Everything around us can be better understood with mathematics. Math can help children understand the many aspects of their world through its connections to themselves as well as other curriculum areas. Teachers who help children see those connections greatly enrich children's learning.
Math and Literacy
Teachers know that building children's vocabularies helps them understand stories they hear and will later read. But by taking a closer look, you can begin to see how much mathematical concepts permeate familiar children's stories. Take "Three Billy Goats Gruff," for example. This story:
- Includes a number in the title
- Explores concepts of ordering (sizes of goats: small, medium, large)
- Investigates correspondences between goats' sizes and voices
- Takes a look at relationships (the larger the goat the louder their hooves)
- Offers exposure to patterning (the repeated dialogue)
Research shows that the extent to which children are exposed to math concepts in their earliest years predicts how well they will do in mathematics in elementary school. More surprisingly, it also predicts how well they will do in reading. Research also shows the reverse - that children who can retell or create stories in their early years do better in mathematics.
Given these connections, we shouldn't debate whether to emphasize literacy or mathematics or social-emotional development. Children need them all. And many times, all can be developed at the same time.
Math and Problem Solving
When children cannot understand why a car does not go down a ramp, using mathematical ideas such as height or how "slanted" the ramp is can help them see the situation in new ways. When they are trying to figure out how to share, mathematics can be similarly helpful. Sharing a tricycle can involve measuring time with an hourglass. Sharing blocks can involve counting or "dealing out" one block to the first person, one block to die second, and so forth. You need mathematics to share well.
Children are impressive problem solvers. They are learning how to learn and learning the rules of the "reasoning game." Problem posing and problem solving are effective ways for children to express their inventiveness and integrate their learning. They develop mathematics, language, and creativity. And they build connections among these - the essence of learning to think inventively.
Connecting Informal and Formal Thinking
Researchers have seen many impressive demonstrations of children's ability to think inventively. Encouraging children to think mathematically, rather than rushing them or showing them how to solve the problem, helps to meet their need for creative intellectual activity.
Throughout the day, we can help children connect their informal understandings to mathematics by helping them represent their ideas. Young children represent their ideas by talking, but also through creating models, art, and block constructions. The geometric patterns children use to build a house with blocks or to thread beads of different colors in the manipulatives area can grow out of jumping back and forth, other movement games, or singing rhythmic songs. Gradually, they begin to see these patterns all around them, including in stories, such as "Three Billy Goats Gruff," and in art. ("See, my drawing uses an ABAB pattern like your blocks did this morning!")
Integrating Math Learning
How do we increase children's math learning without interfering with the heart of the activities we introduce in other subject areas? Let's take a look at picture book sharing. You might begin by encouraging children to look carefully at the book itself, discussing their ideas about what the book might be about, and noting the author and illustrator. Next, read the book, without interrupting with questions or comments. While reading, sit so everyone can see the illustrations. Read smoothly, dramatically, and with a sense of humor whenever appropriate. After reading, help children make connections between the story and their own experiences. Ask open-ended questions. Then, try integrating math by re-reading parts of the book and engaging children in related activities. In many books, the connections are clear. For example, The Very Hungry Caterpillar (by Eric Carle) eats from one to five items of food. With this book you can:
- Show a single page and ask how many different items the caterpillar ate.
- Lead the children in counting aloud to check.
- Encourage them to pretend to be the caterpillar, eating three items of food.
For other books, the mathematics is not so obvious, but it can be just as engaging. For example, after reading Blueberries for Sal (by Robert McCloskey), a teacher returned to the page in which the little girl, Sal, drops blueberries into her pail, "kerplink, kerplank, kerplunk." She then showed children her own "pail and blueberries" (a tin can and small magnets). Children closed their eyes and listened as the teacher dropped a number of magnets into the pail. She asked them to hold up fingers to show the number. She then emptied the can and led the children in counting the magnets to check their guesses.
All Around The Classroom
Here are inventive ways you can integrate math into your learning centers:
Encourage children to use blocks and related toys to act out and talk about scenarios such as three cars on the road. Later in the year, this could be three cars and two trucks on the road ... How many in all?
- Invite children to compare their block buildings. Ask them if they are comparing height, number of blocks, or something else. Say, "Show me," and ask, "How do you know?" whenever appropriate.
- Ask a child to dose her eyes. Hand her a block, have her feel it and then give it back to you. Ask her to open her eyes and see if she can identify the block she held in her hand. At first, have only two or three choices.
- Children naturally put similar blocks together when they are building. Talk to them about this. Ask why they used that particular shape of block.
- Children also naturally create symmetric designs and buildings. They will notice this symmetry and do more of it, more intentionally, if you discuss it with them and the whole group.
DRAMATIC PLAY AREA
Set up shops in the dramatic play area, encouraging children to pretend to buy and sell groceries, toys, and so on. They'll be learning counting, arithmetic, and simple money concepts.
- Use a digital camera to record the mathematical work children do during playtime. Then, use the photographs to stimulate discussion and reflection with children about math concepts.
- Lead children in pretending to be in a ball (sphere) or box (rectangular prism), feeling the faces, edges, and corners.
When children are engaging in a type of movement activity, help them count or perform a certain number of movements. For example, if children are using a play structure as a rabbit home, you might encourage them to hop seven times.
- Use comparison and spatial relation terms to provide directions and to describe what you observe the children doing.
- Encourage games that provide opportunities to work with numbers and patterning, such as hopscotch.
- Ask "Can you make your shadow bigger?... smaller?... look like a bear or a bird?"
- Invite children to collect as many different shapes of leaves as they can find.
- Ask children to count the numbers of objects in the area. For example: "How many trees do we have in this play area? How many tricycles are parked by the bench? How many twigs can you find?"
SAND AND WATER AREA
Make a large number of containers, with as many different shapes and widths as possible, available for pouring and comparing. Which one holds more? How do you know?
- In the sand, discuss the roads children make for small cars. These roads are paths that can be described geometrically, using terms such as "straight" and "curved."
- In the water table, ask, "How many cups will the water pitcher fill?"
Mathematics is all around us. The combination of taking advantage of everyday situations and carefully planning activities is a powerful approach to helping young children learn math and more.