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are playful ways to encourage your child to discover the uses of math
in everyday life.
Ways to Explore Math:
Basic Concepts / 9 Great Activities
by Istar Schwager, Ph.D.
MATH IS MORE
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
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
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
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!
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?
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.
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.
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.
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.
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
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.
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.
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.
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.
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?
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
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.
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.
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
“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
2006 Sesame Workshop (New York, New York) All Rights Reserved.
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