Going Beyond Counting: Exploring Early Math Through Stories

Last month, Mme Rigolotte started a new series to dive deeper into early mathematics. This series is a complement to our introductory post and earlier discussions on concepts like spatial awareness and patterns. With so many free research-based resources available online, our main hope with this series is to raise awareness about early mathematics and share ideas with anyone curious about young children.

We began by exploring how young children process numbers and develop counting skills. Today, we are going beyond counting, and introducing story problems, also known as number stories or math stories (though I would argue that any story, in some way, has math in it : )

How I got Hooked on Early Mathematics

I will be honest—engaging young children with story problems is how I became fascinated with their thinking, and hooked on early mathematics. It has been one of my favorite activities to engage 3 to 5 years old for the past 10 years. I often just start with bringing bags of items like cats, dogs, dinosaurs (or even Pokémon : ), and wait for the magic to happen. Given the imagination of young children, I know they will start telling stories—about cats, dogs, or sometimes a mix of both. These stories open the door to all kinds of mathematical thinking, allowing each child’s uniqueness to shine through.

How to Engage Young Children in Mathematical Thinking through Stories

There are several ways to engage children beyond counting through stories. Depending on their interests, you can adopt a child-centered approach, allowing them to take the lead and build on their ideas. You can also use a more adult-directed approach, guiding them toward a specific math concept, such as addition or subtraction. Alternatively, you can navigate between these two approaches as needed. As often discussed on our blog, listening is key.

Let’s take the example of a story from Petite Clothilde, with Mme Rigolotte following her lead, asking questions that stimulate her mathematical thinking and keep the conversation going:

Petite Clothilde: One day, a dog came to see a cat. They walked around and found more cats!
Mme Rigolotte: More cats?
Petite Clothilde: Yes, two more cats!
Mme Rigolotte: Then, what happened?
Petite Clothilde: The dog wanted to find more dogs!
Mme Rigolotte: Oh? How many more dogs is he looking for?

Here is another example of a story, where Mme Rigolotte takes a more guiding role:

Mme Rigolotte: Once upon a time, there were 3 cats. They were walking around and meet 2 more cats. They all decided to climb on a tree! How many cats are on the tree?

In this scenario, Petite Clothilde may pull out 3 cats, then pull out 2 more, and count them all. Over time, she may draw the cats, use her fingers to count, or simply know that 3 plus 2 equals 5.

Embracing an endless Range of Possibilities

The range of possibilities in these “number stories” is endless. As mentioned above, they offer opportunities to practice balancing talking and listening—something we explored in a previous post. These stories also allow us to dig into a variety of mathematical concepts, such as addition, subtraction, multiplication, and division. Yes, even multiplication and division are concepts young children can explore early on. Of course, it is not about formally teaching them these operations but rather allowing them to explore and make sense of these ideas on their own. Here are a few examples, that Petite Clothilde may say as she plays, or that Mme Rigolotte may add on this guide her further in her thinking.

“There was one cat, then two more came. Now we have three cats!” (addition) “One of the cats got bored and left, so now we have two.” (subtraction) “They found a nice lady who gave each of them two buttons to play with!” (multiplication). “She had 4 more buttons in her bag and wanted to give them to the three cats so they would all be happy. How could she share them?” (division)

And of course, stories offer opportunities to not forget zero! “Petite Clothilde, how many dinosaurs do you gave in your story?”. Giggles, giggles. “Zero!!!!”

Finally, do you remember our post about units? When talking about cats and dogs, Petite Clothilde might eventually change units from “cats” and “dogs” to just “animals” or “pets” once she have counted them all. Opportunities are endless.

Math is Everywhere, including in Stories

We hope the few examples above illustrate how you can go beyond counting to explore more advanced math concepts in a playful, hands-on way. We will continue to dig deeper but for now, what questions do you have to start endorsing stories? They, indeed, allow children to build a deep, intuitive understanding of math concepts early on, setting a strong foundation for future exploration. Let’s all get hooked on early mathematics!