Toddler math concepts — Good Parenting



ThinkstockPhotos 475086040Dear Dr. Debbie,

Can you give me a logical reason why my two-year-old twins constantly dump out the contents of containers? It could be a tub of toy cars, a box of crayons, a bowl of nuts set out for guests on the coffee table, or all the socks from the laundry basket (they actually worked together on this one).

I think I could tolerate this behavior better if there were a good explanation for it.

Playing Pick Up

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Dear PPU,

A reasonable explanation is that it’s fun. Beyond that, there are many math concepts that are being learned when toddlers dump the contents of a container.

A foundational understanding in mathematics is that subtraction is the opposite of addition. Likewise, division is the opposite of multiplication. At the toddler level, empty is the opposite of full. Down is the opposite of up. None is the opposite of all. Out is the opposite of in. There (under the couch) is the opposite of here (in the nut bowl).

One of the early math concepts that very young children show their understanding of is “two-ness.” This is observed when he happily takes the cracker you offer in one hand, but immediately puts out the empty hand to be filled, too. Quantity is a very important concept for understanding how groups of objects differ. “All” and “none” are also quantity concepts, as are “too many” and “not enough.”

Specific quantities can be identified by enumerating. “Two green crayons. “Five red crayons.” Beyond twoness, your children will learn to say the numbers in order, first just by memorizing the sounds: “one, two, three, four, five.” Nursery rhymes and finger plays reinforce this order. (“One, two, buckle my shoe.”) As your children hear you count things out loud, such as the number of steps as you ascend the staircase together, they begin to understand enumeration. Objects that have been dumped out give an opportunity to count them aloud. (You can also practice counting as your refill the containers!) Around age three, a child will start to “subitize” which means to be able to look at a group (up to four objects is pretty good for this age) and say the amount instantly without counting each object.

One to One Correspondence
Counting also demonstrates the concept of one-to-one correspondence, which is to say that the word “five” only refers to a group of one, two, three, four, five objects. Each quantity corresponds to a specific number word. Matching up pairs, for example, Daddy’s blue sock with Daddy’s other blue sock, and my red sock with my other red sock, is another way to demonstrate understanding one-to-one correspondence. More complex thinking beyond simple pairs will have your children making repeating patterns or symmetrical designs with the objects – by color, shape, or other characteristics. Mathematicians love to find repeating patterns.

Multiple objects lend themselves well to being subdivided into categories. In higher math, we have the impressive Venn diagram in which categories can overlap. Obviously crayons or socks can be divided by color. A bowl of nuts might be sorted by size – smaller, middle-sized and larger – or by variety. A tub of cars might be sorted by type – rescue vehicles, service vehicles, sports cars, and family cars. All of these things are easier to sort if they are spilled out on the floor.

Spatial Relationships
A basic concept your children will need for geometry is how objects relate to one another across space. Physical experience is the best way to learn the meanings of such spatial relationships as: above, beside, between, under, far from, close to, etc. Long before they can calculate bisecting an angle, your children need to understand that real objects can move away in different directions from a single point.

If you’re not in a hurry to clean it up, enjoy these opportunities for some terrific math learning.

Dr. Debbie

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