Early Childhood Today: Arwen, as you watch children during free play, what opportunities do you see to build math concepts?

Arwen Lee: I always have unit blocks as an option during free play. The children use blocks to outline their friends. Before they begin, I ask them to think about which child will need the most blocks. The least? They discover that a taller friend needs more blocks than a shorter friend to complete the outline.

In the art center, we have only one spot for painting. We have a waiting list and the children use words such as first, second, third, next, and last to describe their position on the list. In our listening station, I put out two books and four headphones. The children have to figure out if there are too few books, the same amount, or too many. Do they need to share the book or have their own book?

Right now, we are hosting a home for six monarch caterpillars. We feed them twice a day and each needs one leaf. As the caterpillars move into the chrysalis stage, the children conclude that we need fewer leaves.

ECT: Are there specific kinds of materials you include in your learning centers to support math exploration?

Lee: I have lots of paper and pencils in the dramatic-play center so that children can make grocery lists, menus with prices, and write down phone numbers. Our block center is stocked with unit blocks, foam geometrical shapes, manipulatives (pattern blocks, dinosaur and bear counters, and unifix blocks). In our library center, we display books about numbers, patterns, and titles that explore math concepts. We write a number on a card in our art center and provide play dough children can use to make that number of cookies, pizzas, or snakes. In our writing area, we provide gel pens children like to use to write numbers. We also keep a baggie with a number printed on an index card in it. Surrounding this is a larger baggie filled with hair gel. The children like to trace the number with their fingers!

ECT: It's always hard to know when to intervene in children's play. When an opportunity arises, what kinds of questions do you ask children? For example, what might you ask as they play with blocks to reinforce math skills?

Lee: You're right. Knowing when to intervene is the hard part. If a child is having difficulty getting into play, I help start them off-but I back off as quickly as I can. Usually another friend gets involved and I leave. I return to follow up with questions or comments about the play. If a child is actively involved, I will ask a question or two. The kinds of questions I might ask are "How many blocks do you think you'll need to make your tower?" "How many to make a taller tower?" "Why did you pick that block to fit into your wall instead of this one?" I ask the children to tell me how they arrived at their answer. I encourage them to show me.

If they don't respond, I walk away or I start my own building. Sometimes they will take over or start their own. I also ask them to record elaborate structures on paper so they can make them again.

ECT: What about outdoor play? Are there similar ways you can strengthen math concepts outdoors?

Lee: Well, right now they're collecting acorns and after I "ooh" and "ahh" I ask, "How many acorns are in your bucket?" "How do you know?" "How many do you think?" "Can you check?" "Now show me." "Can you write that number in the sand?"

ECT: We know that games can be very useful in helping children develop math skills. Have you found any games to be particularly helpful?

Lee: We play a guessing game where I think of a number and they have to try and guess what it is. I give clues - bigger than 4 and smaller than 10. I also have a cookie sheet divided into 10 sections with electrical tape. The kids count how many magnets I have on it by listening and watching as I place them on the 10 separate sections. I show them how many are on the grid and take them off with a grand gesture. The children tell me how many are left on the grid.

If you were to visit my classroom, you'd also find me talking to myself-on purpose! I talk out loud as I solve problems. For example, we had applesauce and we had to figure out how many spoons we needed. We had 17 children, and someone said "no thank you." So how many spoons do we need? We made groups of 5 spoons and added 5, 10,15 and one more!