The Math-Language Connection
Math requires people of all ages to think about what words mean. When you “talk math,” you have to be precise in your language and thinking. You have to explain your reasoning.Consider a rectangle. It has four straight sides and four right angles, but just because mostshapes we call rectangles have two long sides and two short sides, it doesn’t mean that they have to. Math is an ideal context in which to discuss exactly what words mean — and that words can have different meanings. For example, sometimes people say “straight” when they mean vertical or horizontal, as when a picture is hanging straight on the wall. But other times, straight means not curving, as a straight side of a shape.
Learning how to use language and mathematical thinking benefits children in many areas. If a child doesn’t understand why a toy car does not go down a ramp, then using mathematical ideas, such as height or angle (how slanted is the ramp?) can help her see the situation in new ways. When two kids are trying to figure out how to share something, such as a tricycle, math can be helpful: Set a timer for each child’s turn. Sharing blocks could involve counting or dealing out blocks to each person.
Everything can have a connection to math, and math connects to everything. Jumping, marching, and climbing stairs, for example, are all ways to practice counting. When children recognize, draw, play with, and combine shapes, they are not only learning about geometry, but also might be experimenting with visual art, architecture, and science. When children follow a story, they make mental pictures of the scenes and characters, using such phrases as “eyes as big as saucers,” or the troll is “under the bridge.”
These are all “spatial” ideas, which literally shape our view of the world-we use spatial concepts in almost all thinking. Later in their lives, children will use spatial ideas to think about communication networks, the structure of molecules, geography, and so forth. But spatial thinking is also basic to children’s early cognitive development. In fact, research shows that working with and combining shapes actually improves young children’s math achievements two to three years later-in addition to improving their writing and even their IQ scores!
Can it be true that all thinking involves mathematics? Yes. It all comes down to logic-a branch of mathematics that also happens to be a key aspect of the human thought process. Although logic might seem like the most abstract, least likely area of mathematics for young children to learn to use, researchers see implicit use of logic in all children from an early age. An 18-month-old child pulling a blanket to bring a toy within reach, for example, shows the beginnings of “means-end” analysis. A more explicit example of this early problem-solving ability is displayed by 3-year-old Luke: As he watches his father unsuccessfully look under the van for a washer that had fallen, he says, “Why don’t you just move the car back so you can find it?” Luke used means-end analysis better than his father!
Young children show an impressive ability to think inventively. Encouraging your child to think mathematically at his own pace, rather than “rushing” him or showing him how to solve a problem, is an excellent way to meet his need for creative intellectual activity. If we pose problems and encourage kids to solve them in their own way, we help kids connect their informal knowledge with the more formal, in-school mathematics they’ll learn later. We will ensure that children won’t suffer the fate illustrated by Bill Cosby’s line: “One and one make two. That’s great. What’s a two?”
Making Math Connections Every Day
Throughout the day, you can help your child connect her understandings to math by helping her represent her ideas. In other words, her intuitive ideas can become mathematical. Young children represent their ideas by talking, reading, writing, drawing, and playing. For example, think about some common stories and their connections to math. The Three Billy Goats Gruff includes a number right in the title. To understand the story, a child also needs to understand the concepts of ordering (small, medium, large), correspondences (between the goats’ sizes and voices), relationships (the larger the goat, the louder their hooves),patterning (repetitive dialogue), and so forth.
Most stories depend on logical ideas, such as classification and conditionals (if the troll waits, then a larger goat will be available to him). To help your child connect her ideas through reading, encourage her to look carefully at the book itself and then discuss her ideas about the book’s meaning, noting the author and illustrator. Next, read the book aloud (with a sense of drama and humor, as appropriate) and straight through, without questions or comments from your child. While reading aloud in this way, sit so that she can see the illustrations. After you’re finished, help her connect the story with some of her own experiences. Ask open-ended questions and point out new vocabulary words. Then, develop related math ideas by re-reading parts of it and engaging in related activities.
In many books, the connections are clear. For example, the title character in The Very Hungry Caterpillar, by Eric Carle, eats from one to five items of food.