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Understanding Math Concepts

Understanding Math Concepts

Here are some ideas that parents may use to teach math skills.

Mathematical Development

It is important for parents to understand the difference between the concept of number and the concept of numeral. The concept of number is referring to how many. Numerals are the symbols (such as 0, 1, 2, 3) that represent how many.

Concept of Number:

*   *    

This would be seen as two distinct objects by an infant.

Concept of Numeral:

Most baby books show a numeral, for example a “2” — along with two objects.  

2 * *    

However, this would be seen as three distinct objects by the infant.

There are studies that show that young infants would perceive this as 3 objects because they would see the two objects plus the numeral “2.” This means that each time you use one of these books to teach the concept of numbers, the baby would see one more than the number you are talking about. In other words, when you are trying to teach 2, then your baby sees three distinct objects while you are talking about 2. When you teach 3, then your baby would see 4 objects, and so on.

This research is more than 25 years old, yet new baby books are published showing the numerals near the objects and parents may not even realize that their babies are perceiving one more than they are trying to demonstrate. I recommend demonstrating the concept of number properly from the very beginning.

I also suggest parents use a multisensory and interactive approach and use manipulatives (physical objects that can be moved) to demonstrate all of these concepts. By multisensory, I mean to match in time as precisely as you can, your child’s senses including sight, sound, and touch. You can also think of movement as a sense and match counting to your child’s movements.

More specifically, as you count it is important to match the visual and auditory information along with haptic (touching) information. In other words, you try to match as many sensory systems as you can for your child by saying “1, 2, 3, . . .” as you show distinct objects. [By distinct objects, I mean the objects don’t overlap and they are clearly separate. For example, you may show two oranges that are not touching each other (or appearing to touch each other) and the background is not similar in color to the objects.]

It is even better if you can add the sense of touch by either using your baby’s finger (only if she/he is in mood to do so) to touch the objects as you count them aloud or you touch your baby at the moment that you count her toes or fingers. It is still better if your baby has initiates movements that can be counted such as tapping or touching objects. It is important that these movements match the auditory, visual, and haptic information as much as possible.

A main idea is to turn everyday activities into opportunities to learn about math. Parents can describe what their children are doing and frequently include math words in the descriptions. Use math words such as one, two, three, etc., whole, half, twice as much, one-half, one-third, one-fourth, two-thirds, three-fourths, add, subtract/take away, zero, etc. while eating and playing. It is helpful to do this while toddlers are moving or picking up objects (for example: “You picked up one-half of the six pieces.”).

The following concepts can be demonstrated using toys, crackers, or some other safe objects.

One-to-One Correspondence:

Talk about the one-to-one correspondence of objects and/or people (for example, each person has a spoon "Daddy has a spoon. Mommy has a spoon. Your sister has a spoon and you have a spoon. There are four spoons. How many people are there?" 

Counting:

DO THIS EVERY DAY: Count steps, count crackers, count bounces as you help your baby joyfully bounce, count dots while you or your baby makes dots, count seconds, count floors as you go up in an elevator, count steps while walking, etc. Ask your toddler, "How many crackers would you like?" or "How many dots are on the whiteboard? If we add two more dots, how many dots will there be?” [I recommend starting over and counting all of them again, then pausing before counting the last two.] 

Adding:

Talk about adding one more to a small quantity. "There are two pigs. If we add one more pig [while you are actually adding the pig to the other two pigs], then we have three pigs. Two pigs plus one pig equals three pigs. Two plus one is three!"

Talk about adding one or two to small quantities on a consistent basis when you see this happening in your child's world. This happens frequently while playing with blocks or other toys, so you can help your child learn math words while she is playing with blocks. 

Subtracting:

Talk about taking one away one or two from small quantities. This probably happens many times when your child is playing -- all we have to do is talk about it while it is happening and match our voices to the precise moment that they take one away. For example, "There are four books on the table. Now, you are taking one away so there are only three books on the table.” Later, you can repeat the concept while you are moving objects around and say something such as "four minus one is three" while your child is watching and listening to you.

Multiplying:

Think of multiplying as "groups of." Show the babies groups of the same type of objects and talk about them. For example, put three groups of two animals on the floor and say "I see three groups of two animals. One, two [add a very slight pause after each group of two] -- three, four -- five, six. Three groups of two makes six." If you were doing two groups of three, then you would count 1, 2, 3, [slight pause] 4, 5, 6.

Dividing:

One of the ways that I helped my daughters’ math skills was talking about math concepts while eating. We ate many foods that could be cut fairly accurately into fractions. For example, we ate round Morningstar Farms patties that could be sliced into halves, thirds, fourths, sixths, eighths, sixteenths, etc. Each day I would cut their food into various fractions and talk about it while I did it. I would say something such as, “I am cutting your Chik Patty into four fourths. Each part is 1/4 of the whole patty. I tried to cut it precisely, but it isn’t exact so each part is really about 1/4 of the whole patty. After I had been doing this for many weeks, then I began asking my daughters how they wanted their food cut. I remember Keelin as a toddler telling me that she wanted 1 half, 1 fourth, 1 eighth, and 2 sixteenths. This added up to a whole, so it appeared that she had learned quite a bit from doing this on a daily basis over several months.

Any time you are cutting your toddler’s food in half, you could say what you are doing. For example, I would say something such as “I am trying to cut your food in half. This is about half and this is about half. I can’t cut it exactly in half, but this is very close.” Try to divide toys, food, physical movements, etc. in halves, thirds, fourths, and other fractions. Place six toys on the table and divide them into two groups of three and say what you are doing. Encourage your child to imitate you and do the same. Talk about what you are doing while using math words.

The Concept of Zero:

Please try to point out zero as it occurs in your child’s environment. For example, you can say "You have zero crackers in your hand. Now, you have one cracker in your hand. [Place the cracker in your child’s hand at the moment you say “one.”] If your child no longer has a cracker in his hand, then say, “Now, you have zero crackers in your hand."

I hope parents will try many of these activities as you are playing and interacting with your babies, toddlers, and preschoolers. Good luck and have fun!

—Dr. Robert C. Titzer

Note: In addition to being an infant researcher, Dr. Titzer has a Ph.D. minor in statistics and is a former math teacher.

 

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