Early Childhood Development: On counting and numbers

When I first read Watership Down, I was fascinated by the description of how rabbits looked at numbers. Through Richard Adams’s detailed research and story-telling, I learned that rabbits have concepts of 1, 2, 3, 4, and “more than 4”. This often comes back to me as I watch young children develop their concept of numbers.

Recently, I mentioned to my son that his niece could count to 2, and almost 3. He countered that he has heard her count much higher than that.

But she can’t.

It is true that she can say the numbers, in order, much higher than that. But she can’t actually count higher.

Counting means understanding that one number describes a set of objects. She can do that accurately and easily when there are 1 or 2 objects, and sometimes when there are 3. She isn’t quite as smart as a rabbit yet. Of course, being a human, she’ll far surpass the rabbit’s mathematical ability very quickly.

Watching a young child learn math is fascinating, and it makes you consider about what math is.

 Math is more than numbers

Although there are lot of definitions, it all boils down to understanding quantity.

Math is the understanding of quantity, number and the relationship of quantities. If children aren’t understanding all those elements, they aren’t doing math. No matter how many numbers they can recite.

The building block concepts of math include:

·       Classification: the concept that things can be sorted based on characteristics

·       Seriation: the concept that things can be placed in order

·       One-to-one correspondence: the pairing of items in two different sets

·       Pattern: the arrangement of items

·       Comparison: subtraction, for example, is the comparison of two numbers, size, and quantity.

For our children to develop mathematical knowledge, understanding and ability, they must also develop understanding of these components.

Helping children with math

Reading counting books with our children is a wonderful way for children to consider number concepts. You may notice that many children want to also touch the book. This might be thought of as ‘disruptive’, but it shows us that their minds are working.

Children who touch the picture of counting are also learning to understand one-to-one correspondence, the matching of quantities of items. Each item gets one number, and it’s through touching that they add reality to the assignment of the item and number label.

You can tell children aren’t quite there yet when they don’t touch and speak a number at the same time. Or when the numbers are more randomly ordered, so they touch and count “… 9, 12, 17, 8, 9, 12. There’s 12!”

You may notice that kids often touch and count well to a certain point, and then the touching and naming of numbers gets more random as they get beyond the point they can conceptualize. Or because it’s boring to keep up the exact process for too long.

Making play time count

Once, during a Sunnymont-Westside class, we were playing “Ten in the Bed” and five children were lying down on the floor to begin a new round. Others set about counting how many children there were. They’ve learned to touch and count, so they touched feet and counted to 10.

“Are there 10 children there?” I asked. The kids with more developed math concepts looked troubled, because it didn’t seem like there were 10 kids but they didn’t have a deep enough understanding to explain the problem.

We tried it several times. Finally, I said, “Let’s check this out.” Knowing the children knew numbers up to 2 very well, I counted, touching feet as they had, only the first two children: “1, 2, 3, 4. OK, so that’s 4 children.”

Working this through with numbers they knew, they quickly spotted the problem and then applied their discovery to accurately count the five children lying down.

This is why kids need to experience and consider math concepts at a level where they really know the numbers, in order to learn and understand them.

“'Reciting means saying the numbers from memory in chronological order, whereas counting involves understanding that each item in the set is counted once and that the last number stated is the amount for the entire set,' said Louis Manfra, an assistant professor in Missouri University's Department of Human Development and Family Studies. 'When children are just reciting, they’re basically repeating what seems like a memorized sentence. When they’re counting, they’re performing a more cognitive activity in which they’re associating a one-to-one correspondence with the object and the number to represent a quantity.'”

Enjoying the learning experience together

Learning number and math concepts is in many ways the same as learning all other concepts, for young children. They can learn to recite facts early, but when they develop an understanding, through play and exploration (and a little nudging guidance from their grownups), at their own pace and when their own brains are ready to grasp the concepts, they begin to gain true and deep understanding of the concepts involved.

It makes sense to slow down and enjoy the process of their exploration with them, savoring the true understandings they gain when they gain them.

- Justine

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