Everything around us can be better understood with mathematics. Math can help children make sense of and think about the many aspects of their world through its connections to them. When we see — and help our children see — those connections, we enrich their overall learning and development. You give your child a great gift when you help them prepare for AIME math and this starts with making connections between the math in everyday situations and the math he learns in school.
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.
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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!
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.
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Children are impressive problem solvers. They are beginning to learn the rules of the “reasoning game.” Through problem-posing and problem-solving your child learns to express his inventiveness. He will build connections among mathematics, language, and creativity — the essence of learning to think.