Sunday, June 22, 2008

Laying the Foundation for the Abstract Concept of Numbers

Learning the abstract concept of numbers starts long before the usual introduction of pre-algebra and algebra. It begins when your child is first introduced to the meaning of numbers by counting. Yes, counting is where the development of number sense all begins.

I remember when our son was two and I was participating in an exercise class. We all took our children along and they played next to us while we exercised. Our son, interested in numbers from early on, was fascinated by the class leader's counting out loud, "One, two, three, four; two, two, three, four; three, two, three, four; four, two, three, four; ("again") one, two, three, four; two, two, three, four; three, two, three, four; four, two, three, four . . ." And our son was fascinated by the words. We adults understood that there were two sets of counting patterns being used at once, but to our son, these were just words, recited along in a pattern, with a nice rhythm, and he was intrigued, taking it all in.

A few days later, I heard him repeating the number words, in random order. He had no sense of counting; to him the words were meaningless. Ooops!

Children love counting. Counting games, counting songs, and counting rhymes all serve to draw our children's interest to the fun of counting, and at an early age.

Counting is where the understanding of the concepts and the meaning of a number begins. And it is important to know that there is much more to counting than merely calling out the numbers.

Here are a few ways to properly start your child counting so that early on, he/she will not only begin to grasp the meaning of numbers and will also apply "counting" to objects around him

Assemble a set of objects in a plastic bowl or tub. They may be pennies, blocks, craft sticks, toys, anything. You also need a second empty container. Have your child pick up an object, place it in the empty bin, while saying its number, beginning with "one". (Demonstrate this yourself. Children love to copy.) It is important that your child actually picks up the object and moves it, rather than sliding it across to another pile. Begin with 10 objects or less. Be sure that your child only picks up one object at a time.

After your child has moved the last object to the other bowl, ask, "How may trucks are in your other tub?" Your child should learn to properly say the last number he counted. Vary the number of objects in the tub. It is also important to vary the objects you use so that he/she understands that numbers are used to refer to different types of objects.

This early activity of counting, using concrete objects, though simple, is part of the learning of the abstract number concepts to come later.

And this is important: have one tub on one side of his body and the other on the other side. We want his/her hand to cross the midline of the body with each motion. We know that the brain cells fire away each time an arm or leg crosses that midline.

As your child gets older, and after he/she masters this first counting activity, there is something else very important that you must do. You must develop a sense of "zero". So this is the next step in the counting exercise: Teach your child to start counting with "zero". Before any objects are moved, teach your child that there are "zero" objects in the second tub. Teach him to say "zero" before he begins, followed by "one" as the counting and moving of objects begins.

Next, using blocks that are numbered, or making your own on pieces of paper of cardboard, teach your child the symbols (digits, numerals) that stand for each number from 0 to 20. Line them up in order and point to them as you recite the numbers. Have your child recite them with you as you point to the symbols. Then have your child recite them alone.

Later on, with the blocks still in proper order, point to the symbols in random order and have your child name them.

Much later, mix them up and have your child find them in order and say them as you and he line them up in order.

As your child learns, you can gradually increase the number set up to 20.

Books that have counting pictures can be useful. Point to the symbol and ask your child what it is. Sing counting songs with him/her. Avoid songs that count backwards at first.

Count the silverware as you place it by his plate, or as you remove it from the dishwasher, remembering to begin with "zero". Count his/her socks as you place them into his drawer. For an older child who has mastered the counting of single objects, count the socks in groups of two: "one, two," "three, four", etc., which will lead to counting by multiples of two.


Anonymous said...

I'd first start with 2. Let's pretend I don't know anything about number. If you pointed to one block and said one block, I wouldn't get it. You could be talking about its color or some other attribute for all I know. Or maybe "one block" is its full name?
But if you showed me 2 blocks and said "2 blocks" and then continue the process with 2 circles, 2 apples, 2 puppies, etc I would begin to understand that '2' is referring to the number of objects. Then you'd show me 3 blocks, circles, apples, puppies etc and I would know what 3 means.

Once I know 2,3,4,5 etc you would then tell me that they are all numbers , that 1 and 0 are also numbers and now you can say this is 1 block, this tub has 0 blocks and I would understand you were referring to its number.