Developing Math

Speaking of Mary "counting," John showed me a leap in cognition this morning. Lately he has been getting good at holding up the correct number of fingers (as in, "I am three!"). I forget entirely what we were talking about, but he held up one hand with five fingers and one hand with two fingers and asked me, "What is five and two?" Well, I picked my jaw up off the floor (because I'm a first-time mom to him, of course) and said, "Let's count and find out!" So he began counting on one hand and carried it to the second hand and told me triumphantly, "Seven!" We did it several times and began experimenting with other numbers. So neat!

The other numerical thing John is working on these days is time. He often asks me over and over what "this time is," and moves the hands on his clock.

In the post about Mary counting her "two scrapes," I referenced a book ("Your Child's Growing Mind: Brain Development and Learning from Birth to Adolescence" by Jane M. Healy, PhD) I'd read recently about neurological development in children concerning education. Here is the pertinent paragraph (pp. 339-340) on our littlest ones counting:

Can He Really Count?

Counting is one of the first elements of arithmetic that parents consciously teach. "Billy can count to twenty!" exclaims an excited mother of a three-year-old. What she means is that Billy has learned to recite the numbers from one to twenty. She would be surprised to learn that he cannot actually count, since there are several aspects of that skill that he will not master for another year or two.

1. Reciting numbers in order.
2. Pointing to a few objects in a row and saying a number while touching each object; starts around age three.
3. Accurately counting, or enumerating, an array of objects; this ability is called rational counting with one-to-one correspondence; it does not usually develop until at least age four and often later.
4. Mentally counting a number of objects without touching them; the child has internalized the idea of a "number." By age five children may be able to "see" how many are in groups of up to six.
5. Understanding the difference between being fifth in a line and representing the quantity "5."
6. Being able to add or subject from a given number. While even infants seem to have an innate sense of numerosity (how many), it takes about five years for children to solve oral problems of add and take away by using counting strategies. ("I've got six oranges in the bowl; if we eat four, how many will I have left?" "Yes, you'll always be two years older than Matt. When he is seven, how old will you be?")

Most children between ages three and five have some definite ideas about what counting is; they believe it is necessary to go from left to right, start at the end of a line, and go in order. Only later do they begin to grasp the concept of numerosity so that they can size up an array of objects that are not in a row or tell you how many marbles you are holding in one hand. In fact, although some twelve-month-olds can tell the difference between three and five objects, the abstract notion of "number" is slow to develop. Many of us were taught in school that the word "number" means the printed symbol on the page, but now we call written figures "numerals."