## Sunday, August 16, 2015

### Counting Dots

A teacher asked me about the Counting Dots activity I did in her teacher workshop I facilitated a couple weeks ago. I did the Counting Dots activity as a follow-up to Max Ray's Ignite talk: Why 2 > 4. I believe we teachers need to experience how valuable it is to listen to each other share strategies. If we're going to do it in our classrooms with students and value student thinking by listening to them, then we need to practice ourselves. You know? Build that muscle memory.

I was inspired by Dan Meyer's 2014 NCTM talk titled Video Games & Making Math More Like Things Students Like. You can find his specific reference to Counting Dots at the 30-minute mark. This link includes Dan's NCTM session and references to Ruth Parker's work, who according to Dan popularized Counting Dots.

I also made a video of the exact slides I used with teachers, a few extensions to counting dots, and a behind-the-scenes for anyone interested in making their own.

Questions? Let me know.

Dots,
1200

Graham Fletcher shares an insightful article on Subitizing.

Dan Kearney shares more goodness from Steve Wyborney.

1. Love the low-entry, high-scalability of counting dots.
One thing to "add another wrinkle" as you put it... counting dots is also called subitizing which I'm sure you knew. When students subitize, they identify a quantity of dots by grouping parts of the whole (which you mentioned in the video), however no part will be greater than 5.
Doug Clements wrote a bang-up article on subtizing which is super insightful on the topic. http://gse.buffalo.edu/fas/clements/files/subitizing.pdf
Figured you might want to check it out as you continue to stay true to your #1TMCthing.

1. Hey Graham. Great article! Thanks for sharing!

2. also look at Steve Wyborney's work, http://www.stevewyborney.com/?p=504

1. Super Steve!
Thanks Dan. How'd I miss this?

3. Jo Boaler is all about this too. It sounds like counting Dots is a safe introduction to Number Talks. I like how you can interpret the students visualization and then write an expression that represents their thinking, making that connection.

1. I can't find this, Martin. Have a link?

2. Here is a youtube video of Boaler conducting a dot card number talk. https://www.youtube.com/watch?v=-pJhCAiaV-Q

3. Thanks Denise!

4. I like that this has low barriers to entry but many possibilities. I'm thinking of using it on the first day of school with my 8th graders next week with the emphasis being on active listening. The missing dots reminds of the border problem from Jo Boaler over at youcubed.com. Thanks.

5. Andrew
Here is how I used the Counting Dots lesson. I created my own ppt of "Counting Dots" to try out on my 8th math group. When I watched the video, I saw the potential for application to modeling the concept adding integers. We started with easy amounts to count, and the strategy we came up with was "count by counting", but as the number of dots increased they came up with new strategies. When adding integers, the number line or algebra tiles can be used for smaller quantities but new strategies were necessary to count larger quantities.
Thanks for Sharing!

1. Thanks Dan.
I'm definitely intrigues with the idea of using this as another representation for students to better understand integers