “What is
the third next whole number we would hit if we kept counting?” And who would say it?
Students’ thinking mostly centered on the pattern of
whole numbers for every 4, and each number being 3 higher. Why would that be?
There was an audible gasp when the student shared 25 1/4 + 27/4 is 25 + 28/4.
I am seeing the culture-setting power that Sadie
described, including accepting mistakes, willingness to share, and valuing of
process over answer. This practice has made an impression on students as well,
becoming the topic of several of their first blog posts for class:
Now, form a circle. Start at 5 and count back by
eleven hundredths. . . .
This is my last Blogarithm post. It’s been fun to
share some of what I value from the online community of math teachers. I hope
you, too, consider tweeting or blogging.
John Golden, @mathhombre, is a member of the department
of mathematics at Grand Valley State University in Michigan. He teaches math
and elementary and secondary teacher preparation courses. At
mathhombre.blogspot.com, he blogs about math games, geometry and GeoGebra, lesson
ideas, and teacher prep.