As Monkey slowly learns to talk, my husband and I find it fascinating to observe when and where he uses his “words.” On a hike in the spring he was “woof-woof”-ing at deer, squirrels – any animal we encountered. Now, a couple months later, he seems much better, though not perfect, at differentiating between dogs and not-dogs. I have every bit of confidence that eventually, as he encounters and names more and more animals, he will understand the difference between dog and not-dog as well as any adult.

For a child to learn what a dog is, they need two kinds of experiences:

1. Experience observing things that are like dogs, but are not, and giving them names – some things with four legs and fur are dogs, but some are squirrels, some are deer, some are horses…

2. Experience observing lots of kinds of dogs and hearing them called “dog.” We own a big German Shepherd mix, but in our family and in our neighborhood, Monkey has played with big dogs and little dogs, grown dogs and puppies. He is developing a large context for the word “dog.”

This is exactly the way kids learn about shapes. But children’s experiences with shape are often much more limited than their experiences with animals. Take a look at all the real-world examples of “triangle” in the pictures below:

These are all great examples of triangles to point out to your toddler or preschooler as they learn what it means for something to be a triangle. The problem is that, as varied as the contexts might be, these triangles are all the same! They’re all equilateral triangles (all sides and angles are the same) – what we might call the prototypical triangle, or the kind of shape we think about or draw automatically in response to the term “triangle.” We all have prototypes for words and concepts – particular images that come to mind when we hear the word. But when the prototype is all a child encounters (or even most of a what a child encounters), they miss out on the wide variety of objects that are considered triangles, and they lose some opportunity to identify what a triangle really is – not a “shape that looks like this,” but a shape made up of three straight sides.

Everything in the picture below is a triangle, but many children will fail to identify at least some of them as triangles because they don’t “look right.” They’re turned the wrong way, they’re too skinny, they’re upside down, they’re funny-shaped.

Non-prototypical triangles like these are harder to find in real life. Not impossible, just harder. So when you give your child the opportunity to identify, reason with, and talk about a wide variety of types of shapes, they have a huge leg up when it comes to learning geometry later on in school settings.

What can parents do to help their kids gain a broader experience with shapes?

• Toddler: You are probably already pointing out and naming simple shapes to your child. You’ll likely focus mostly on prototypical rectangles, squares, triangles, but be on the lookout for non-prototypical shapes as well – long skinny rectangles, squares standing on a corner, triangles with sides that are all different lengths. Children’s books with nice, solid, colorful illustrations can be a great place for finding a variety of shapes.

• Preschool: Have your child identify shapes in real life, and shapes that you draw yourself. Play sorting games (look for an upcoming blog post). Have your child draw shapes. Most importantly, when your child identifies a shape, ask, “How do you know?” Do they say something is a triangle because it is pointy? Has three sides? Looks like one? The correct answer is less important at this point than getting them to articulate what they are noticing.

• Early Grades: Give names to less standard shapes: octagons, trapezoids, rhombuses, kites. Notice shapes that have more than one name – a square is also a kind of rectangle (and a rhombus and a kite!). Keep asking the question, “How do you know?” and challenge your child. If something is a triangle because “it’s pointy,” find something that’s pointy and not a triangle to help them focus on what really makes it a triangle.