Mental play with dots

You may already be aware of Number Talks as a powerful solution for building conceptual understanding, confidence and precision in everyday arithmetic.

Well, Dot Number Talks have a very important and powerful role to play. I won't go on about that now (you can explore via the link above). For now, here's an invitation to play.

What to do: Take some time to look at the dots below and make sense of what you see. If you find one way of knowing how many dots altogether, see if you can find a second way of knowing. Notice whether you get the same answer both times.

When you're ready: When you've created a couple of solutions and/or shared ideas with someone nearby, you might like to check out this 45 second video to see how your ways of knowing are similar and different to some other ways of thinking. You might like to consider also which of the solutions (ways of seeing the dots) is your favourite. 

Something to note: There is more than one way to solve a problem efficiently (it's a myth that there is 'only one right way'). Considering that there are multiple methods for approaching problems can be a powerful way to celebrate the mathematical diversity in a group.

Part of this activity is to notice anything that is surprising or interesting to you in someone else's 'way of seeing'. Maybe you'll see something in a new way. Maybe the task or video will simply spark a little joy in you, or someone you know ✨ 

Why play with dots in this way?

If you played along, you might have some of your own ideas about why this is a valuable exercise. But here are three reasons from research to engage regularly in mental play with dots and arithmetic. 

1. Develop adaptive reasoning. Adaptive reasoning refers to the capacity to think logically about the relationships among concepts and situations (1). Thinking about a question or problem in multiple ways supports connections and using logic to explain how we know something is true supports mathematical precision. When we verbalise our 'way of seeing' or of working something out, it gives us an opportunity to pick up on errors. It also helps us build skills for 'working something out', an important area that rote learning approaches completely ignore.
2. Build subitising skills. 'Subitising' is an important skill that involves recognising a small number of things (up to 4) without counting, and even more than 4 when there is a familiar structure in place (like 5 dots on a dice). Engaging regularly in dot talks provides a playful context in which to apply and develop subitising skills which are a foundational skill that children require.
3. Develop groupitising ability. 'Groupitising' is the ability to use subitising to group a collection of dots. A study from 2023, of over 1,200 in grade 3-8,  linked groupitising ability to high achievement in arithmetic (2). 

For more on using dot number talks across the ages, here is an article I wrote for MAV that draws on research and classroom experience. 

References:

(1) National Research Council. 2001. Adding It Up: Helping Children Learn Mathematics. Washington, DC: The National Academies Press. https://doi.org/10.17226/9822 

(2) https://newsroom.unl.edu/announce/csmce/16039/89014