**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:

- Pam Wilson, getting started
- Malke Rosenfeld, walk through
- James Cleveland, in Algebra II
- Frank Noschese, in physics

**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:

- Jennifer Moon, Counting Circles
- Sam Dunneback, Counting Circle
- Brian Forster, More Than Answers
- Brooke Ramsey, Act I • Amanda VanderMeulen, Counting Circles

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.

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