How to teach counting

Counting is matching each object to one number word, in order, to find how many. It rests on several ideas at once: saying the number names in the right order, touching each object exactly once, and knowing the last number said is the total, which is the cardinal principle.

Counting develops from Pre-K to Grade 1. Very young children first learn to say the number names in order, then to match one number to one object, and then to understand that the last number counted tells how many there are altogether.

One-to-one correspondence is matching exactly one number word to each object, touching or moving each one as its number is said, so none is counted twice or skipped. It is a key counting principle, and children who recite numbers without matching them to objects have not yet mastered it.

The cardinal principle is knowing that the last number said when counting a group tells how many there are altogether, not just the name of the last object. A child who recounts every time you ask 'how many' has not yet grasped it, so this idea needs stressing.

This happens when one-to-one matching is not secure, especially with objects scattered rather than in a line. Having the child touch or move each object as they say its number, and arranging items in a row, helps ensure each is counted exactly once.

No. The total stays the same however the objects are arranged, whether spread out or pushed together. Young children often think a spread-out row has more, so counting the same objects in different arrangements teaches that quantity does not change when things are moved.

Once counting is secure, children move on to the number line, skip counting and comparing numbers. Counting underpins all of these, so a reliable grasp of one-to-one matching and the cardinal principle makes the next steps much smoother.