Mathematical experiences for very young children should build largely upon their play and the natural relationships between learning and life in their daily activities, interests, and questions.
Exploring the Math in Play

Children become intensely engaged in play. Pursuing their own purposes, they tend to tackle problems that are challenging enough to be engrossing yet not totally beyond their capacities. Sticking with a problem — puzzling over it and approaching it in various ways — can lead to powerful learning, in addition, when several children grapple with the same problem, they often come up with different approaches, discuss various strategies, and learn from one another. These aspects of play can promote thinking and learning in mathematics as well as in other areas.

Young children explore patterns and shapes, compare sizes, and count things. But how often do they do that? And what does it mean for children's development? When children were studied during free play, six categories of mathematics content emerged.

1. Classifying. One girl, Anna, took out all the plastic bugs from the container and sorted them by type of bug and then by color.

2. Exploring magnitude (describing and comparing the size of objects). When Brianna brought a newspaper to the art table to cover it, Amy remarked, "This isn't big enough to cover the table."

3. Enumerating (saying number words, counting, instantly recognizing a number of objects, or reading or writing numbers). Three girls drew pictures of their families and discussed how many brothers and sisters they had and how old their siblings were.

4. Investigating dynamics (putting things together, taking them apart, or exploring motions such as flipping). Several girls flattened a ball of clay into a disk, cut it, and made "pizza."

5. Studying pattern and shape (identifying or creating patterns or shapes, or exploring geometric properties). Jennie made a bead necklace, creating a yellow-red color pattern.

6. Exploring spatial relations (describing or drawing a location or direction). When Teresa put a dollhouse couch beside a window, Katie moved it to the center of the living room, saying, "The couch should be in front of the TV."

The range of mathematics explored during free play is impressive. We can see that free play offers a rich foundation on which to build interesting mathematics. These everyday experiences form the foundation for later mathematics. Later, children elaborate on these ideas. We call this process "mathematization." And we recognize that children need both these foundational experiences, as well as specific math activities.

Here are some activities for your classroom to add a bit of sparkle and creativity. As children work, ask critical questions such as "Did you try this?" "What would have happened if?" "Do you think you could?" to enhance children's understanding of mathematical ideas and vocabulary.
Use dramatizations . Invite children pretend to be in a ball (sphere) or box (rectangular prism), feeling the faces, edges, and corners and to dramatize simple arithmetic problems such as: Three frogs jumped in the pond, then one more, how many are there in all?

Use children's bodies. Suggest that children show how many feet, mouths, and so on they have. When asked to show their "three arms," they respond loudly in protest, and then tell the adult how many they do have and show ("prove") it. Then invite children to show numbers with fingers, starting with the familiar, "How old are you?" to showing numbers you say, to showing numbers in different ways (for example, five as three on one hand and two on the other).

Use children's play. Engage children in block play that allows them to do mathematics in numerous ways, including sorting, seriating, creating symmetric designs and buildings, making patterns, and so forth. Then introduce a game of Dinosaur Shop. Suggest that children pretend to buy and sell toy dinosaurs or other small objects, learning counting, arithmetic, and money concepts.

Use children's toys. Encourage children to use "scenes" and toys to act out situations such as three cars on the road, or, later in the year, two monkeys in the trees and two on the ground.

Use children's stories. Share books with children that address mathematics but are also good stories. Later, help children see mathematics in any book. In Blueberries for Sal, by Robert McCloskey (Penguin, 1993), children can copy "kuplink, kuplank, kuplunk!" and later tell you the number as you slowly drop up to four counters into a coffee can.
Use children's natural creativity. Children's ideas about mathematics should be discussed with all children. Here's a "mathematical conversation" between two boys, each 6 years of age: "Think of the biggest number you can. Now add five. Then, imagine if you had that many cupcakes." " Wow, that's five more than the biggest number you could come up with!"

Use children's problem-solving abilities. Ask children to describe how they would figure out problems such as getting just enough scissors for their table or how many snacks they would need if a guest were joining the group. Encourage them to use their own fingers or manipulatives or whatever else might be handy for problem solving.

Use a variety of strategies. Bring mathematics everywhere you go in your classroom, from counting children at morning meeting to setting the table, to asking children to clean up a given number or shape of items. Also, use a research-based curriculum to incorporate a sequenced series of learning activities into your program.

Use technology. Try digital cameras to record children's mathematical work, in their play and in planned activities, and then use the photographs to aid discussions and reflections with children, curriculum planning, and communication with parents. Use computers wisely to mathematize situations and provide individualized instruction.

Use assessments to measure children's mathematics learning. Use observations, discussions with children, and small-group activities to learn about children's mathematical thinking and to make informed decisions about what each child might be able to learn from future experiences. Also try computer assessments. Use programs that assess children automatically.

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