# Playing with Math at the Playground

By Herbert P. Ginsburg

It is often said that math is all around us. Playgrounds, for instance, can be a great place for caregivers and children to explore the math around them as they play. Let’s see what that means for a young child and a caregiver. (I have italicized the everyday math words used in this blog post.)

# Notice Math Around You

Cassie, 2 years and 3 months old, is at her local playground. Math is all around her, whether she notices it or not. Some of this math would be easy for her; some would be hard and best saved for when she is older; and some will have just the right amount of challenge to be fun and promote learning.

For example, as Cassie is climbing steps on her way to the top of the play structure, the steps can be counted. There are about three steps to start, and then about four or fiveto get to the next level. This is a lot of steps to climb (especially for a young child!). The steps provide manyopportunities for you to promote number learning by talking about counting and quantity (e.g., lots, more, and fewer) as she climbs.

At the start, Cassie climbs to the top, going up and up and up. Later, Cassie climbs to the bottom, going down and down and down.This is all about direction, which is an important part of spatial relations, a key early math topic.

When Cassie begins to climb again, she is at the bottom; when she reaches the top, she is up high, higherthan she was at the beginning. This is all about understanding height and differences in height — again, a part of spatial relations.

Also, notice the white pole with the orange object that resembles a sunflower. It has a big circle in the middle, surrounded by six incomplete circles (partially cut-off circles). Within each of those six are seven smaller circles. The smaller circles and larger incomplete circles are shapes. Their arrangement — circle in the middle, incomplete circles surrounding it, and smallercircles within the incomplete circles — is also all about spatial relations.

So, math is all around us in the sense that it’s there to be seen if you look for it. This everyday math is very different from the formal math you learned in school. But young children love to engage in and learn about everyday math, and it can serve as the foundation for their later learning and success in school.

# Talk About Math in Everyday Life

How can you use the math that is all around us to support your child’s math development? Help your child to see basic math in the everyday world, for example at the playground. The best way to do this is by using language to point out and explore the math in their world.

Here are some examples of what you can say to a 2- or 3-year-old in this setting (again, I have italicized the everyday math words):

• “Let’s count the steps: One, two, three. There are three steps. Look, now there are more steps.”
• “Here’s one more step, and one moreagain. Almost at the toptwo more steps.”
• “We are going up, up, and up. Look down. We’re up high now.”
• “Now we’re going to go down. Take one step down. Now another step.
• “Now look back. Look how far down we’ve come. We’re almost at the bottom. Only two more steps left.
• “Look at the big orange circle over there on the white pole. Look at all these little circles. There are so many of them. Let’s count them.”

# Keep the Conversation Going

After making comments on the math, try to keep the conversation going. The child may make a reply that you will then want to respond to. For example, if you say, “Look, now there are more steps,” your child may say, “Lots of steps!” And then you can say, “Yes, lots of steps. Let’s count them.”

What’s the right number of comments to make? Saying all the examples above would be overwhelming. Say only as much as you feel comfortable saying and what you think your child will understand.

Keep in mind that everyday math conversations are not lessons. Math talk is meant to be a conversation about features of the world that your child will find interesting. Let children enjoy the playground. That, after all, is the primary goal!

# A Final Note

Here is a list of all of the everyday math words in this blog post (I hope I didn’t miss any). At the end, I was amazed at how many there were. There were so many that I decided to list them.

You may think that at least some of these words are iffy; that they are not very “mathy.” It’s true that they do not include words like “equation” or the “equals” sign. But informal math is so fundamental to our lives (and children’s too) that we may not recognize it in the words we speak, just as we are not aware of breathing air. A word like “any” as in, “Do you want any cookies?“ could be translated in formal math language as, “Do you want at least one cookie from the larger set of cookies?” Clearly “any” is intended to convey a mathematical idea. Think about that as you read my list.

Anyway, here are the informal math words. So many of them! Isn’t that amazing? Like totally! Did I miss any? (Math translation: Is there at least one other math word that could be included in this set?)

1. A few
2. A lot
3. Above
4. After all
5. Again
6. All
7. Almost at the bottom
8. Almost at the top
9. Amount
10. Another step
11. Any
12. Around
13. Arrangement
14. As much as
15. At the end
16. At the start
17. Beginning
18. Best
19. Big
20. Bottom
21. Circle
22. Count
23. Differences
24. Direction
25. Down
26. Down and down and down
27. Each
28. Fewer
29. Final
30. Four
31. Height
32. Higher
33. How far down
34. How many
35. In
36. Incomplete37. Just the right (amount)
38. Larger
39. Lots
40. Many
41. Middle
42. More
43. Next level
44. Number
45. Often
46. Older
47. On
48. One more again
49. One step down
50. One, two, three
51. Only as much as
52. Only two more steps left
53. Partially cut-off
54. Primary
55. Quantity
56. Ran out of
57. Seven
58. Shapes
59. Six
60. Smaller
61. Some
62. So many
63. Spatial relations
64. Surround
65. Top
66. Totally
67. Two more
68. Up and up and up
69. Up high
70. Very different from
71. Within

Herbert P. Ginsburg is the Jacob H. Schiff Professor Emeritus of Psychology and Education at Teachers College, Columbia University. He is a member of DREME’s Family Math and Early Math Resources for Teacher Educators projects.

Originally published on the DREME website: https://dreme.stanford.edu/news/playing-math-playground

A network of scholars in early math education, conducting research & developing materials to promote young children’s math learning. https://dreme.stanford.edu

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A network of scholars in early math education, conducting research & developing materials to promote young children’s math learning. https://dreme.stanford.edu