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Here are playful ways to encourage your child to discover the uses of math in everyday life.

Fun Ways to Explore Math:
5 Basic Concepts / 9 Great Activities
by Istar Schwager, Ph.D.

The big little duck is the mommy” said Annie. ‘And the little little duck is the baby.” She had finished counting the toy animals in the barn she’d constructed and had moved on to grouping them into families, Without realizing it, Annie was using math concepts in her play.

Learning about patterns, sizes, shapes, amounts, and other relationships is as natural to young children as eating and speaking. If you look at the activities and games children gravitate to, you’ll see how many of them are based on mathematical ideas. From musical chairs to dominoes: from “Where Is Thumbkin?” to fitting tops on pots, preschoolers are immersed in math.

Math is so fundamental that Jean Piaget, the Swiss psychologist who taught us to respect the special logic of young children, viewed math relations as a focal point of children’s understanding of the world. One of Piaget’s major contributions was to help point out the value of a child’s touching, holding, lifting, and otherwise handling real objects to learn about their properties. And he stressed that these experiences form the basis for the more abstract thinking children develop later. The work of Piaget and others has had an impact on how math is viewed and taught today.

What Is Math, Really? 5 Basic Concepts
Increasingly, computational skills are considered just one aspect of mathematics—useful but not all that important. While it is certainly practical to know how to add and subtract, the calculator has freed us to see these skills as relatively mechanical. Math is based in the physical world; it’s less of a paper and pencil kind of activity than we sometimes think. It is hands-on experience with real objects, complete with their textures and weights, that familiarizes children with a wide range of math concepts. Even grown-up mathematicians use three- dimensional models and real-life comparisons in problem-solving as a way to understand relationships.

Many of the ideas that underlie math are really quite simple. Here are some of the most basic concepts. Recognizing how much of our everyday lives involve these math basics can be an eye opener!

Comparing: Comparisons can be made with any real objects. How are objects the same? How are they different? Comparisons can also be made between objects of different sizes. Which book is wide? Which book is narrow? Is there more juice in Brian’s glass and less in Tara’s? Which two crayons are the same color?

Making comparisons is fundamental to understanding relationships in math. Equations (2 + 2 = 4) and equivalences (the four small squares are equal in area to the one big square) are based on knowing when things are the same or different.

Sorting: Grouping objects by similarities is also basic to an understanding of mathematics. Whether it’s sorting blocks or socks or pebbles, kids need experience with actual objects to get the idea that things can be grouped.

Grouping is fundamental to understanding that 5 is 5 is 5...whether it’s five raisins or five Band-Aids or five children. Groups may have qualities in common with each other—for instance, each group has five things in it. Another feature of groups is that all group members have something in common. For example, kids can sort out all the green clothes in the hamper or all the bath toys that float.

Sequencing: Young children tend to think in terms of the extremes—big and little, fat and skinny, short and tall. It takes time and experience for them to grasp that there can be gradations—short, medium, and tall. And concepts such as tall, taller, and tallest are even more sophisticated. Yet handling objects of different sizes and dimensions (blocks, for example) gives kids the chance to see that relationships often go step-by-step.

Sequences in time also help children understand math better. Days follow a certain pattern: first we have breakfast, then lunch, then dinner. Certain activities, too, proceed in a set sequence: Mom always adjusts the car mirror, then fastens her seatbelt, then turns on the engine, then puts on the radio. Before young children can learn to tell time, they need to grasp the basics: that yesterday came before today; that tomorrow is always in the future.

Correspondence: One-to-one correspondence is the matching of objects in one set with objects in another set. Experience with making things correspond helps kids understand number concepts better. Learning that one straw goes into each of the milk glasses or that two raisins go on top of each cookie helps children grasp the idea of correspondence.

This idea is well developed in the story of “The Three Bears” in which there are three bowls of porridge, three chairs, and three beds—one for each of the three bears. And it’s clear that one bowl or chair or bed goes with each of the bears.

A child with a lot of experience handling objects will have an easier time understanding number groups, multiplication, and division years later when these subjects are introduced formally in school.

Part/Whole Relationships: A wheel is a part of a tricycle. The handle bars are another part. Children play with whole objects all the time, but they don’t always think of the parts separately. It may not be until an object is broken, or a child is constructing a toy or building with blocks that the idea that a whole is made up of parts truly takes form.
Another aspect of part/whole relationships hits home for children when they’re faced with sharing. There are two people and one orange. There are four children and three slices of pizza left over. Certainly, understanding the relationship of parts to the whole is basic to eventually understanding fractions and percentages.

How Can Parents Help Prepare Their Children for Learning Math?
There are many ways parents can introduce their children to math concepts through everyday activities. Keep in mind that by encouraging your children to handle and group and count actual objects, you’re helping them develop a real understanding of the principles that underlie the formulas and equations they will later learn.

Here are 9 ways to encourage math learning:

Cooking: Math abounds in the kitchen. Let your child be an apprentice chef, and you’ll give him food for much math thought. Just working with such ideas as “more,” “less,” “some,” “a few,” and “none” exposes him to the idea that you can compare quantities. He’ll also learn that expressions of amounts are often relative, and that there are many words that can be used to describe quantities.

Cooking can mean scraping the carrots until there is “enough” to make the carrot cake. It can mean adding a little “more” flour to the board on which you’re kneading the bread.

Following recipes also provides informal and often delicious exposure to different types of standard measures—whether pouring a half cup of flour, counting three teaspoons of vanilla, or finding a pint of cream among the taller milk quarts in the supermarket. Cooking requires timing, too, which may involve stirring the pudding for five minutes, or coming back after an hour to see if the bread has risen.

Kids in the kitchen get a first-hand look at measuring time and an understanding of what can happen during a certain amount of time. Even the eating can be a math experience. “I want more spaghetti sauce and less spaghetti.”

Setting the Table: Did your older child just invite a friend to stay for lunch? Is the entire Ohio branch of the family coming for Thanksgiving dinner? If you need an extra pair of hands and want to involve your preschooler in some learning at the same time, ask her to help set the table. She can count out the plates, make sure there are enough chairs to go around, and even make place cards. All of this helps kids learn about correspondence.

Construction: If your child doesn’t look like a carpenter, look again. Making things out of paper, wood, and other materials is not only fun, but introduces children to lots of math basics. Both younger and older children can work with cartons, straws, leaves, sticks, and other items to create three-dimensional constructions—bridges, spaceships, what ever.

With adult supervision and help, older preschoolers can make things out of wood, too. Making toy boats, doll furniture, and trucks helps kids learn about part/whole relations, and about the difference between perpendicular and parallel.

If you’re not comfortable using a hammer and nails with your preschooler, try glue; it holds wood pieces together pretty well. Projects can be completed in different phases, if your child is old enough to wait. Completing projects in phases can he a useful lesson in sequencing. And what better way to discover the properties of “three dimensional” than to first put together and then paint each of the sides of a dollhouse or toy garage?

Block Building: Is it the civic center? The new library? The Statue of Liberty? There are many types of blocks and construction toys that lend themselves to math learning.
In trying to make walls that are the same height, children discover that two square pieces can be equal in size to one of the rectangular pieces. Kids get a lot of experience comparing and a chance to see what happens when things are and aren’t the same, too. As they become more sophisticated builders, they figure out how to make windows, doors, and ramps.

Kids work hard on these constructions. Letting the building stand a few days before you ask that she dismantle it will give your child a chance for more play and renovation… and will let her know that her latest architectural contribution is valued.

Sorting Laundry: A prize to anyone who can find the mate to the blue sock with the brown design around the toe! Sorting clothes may seem a humdrum chore to you, but to your child it can provide an adventure in matching and comparing. He can help you put all the shirts or underwear together. Or he can sort everything into adults’ clothes and children’s . And folding gives kids experience with shapes and symmetry.

Puzzles: Which way does the piece fit? Puzzles are popular with preschoolers because they offer a challenging and usually rewarding chance to deal with matching shape and direction. If you and your child work on puzzles together, you can discuss some techniques for solving them. For instance, looking at shape clues and color clues, matching details, and finding continuity in the picture. And don’t be surprised if there are some puzzles your child is more adept at than you are. (The ability to do 12- piece puzzles of farm animals seems to decline with age.)

Money: Money is one of those mysteries of the adult world that little children find most intriguing. Let your child learn the names and relative values of different coins. You can com pare values and even sequence the coins by their worth. Playing store and helping make actual purchases gives children a better understanding of how money is saved, spent, and exchanged for goods and services.

Body Awareness: “I’m five years old, I weigh 42 pounds, and I’m 44 inches tall in my blue sneakers.” Learning their vital statistics is fun for kids. Scales and growth charts give them a chance not only to learn more about themselves, but also how size and weight are measured and what these measurements mean. Children can measure their friends, dolls, and even their pets.

A good introduction, which helps kids really understand the underlying concepts, is to use non-standard measures. How many of Jenny’s steps does it take to get to the other side of the yard? How many of Andrew’s steps? When Daddy gets on the see saw, does it take two or three children to balance him on the other side?

As we share activities like these with our children, we’re also using the language of mathematics in an easy, informal way, which makes it an everyday part of our kids’ vocabularies. Children who are comfortable with math language and math concepts are likely to be among those who consider math a “favorite subject.”

Istar Schwager, Ph.D., is an educational psychologist and the
founder of

1986, 2006 Sesame Workshop (New York, New York) All Rights Reserved.

How is your child learning math? -- let us know.

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