Early Childhood Math: the beginning.

Before children are ready for first grade math, they need some basics about numbers, and comparison and conditional language.

Children first must learn to count. Knowing how to count has several components:

• Children must know the number names and counting order. This is rote, linguistic knowledge. It is learned by repetition: through counting rhymes and songs, through counting books, and by counting lots and lots of things, out loud, together with an adult or older friend. Kindergarten is the time when most often we try to help all children reach a level of knowing the counting order: first to 10,then to 20, and finally to 100.
• Children must know how to count objects. This also takes lots of practice: children count objects as a class, with an older partner, or by themselves over and over before they have mastered the technique. There is organization and planning skills to be learned in counting objects: how to make sure you count all of the objects, and not miss any, and how to make sure you didn't count any twice.
• Children need to associate number names with numbers of objects. Children should be able to look at small sets of objects (1, 2, 3, 4) and tell how many even without counting. Children should associate numbers with groups of objects: 8 crayons in a box, 12 eggs in a carton, 10 squares on a ten-frame, 5 fingers on a hand. Children need practice associating numbers with amounts, so that they internalize that a number tells how many. If I count 5 fingers, then the number 5 tells my how many fingers are on one hand, it's not, for instance, the name of the last finger I counted. Children need experiences asking for and producing amounts of objects. A teacher can ask: how many blocks do you want? or how many carrot sticks do you want? or, turning the task around, can ask children to get and show a number of blocks or objects.

Children do a lot of this learning at the kindergarten and pre-kindergarten level. One major math goal in kindergarten is for all children to have a foundational understanding of numbers as meaning "how many" and have the foundational skills of being able to count (a common goal is counting to 100) and count objects. Some children come into kindergarten with this foundation, but some do not, and the teacher needs to be aware of what each child knows and does not know so that he or she can help the children learn and move from what they do know to what they need to learn next.