Everywhere Math

In this video, my children are observing some slugs we’d brought inside to be our guests for a night. I was forever asking them questions that began “How many …” It’s a lovely, simple way to begin a mathematical conversation with young children. At a certain point in the video, however, we can see that quantifying our slugs raises additional questions: Do we have the same number of slugs? If not, who has more? And, most pressingly, how can we remedy this situation and make it fair?!

I wish I could go back in time and find out more about my children’s thinking! It’s likely that in the moment I could tell our time was up. Preschoolers will not give you an unlimited amount of time, and they’ll let you know when they’re done! They’ll stop engaging with you, walk away, introduce a brand new topic, or say, “Mommy, I don’t want to talk about that anymore.”

Young Children Understand A LOT

I wish I could understand Alex’s counting more deeply! When I ask how many slugs he has, he says assertively, but independent of engagement with the slugs in front of him, “One!” Then he looks down and counts (beautifully, I want to add!), “Two, three, four, five.” He’s done a couple of things that, now that I know a lot more about very young children’s development of mathematical thinking, really impress me. He’s assigned one count to each slug, even though he appears to have started his count of the slugs at “two.” He also understands that counting is a way to answer the question “How many?” These are important understandings and skills for such a young person!

The Difference Between Counting & Perceiving

In contrast, his big sister did NOT count to check his work. When I ask if he really has five slugs, she pauses and then says no, he has four. In that moment, she has subitized: that means she has ascertained the number of slugs visually and didn’t appear to need to count them to confirm the total. (Without getting too far into the weeds, we call this perceptual subitizing and most people can perceive the total number in a collection of about up to 6 or 7 randomly arranged objects. If we arrange the objects in equal groups (e.g., groups of five or ten), however, we can bring additional understandings to bear upon the question “how many,” and in that case we are engaging in conceptual subitizing.)

The question of how many slugs Eloise needs in order to have four — the same number of slugs her brother has — likely appears pretty simple to many of us. But this is a very complex question for such a young mathematical thinker! And she’s gone a long way toward grappling with it. She knows 4 slugs is more than 2 slugs. She knows she needs more slugs to restore fairness to our family slug situation. And she knows that if both she and her brother have 4 slugs apiece, that would be a fair situation. But thinking about how much she needs to get from her current 2 slugs to 4 slugs isn’t quite clicking.

Following Children's Lead Toward Justice

At a certain point, I invite her to use her fingers as though they are slugs, and here’s where I lose her! I could tell we were done when I asked if she’d like to use her fingers to show the slugs and she said “No.” I’m not sure if she was tired of my prodding or whether the idea of representing a real thing (slugs) with something else (fingers) was just a little too uncomfortable at that moment. I was happy to stop because she seemed grouchy, it was night time, and I didn't have any more slugs in that moment. However, if I'd had more slugs at the ready, we could have truly established fairness by adding two more slugs to her collection to create two equal collections: four slugs for Alex, four slugs for her. That might have met both her intellectual need for a concrete, literal mathematical solution and her emotional need for resolution and fairness.

We can help even very young children use mathematics as one way to consider an emotionally or socially charged situation and bring some resolution to it … or at least consider what would be required to achieve resolution. Now that my children are preteens and teens, I can see they have not lost their inclination to strive for fairness and, more broadly, justice. But as they mature, their ability to advocate for themselves and others, and their agency to remedy many problems on their own, has increased. Similarly, their perspectives have broadened and their understanding of the world has expanded. Mathematics is one of many tools they can use to understand the world they are part of and to promote justice in that world.

About This Site

Everywhere Math helps families of elementary-age and middle-grades children think about math wherever they happen to be: the more you look for opportunities to do math, the more you'll see math everywhere! We'll also discuss how to help children with schoolwork in an online or blended setup.

The newest post is always here on the home page. Past posts, activities, and other resources are available via the links above.

This site is meant to complement, not replace, instruction from teachers. The mathematical ideas featured here are ones usually addressed in elementary and middle school. Don't be alarmed if your child isn't familiar with some of these ideas: they might not have learned the math yet, they might have forgotten, or they might not recognize the math in a new setting.