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What to expect in preschool: Math

Sharing pretzels and building block towers: Preschool math means recognizing that numbers and patterns are part of everyday life.

By Diana Townsend-Butterworth

On any given day, your child and his preschool pals divide cookies or pretzels into equal piles for snacks. They build bridges and tall towers with wooden blocks. They string beads into colorful patterns. They weigh the class rabbit and measure the length and width of its cage. They learn to balance a seesaw when one child is heavier than another. They discover which trucks are too big to fit in the toy garage and compare the number of shells they find at the beach.

Preschoolers do math even though they are not sitting at desks with workbooks or memorizing multiplication tables. Math is helping them to make sense of the world around them and teaching them to reason and problem solve. It's not limited to a specific period or time of day, says Marilou Hyson, associate executive director for professional development at the National Association for the Education of Young Children (NAEYC). Instead it is a natural part of young children's play and daily activities. They explore mathematical concepts as they sort, classify, compare quantities, balance blocks, notice shapes, and find patterns.

Preschool teachers build on children's prior knowledge and capitalize on their spontaneous discoveries to further their understanding of mathematical concepts. As children build with blocks, their teacher introduces the concepts of higher, lower, in front of, behind, larger, smaller, equal, horizontal, vertical, parallel, odd, and even, says Mary Jane Belt, a teacher in Long Island, New York. When the class does an art project, such as putting feathers on the outline of a duck, the teacher might say the duck needs six feathers for his tail. One child puts on two feathers and a second child puts on three. The teacher then asks, "How many feathers does the duck have? Let's count them. Does he need more? How many?" When children are in the literacy area listening to a story, the teacher might ask: "How many elephants do you see on this page? How many do you see with their trunks in the air? How many have babies with them?"

The NAEYC and the National Council of Teachers of Mathematics have outlined the following as particularly important parts of mathematical learning in preschool:

  • Numbers: Children learn about numbers by counting objects and discussing the results: "You gave Chris six goldfish crackers. How many does Susie need?" Children count spaces on board games. They count the days until their birthdays. The teacher might say, "Yesterday there were 12 days until your birthday. How many days are there now?" Preschoolers read counting books and recite nursery rhymes with numbers.
  • Geometry and spatial relations: Children practice constructing shapes and discussing their properties. They see skinny triangles and fat triangles and upside-down triangles and gradually realize that they are all still triangles.
  • Measurement: Children compare the height of a block tower with the height of a desk or table. They measure each other and the distance from the kitchen corner to the water table. They learn that this block is too short to make a bridge over the road. Teachers reinforce children's findings by asking questions and making observations: "I wonder if this block is long enough to bridge the road. Let's try it."
  • Patterns/geometry: Children become aware of patterns in their clothes. They learn to recognize patterns of different colors and sizes in beads and blocks. They practice reproducing simple patterns by stringing beads and copying designs with colored blocks.
  • Analyzing data: Children sort objects by color, size and shape; count them; and record the data on graphs and charts. These charts might reflect the class pet's growth, the number of rainy days in February, how many bean plants have sprouted, or the number of children with a birthday in March.

Diana Townsend-Butterworth is a former teacher and head of the junior school at St. Bernard's School in New York City. She is the author of Your Child's First School and Preschool and Your Child.

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